{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "toc_visible": true
    },
    "kernelspec": {
      "name": "ir",
      "display_name": "R"
    },
    "language_info": {
      "name": "R"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# 第3回 記述統計学"
      ],
      "metadata": {
        "id": "obnzB1V21pax"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "[![open in colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/slt666666/biostatistics_text_wed/blob/main/source/_static/colab_notebook/chapter3.ipynb)"
      ],
      "metadata": {
        "id": "8cquOWvq8ag4"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## はじめに\n",
        "\n",
        "\"統計学\"、\"統計的手法\"などの言葉を聞くと、何か大量の数値データを計算してどうにかすることを思い浮かべる人は多いのではないでしょうか？\n",
        "\n",
        "この傾向は、統計学に触れてこなかった人達だけでなく、統計学をある程度学んだ人にも良く見られる傾向です。\n",
        "\n",
        "しかし、統計学で最も重要なことは、計算をしたり何らかの値を導き出すことではなく、「データが何を語っているのかを捉える」ことになります。\n",
        "\n",
        "そのための第一歩にして、最も重要なステップが「データを眺める」ことになります。データを正しく効率的に眺める方法を**記述統計学**と呼びます。\n",
        "\n",
        "記述統計学は、個々の観測結果を集めたデータの特徴を記述するために、得られたデータを整理したり要約する方法を指します。\n",
        "\n",
        "ある程度統計学を学び色んな手法が使えるようになると、この「データを眺める」というステップをすっ飛ばして、いきなり回帰分析やら検定やらを適用しがちになります。\n",
        "\n",
        "しかし、それは正しい考え方ではなく、まずデータの全体像を掴むのが最初のステップだということを忘れないようにしてください。\n",
        "\n",
        "なぜまず最初にデータを眺めることがそれほど重要なのかは、また後程説明していきます。"
      ],
      "metadata": {
        "id": "2bLFQcxy824O"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 1次元のデータ\n",
        "\n",
        "通常、観測によって得られる各個体毎のデータは、2種類以上の観測値が得られます。\n",
        "\n",
        "例えば、ある植物を観測した場合、草丈や葉の長さ、光合成速度や花の色など、様々な観測値が得られます。\n",
        "\n",
        "まずは、この得られたデータのうち1つに着目し、集団のデータを整理・要約していく方法について説明していきます。\n",
        "\n",
        "(このような1種類のデータを1次元のデータと呼ぶ。)\n",
        "\n"
      ],
      "metadata": {
        "id": "KVWnSn0U9717"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### データの種類\n",
        "\n",
        "データにはいくつかの種類があり、その特性によって扱い方も異なります。\n",
        "\n",
        "大きなくくりとしてはカテゴリ型(質的)データと数値型(量的)データがあり、その中でも更にいくつか種類があります。\n",
        "\n",
        "ここではいくつかの代表的なデータの種類を紹介します。\n",
        "\n",
        "ある植物のサンプルデータを参考に説明していきます。"
      ],
      "metadata": {
        "id": "qHh6WOVRMIsx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# サンプルデータの読み込み\n",
        "df <- read.csv(\"https://raw.githubusercontent.com/slt666666/biostatistics_text_wed/refs/heads/main/source/_static/data/chapter3_data.csv\")\n",
        "df"
      ],
      "metadata": {
        "id": "q_hlZIOZ_Fee",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "7e2d01ed-cde2-4fb2-8a44-487b22824a8c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A data.frame: 200 × 7</caption>\n",
              "<thead>\n",
              "\t<tr><th scope=col>X</th><th scope=col>Flower</th><th scope=col>Resistance</th><th scope=col>Age</th><th scope=col>Height</th><th scope=col>Leaf_length</th><th scope=col>Leaf_width</th></tr>\n",
              "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><td>サンプル1 </td><td>Yellow</td><td>Normal     </td><td> 1</td><td>65.78827</td><td> 7.834566</td><td>1.2310844</td></tr>\n",
              "\t<tr><td>サンプル2 </td><td>Purple</td><td>Weak       </td><td> 1</td><td>26.70546</td><td> 4.654080</td><td>0.6596468</td></tr>\n",
              "\t<tr><td>サンプル3 </td><td>Blue  </td><td>Very strong</td><td>18</td><td>31.67394</td><td> 6.657642</td><td>0.5777713</td></tr>\n",
              "\t<tr><td>サンプル4 </td><td>Blue  </td><td>Very strong</td><td> 2</td><td>41.59529</td><td> 4.530526</td><td>1.0155126</td></tr>\n",
              "\t<tr><td>サンプル5 </td><td>Blue  </td><td>Very strong</td><td> 4</td><td>40.18388</td><td> 6.621776</td><td>0.5938072</td></tr>\n",
              "\t<tr><td>サンプル6 </td><td>Blue  </td><td>Very strong</td><td> 4</td><td>28.85123</td><td> 6.452588</td><td>0.3979530</td></tr>\n",
              "\t<tr><td>サンプル7 </td><td>Purple</td><td>Weak       </td><td>19</td><td>38.82291</td><td> 4.279560</td><td>0.9062809</td></tr>\n",
              "\t<tr><td>サンプル8 </td><td>Blue  </td><td>Very strong</td><td>23</td><td>30.98029</td><td> 4.659435</td><td>0.5892911</td></tr>\n",
              "\t<tr><td>サンプル9 </td><td>Yellow</td><td>Normal     </td><td>16</td><td>48.80066</td><td> 8.535383</td><td>0.7677384</td></tr>\n",
              "\t<tr><td>サンプル10</td><td>Purple</td><td>Weak       </td><td> 7</td><td>29.53996</td><td> 3.477631</td><td>0.5385743</td></tr>\n",
              "\t<tr><td>サンプル11</td><td>Yellow</td><td>Normal     </td><td>15</td><td>47.00730</td><td> 8.951398</td><td>0.9601034</td></tr>\n",
              "\t<tr><td>サンプル12</td><td>Red   </td><td>Normal     </td><td>17</td><td>53.56526</td><td> 7.070920</td><td>0.6897565</td></tr>\n",
              "\t<tr><td>サンプル13</td><td>Blue  </td><td>Very strong</td><td>15</td><td>31.83995</td><td> 5.873062</td><td>0.5740251</td></tr>\n",
              "\t<tr><td>サンプル14</td><td>Red   </td><td>Normal     </td><td> 3</td><td>57.23582</td><td>10.641621</td><td>1.0266159</td></tr>\n",
              "\t<tr><td>サンプル15</td><td>Blue  </td><td>Normal     </td><td>21</td><td>37.34221</td><td> 5.577850</td><td>0.4910724</td></tr>\n",
              "\t<tr><td>サンプル16</td><td>Purple</td><td>Weak       </td><td>13</td><td>29.32653</td><td> 4.846040</td><td>0.5706115</td></tr>\n",
              "\t<tr><td>サンプル17</td><td>Yellow</td><td>Normal     </td><td>25</td><td>52.61834</td><td> 6.664918</td><td>1.1178341</td></tr>\n",
              "\t<tr><td>サンプル18</td><td>Yellow</td><td>Normal     </td><td>10</td><td>43.64418</td><td> 6.137423</td><td>0.6880305</td></tr>\n",
              "\t<tr><td>サンプル19</td><td>Red   </td><td>Normal     </td><td>24</td><td>59.90945</td><td>10.149776</td><td>0.9190133</td></tr>\n",
              "\t<tr><td>サンプル20</td><td>Yellow</td><td>Normal     </td><td> 3</td><td>52.29948</td><td>10.205240</td><td>1.0951992</td></tr>\n",
              "\t<tr><td>サンプル21</td><td>Yellow</td><td>Normal     </td><td> 4</td><td>71.59820</td><td>11.462912</td><td>1.1321516</td></tr>\n",
              "\t<tr><td>サンプル22</td><td>Blue  </td><td>Normal     </td><td>18</td><td>40.34838</td><td> 7.003064</td><td>0.5903145</td></tr>\n",
              "\t<tr><td>サンプル23</td><td>Red   </td><td>Normal     </td><td>20</td><td>66.84285</td><td>10.286368</td><td>1.0218066</td></tr>\n",
              "\t<tr><td>サンプル24</td><td>Red   </td><td>Normal     </td><td>25</td><td>50.39984</td><td> 9.141129</td><td>0.6451531</td></tr>\n",
              "\t<tr><td>サンプル25</td><td>Yellow</td><td>Normal     </td><td> 5</td><td>62.03321</td><td> 7.533771</td><td>0.8993173</td></tr>\n",
              "\t<tr><td>サンプル26</td><td>Red   </td><td>Normal     </td><td>13</td><td>63.60514</td><td>10.040415</td><td>1.0591647</td></tr>\n",
              "\t<tr><td>サンプル27</td><td>Red   </td><td>Normal     </td><td>15</td><td>65.38000</td><td> 9.384388</td><td>1.2840807</td></tr>\n",
              "\t<tr><td>サンプル28</td><td>Purple</td><td>Weak       </td><td> 1</td><td>29.90585</td><td> 3.294802</td><td>0.3962400</td></tr>\n",
              "\t<tr><td>サンプル29</td><td>Red   </td><td>Normal     </td><td>11</td><td>60.19023</td><td> 7.558168</td><td>1.1354616</td></tr>\n",
              "\t<tr><td>サンプル30</td><td>Yellow</td><td>Normal     </td><td> 9</td><td>66.46125</td><td> 6.931840</td><td>0.9225667</td></tr>\n",
              "\t<tr><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td></tr>\n",
              "\t<tr><td>サンプル171</td><td>Blue  </td><td>Very strong</td><td>19</td><td>22.60525</td><td> 5.666858</td><td>0.5020847</td></tr>\n",
              "\t<tr><td>サンプル172</td><td>Red   </td><td>Normal     </td><td>20</td><td>61.08874</td><td> 7.684547</td><td>0.8189618</td></tr>\n",
              "\t<tr><td>サンプル173</td><td>Purple</td><td>Weak       </td><td>23</td><td>26.80917</td><td> 6.769459</td><td>0.3716374</td></tr>\n",
              "\t<tr><td>サンプル174</td><td>Yellow</td><td>Normal     </td><td>21</td><td>56.89745</td><td> 7.204118</td><td>0.9432215</td></tr>\n",
              "\t<tr><td>サンプル175</td><td>Red   </td><td>Normal     </td><td>18</td><td>57.96699</td><td> 9.646074</td><td>1.1210375</td></tr>\n",
              "\t<tr><td>サンプル176</td><td>Red   </td><td>Normal     </td><td>19</td><td>66.12513</td><td>10.118793</td><td>0.9609095</td></tr>\n",
              "\t<tr><td>サンプル177</td><td>Purple</td><td>Weak       </td><td> 6</td><td>20.99969</td><td> 6.299875</td><td>0.6934825</td></tr>\n",
              "\t<tr><td>サンプル178</td><td>Purple</td><td>Weak       </td><td>17</td><td>31.66969</td><td> 4.564230</td><td>0.6069522</td></tr>\n",
              "\t<tr><td>サンプル179</td><td>Red   </td><td>Normal     </td><td>10</td><td>59.57610</td><td> 6.709022</td><td>0.8978995</td></tr>\n",
              "\t<tr><td>サンプル180</td><td>Blue  </td><td>Normal     </td><td> 9</td><td>28.66669</td><td> 5.161722</td><td>0.5359009</td></tr>\n",
              "\t<tr><td>サンプル181</td><td>Purple</td><td>Weak       </td><td>21</td><td>25.78500</td><td> 3.546704</td><td>0.6915299</td></tr>\n",
              "\t<tr><td>サンプル182</td><td>Purple</td><td>Weak       </td><td>22</td><td>35.35861</td><td> 7.235764</td><td>0.9136668</td></tr>\n",
              "\t<tr><td>サンプル183</td><td>Purple</td><td>Normal     </td><td>25</td><td>40.67800</td><td> 4.258611</td><td>0.6854165</td></tr>\n",
              "\t<tr><td>サンプル184</td><td>Yellow</td><td>Normal     </td><td>10</td><td>62.71454</td><td> 8.695516</td><td>0.8301335</td></tr>\n",
              "\t<tr><td>サンプル185</td><td>Purple</td><td>Weak       </td><td> 2</td><td>33.68824</td><td> 6.615134</td><td>0.6216764</td></tr>\n",
              "\t<tr><td>サンプル186</td><td>Red   </td><td>Normal     </td><td>11</td><td>56.44637</td><td> 8.730434</td><td>1.0568722</td></tr>\n",
              "\t<tr><td>サンプル187</td><td>Purple</td><td>Weak       </td><td> 6</td><td>29.52112</td><td> 4.966718</td><td>0.7449458</td></tr>\n",
              "\t<tr><td>サンプル188</td><td>Red   </td><td>Normal     </td><td>22</td><td>62.61242</td><td> 9.031238</td><td>0.8633003</td></tr>\n",
              "\t<tr><td>サンプル189</td><td>Yellow</td><td>Normal     </td><td>20</td><td>58.81326</td><td> 6.991399</td><td>1.1568745</td></tr>\n",
              "\t<tr><td>サンプル190</td><td>Red   </td><td>Normal     </td><td> 1</td><td>64.52315</td><td> 9.342552</td><td>1.0034172</td></tr>\n",
              "\t<tr><td>サンプル191</td><td>Blue  </td><td>Very strong</td><td> 4</td><td>27.70623</td><td> 4.506814</td><td>0.8308974</td></tr>\n",
              "\t<tr><td>サンプル192</td><td>Red   </td><td>Normal     </td><td>12</td><td>62.16707</td><td>10.141846</td><td>1.0515442</td></tr>\n",
              "\t<tr><td>サンプル193</td><td>Red   </td><td>Normal     </td><td>21</td><td>63.54447</td><td>10.961013</td><td>0.8703741</td></tr>\n",
              "\t<tr><td>サンプル194</td><td>Yellow</td><td>Normal     </td><td> 2</td><td>61.38525</td><td> 8.735638</td><td>0.8996846</td></tr>\n",
              "\t<tr><td>サンプル195</td><td>Blue  </td><td>Very strong</td><td>19</td><td>26.30057</td><td> 5.154804</td><td>0.6980355</td></tr>\n",
              "\t<tr><td>サンプル196</td><td>Yellow</td><td>Normal     </td><td>10</td><td>66.18592</td><td> 7.352300</td><td>1.1494283</td></tr>\n",
              "\t<tr><td>サンプル197</td><td>Yellow</td><td>Normal     </td><td>22</td><td>68.75301</td><td> 8.775325</td><td>0.8842629</td></tr>\n",
              "\t<tr><td>サンプル198</td><td>Purple</td><td>Normal     </td><td> 7</td><td>38.77561</td><td> 4.751376</td><td>0.6887839</td></tr>\n",
              "\t<tr><td>サンプル199</td><td>Red   </td><td>Normal     </td><td>15</td><td>67.75607</td><td>11.417932</td><td>1.0545072</td></tr>\n",
              "\t<tr><td>サンプル200</td><td>Yellow</td><td>Normal     </td><td> 3</td><td>68.71653</td><td>11.187747</td><td>0.9340436</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ],
            "text/markdown": "\nA data.frame: 200 × 7\n\n| X &lt;chr&gt; | Flower &lt;chr&gt; | Resistance &lt;chr&gt; | Age &lt;int&gt; | Height &lt;dbl&gt; | Leaf_length &lt;dbl&gt; | Leaf_width &lt;dbl&gt; |\n|---|---|---|---|---|---|---|\n| サンプル1  | Yellow | Normal      |  1 | 65.78827 |  7.834566 | 1.2310844 |\n| サンプル2  | Purple | Weak        |  1 | 26.70546 |  4.654080 | 0.6596468 |\n| サンプル3  | Blue   | Very strong | 18 | 31.67394 |  6.657642 | 0.5777713 |\n| サンプル4  | Blue   | Very strong |  2 | 41.59529 |  4.530526 | 1.0155126 |\n| サンプル5  | Blue   | Very strong |  4 | 40.18388 |  6.621776 | 0.5938072 |\n| サンプル6  | Blue   | Very strong |  4 | 28.85123 |  6.452588 | 0.3979530 |\n| サンプル7  | Purple | Weak        | 19 | 38.82291 |  4.279560 | 0.9062809 |\n| サンプル8  | Blue   | Very strong | 23 | 30.98029 |  4.659435 | 0.5892911 |\n| サンプル9  | Yellow | Normal      | 16 | 48.80066 |  8.535383 | 0.7677384 |\n| サンプル10 | Purple | Weak        |  7 | 29.53996 |  3.477631 | 0.5385743 |\n| サンプル11 | Yellow | Normal      | 15 | 47.00730 |  8.951398 | 0.9601034 |\n| サンプル12 | Red    | Normal      | 17 | 53.56526 |  7.070920 | 0.6897565 |\n| サンプル13 | Blue   | Very strong | 15 | 31.83995 |  5.873062 | 0.5740251 |\n| サンプル14 | Red    | Normal      |  3 | 57.23582 | 10.641621 | 1.0266159 |\n| サンプル15 | Blue   | Normal      | 21 | 37.34221 |  5.577850 | 0.4910724 |\n| サンプル16 | Purple | Weak        | 13 | 29.32653 |  4.846040 | 0.5706115 |\n| サンプル17 | Yellow | Normal      | 25 | 52.61834 |  6.664918 | 1.1178341 |\n| サンプル18 | Yellow | Normal      | 10 | 43.64418 |  6.137423 | 0.6880305 |\n| サンプル19 | Red    | Normal      | 24 | 59.90945 | 10.149776 | 0.9190133 |\n| サンプル20 | Yellow | Normal      |  3 | 52.29948 | 10.205240 | 1.0951992 |\n| サンプル21 | Yellow | Normal      |  4 | 71.59820 | 11.462912 | 1.1321516 |\n| サンプル22 | Blue   | Normal      | 18 | 40.34838 |  7.003064 | 0.5903145 |\n| サンプル23 | Red    | Normal      | 20 | 66.84285 | 10.286368 | 1.0218066 |\n| サンプル24 | Red    | Normal      | 25 | 50.39984 |  9.141129 | 0.6451531 |\n| サンプル25 | Yellow | Normal      |  5 | 62.03321 |  7.533771 | 0.8993173 |\n| サンプル26 | Red    | Normal      | 13 | 63.60514 | 10.040415 | 1.0591647 |\n| サンプル27 | Red    | Normal      | 15 | 65.38000 |  9.384388 | 1.2840807 |\n| サンプル28 | Purple | Weak        |  1 | 29.90585 |  3.294802 | 0.3962400 |\n| サンプル29 | Red    | Normal      | 11 | 60.19023 |  7.558168 | 1.1354616 |\n| サンプル30 | Yellow | Normal      |  9 | 66.46125 |  6.931840 | 0.9225667 |\n| ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |\n| サンプル171 | Blue   | Very strong | 19 | 22.60525 |  5.666858 | 0.5020847 |\n| サンプル172 | Red    | Normal      | 20 | 61.08874 |  7.684547 | 0.8189618 |\n| サンプル173 | Purple | Weak        | 23 | 26.80917 |  6.769459 | 0.3716374 |\n| サンプル174 | Yellow | Normal      | 21 | 56.89745 |  7.204118 | 0.9432215 |\n| サンプル175 | Red    | Normal      | 18 | 57.96699 |  9.646074 | 1.1210375 |\n| サンプル176 | Red    | Normal      | 19 | 66.12513 | 10.118793 | 0.9609095 |\n| サンプル177 | Purple | Weak        |  6 | 20.99969 |  6.299875 | 0.6934825 |\n| サンプル178 | Purple | Weak        | 17 | 31.66969 |  4.564230 | 0.6069522 |\n| サンプル179 | Red    | Normal      | 10 | 59.57610 |  6.709022 | 0.8978995 |\n| サンプル180 | Blue   | Normal      |  9 | 28.66669 |  5.161722 | 0.5359009 |\n| サンプル181 | Purple | Weak        | 21 | 25.78500 |  3.546704 | 0.6915299 |\n| サンプル182 | Purple | Weak        | 22 | 35.35861 |  7.235764 | 0.9136668 |\n| サンプル183 | Purple | Normal      | 25 | 40.67800 |  4.258611 | 0.6854165 |\n| サンプル184 | Yellow | Normal      | 10 | 62.71454 |  8.695516 | 0.8301335 |\n| サンプル185 | Purple | Weak        |  2 | 33.68824 |  6.615134 | 0.6216764 |\n| サンプル186 | Red    | Normal      | 11 | 56.44637 |  8.730434 | 1.0568722 |\n| サンプル187 | Purple | Weak        |  6 | 29.52112 |  4.966718 | 0.7449458 |\n| サンプル188 | Red    | Normal      | 22 | 62.61242 |  9.031238 | 0.8633003 |\n| サンプル189 | Yellow | Normal      | 20 | 58.81326 |  6.991399 | 1.1568745 |\n| サンプル190 | Red    | Normal      |  1 | 64.52315 |  9.342552 | 1.0034172 |\n| サンプル191 | Blue   | Very strong |  4 | 27.70623 |  4.506814 | 0.8308974 |\n| サンプル192 | Red    | Normal      | 12 | 62.16707 | 10.141846 | 1.0515442 |\n| サンプル193 | Red    | Normal      | 21 | 63.54447 | 10.961013 | 0.8703741 |\n| サンプル194 | Yellow | Normal      |  2 | 61.38525 |  8.735638 | 0.8996846 |\n| サンプル195 | Blue   | Very strong | 19 | 26.30057 |  5.154804 | 0.6980355 |\n| サンプル196 | Yellow | Normal      | 10 | 66.18592 |  7.352300 | 1.1494283 |\n| サンプル197 | Yellow | Normal      | 22 | 68.75301 |  8.775325 | 0.8842629 |\n| サンプル198 | Purple | Normal      |  7 | 38.77561 |  4.751376 | 0.6887839 |\n| サンプル199 | Red    | Normal      | 15 | 67.75607 | 11.417932 | 1.0545072 |\n| サンプル200 | Yellow | Normal      |  3 | 68.71653 | 11.187747 | 0.9340436 |\n\n",
            "text/latex": "A data.frame: 200 × 7\n\\begin{tabular}{lllllll}\n X & Flower & Resistance & Age & Height & Leaf\\_length & Leaf\\_width\\\\\n <chr> & <chr> & <chr> & <int> & <dbl> & <dbl> & <dbl>\\\\\n\\hline\n\t サンプル1  & Yellow & Normal      &  1 & 65.78827 &  7.834566 & 1.2310844\\\\\n\t サンプル2  & Purple & Weak        &  1 & 26.70546 &  4.654080 & 0.6596468\\\\\n\t サンプル3  & Blue   & Very strong & 18 & 31.67394 &  6.657642 & 0.5777713\\\\\n\t サンプル4  & Blue   & Very strong &  2 & 41.59529 &  4.530526 & 1.0155126\\\\\n\t サンプル5  & Blue   & Very strong &  4 & 40.18388 &  6.621776 & 0.5938072\\\\\n\t サンプル6  & Blue   & Very strong &  4 & 28.85123 &  6.452588 & 0.3979530\\\\\n\t サンプル7  & Purple & Weak        & 19 & 38.82291 &  4.279560 & 0.9062809\\\\\n\t サンプル8  & Blue   & Very strong & 23 & 30.98029 &  4.659435 & 0.5892911\\\\\n\t サンプル9  & Yellow & Normal      & 16 & 48.80066 &  8.535383 & 0.7677384\\\\\n\t サンプル10 & Purple & Weak        &  7 & 29.53996 &  3.477631 & 0.5385743\\\\\n\t サンプル11 & Yellow & Normal      & 15 & 47.00730 &  8.951398 & 0.9601034\\\\\n\t サンプル12 & Red    & Normal      & 17 & 53.56526 &  7.070920 & 0.6897565\\\\\n\t サンプル13 & Blue   & Very strong & 15 & 31.83995 &  5.873062 & 0.5740251\\\\\n\t サンプル14 & Red    & Normal      &  3 & 57.23582 & 10.641621 & 1.0266159\\\\\n\t サンプル15 & Blue   & Normal      & 21 & 37.34221 &  5.577850 & 0.4910724\\\\\n\t サンプル16 & Purple & Weak        & 13 & 29.32653 &  4.846040 & 0.5706115\\\\\n\t サンプル17 & Yellow & Normal      & 25 & 52.61834 &  6.664918 & 1.1178341\\\\\n\t サンプル18 & Yellow & Normal      & 10 & 43.64418 &  6.137423 & 0.6880305\\\\\n\t サンプル19 & Red    & Normal      & 24 & 59.90945 & 10.149776 & 0.9190133\\\\\n\t サンプル20 & Yellow & Normal      &  3 & 52.29948 & 10.205240 & 1.0951992\\\\\n\t サンプル21 & Yellow & Normal      &  4 & 71.59820 & 11.462912 & 1.1321516\\\\\n\t サンプル22 & Blue   & Normal      & 18 & 40.34838 &  7.003064 & 0.5903145\\\\\n\t サンプル23 & Red    & Normal      & 20 & 66.84285 & 10.286368 & 1.0218066\\\\\n\t サンプル24 & Red    & Normal      & 25 & 50.39984 &  9.141129 & 0.6451531\\\\\n\t サンプル25 & Yellow & Normal      &  5 & 62.03321 &  7.533771 & 0.8993173\\\\\n\t サンプル26 & Red    & Normal      & 13 & 63.60514 & 10.040415 & 1.0591647\\\\\n\t サンプル27 & Red    & Normal      & 15 & 65.38000 &  9.384388 & 1.2840807\\\\\n\t サンプル28 & Purple & Weak        &  1 & 29.90585 &  3.294802 & 0.3962400\\\\\n\t サンプル29 & Red    & Normal      & 11 & 60.19023 &  7.558168 & 1.1354616\\\\\n\t サンプル30 & Yellow & Normal      &  9 & 66.46125 &  6.931840 & 0.9225667\\\\\n\t ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮\\\\\n\t サンプル171 & Blue   & Very strong & 19 & 22.60525 &  5.666858 & 0.5020847\\\\\n\t サンプル172 & Red    & Normal      & 20 & 61.08874 &  7.684547 & 0.8189618\\\\\n\t サンプル173 & Purple & Weak        & 23 & 26.80917 &  6.769459 & 0.3716374\\\\\n\t サンプル174 & Yellow & Normal      & 21 & 56.89745 &  7.204118 & 0.9432215\\\\\n\t サンプル175 & Red    & Normal      & 18 & 57.96699 &  9.646074 & 1.1210375\\\\\n\t サンプル176 & Red    & Normal      & 19 & 66.12513 & 10.118793 & 0.9609095\\\\\n\t サンプル177 & Purple & Weak        &  6 & 20.99969 &  6.299875 & 0.6934825\\\\\n\t サンプル178 & Purple & Weak        & 17 & 31.66969 &  4.564230 & 0.6069522\\\\\n\t サンプル179 & Red    & Normal      & 10 & 59.57610 &  6.709022 & 0.8978995\\\\\n\t サンプル180 & Blue   & Normal      &  9 & 28.66669 &  5.161722 & 0.5359009\\\\\n\t サンプル181 & Purple & Weak        & 21 & 25.78500 &  3.546704 & 0.6915299\\\\\n\t サンプル182 & Purple & Weak        & 22 & 35.35861 &  7.235764 & 0.9136668\\\\\n\t サンプル183 & Purple & Normal      & 25 & 40.67800 &  4.258611 & 0.6854165\\\\\n\t サンプル184 & Yellow & Normal      & 10 & 62.71454 &  8.695516 & 0.8301335\\\\\n\t サンプル185 & Purple & Weak        &  2 & 33.68824 &  6.615134 & 0.6216764\\\\\n\t サンプル186 & Red    & Normal      & 11 & 56.44637 &  8.730434 & 1.0568722\\\\\n\t サンプル187 & Purple & Weak        &  6 & 29.52112 &  4.966718 & 0.7449458\\\\\n\t サンプル188 & Red    & Normal      & 22 & 62.61242 &  9.031238 & 0.8633003\\\\\n\t サンプル189 & Yellow & Normal      & 20 & 58.81326 &  6.991399 & 1.1568745\\\\\n\t サンプル190 & Red    & Normal      &  1 & 64.52315 &  9.342552 & 1.0034172\\\\\n\t サンプル191 & Blue   & Very strong &  4 & 27.70623 &  4.506814 & 0.8308974\\\\\n\t サンプル192 & Red    & Normal      & 12 & 62.16707 & 10.141846 & 1.0515442\\\\\n\t サンプル193 & Red    & Normal      & 21 & 63.54447 & 10.961013 & 0.8703741\\\\\n\t サンプル194 & Yellow & Normal      &  2 & 61.38525 &  8.735638 & 0.8996846\\\\\n\t サンプル195 & Blue   & Very strong & 19 & 26.30057 &  5.154804 & 0.6980355\\\\\n\t サンプル196 & Yellow & Normal      & 10 & 66.18592 &  7.352300 & 1.1494283\\\\\n\t サンプル197 & Yellow & Normal      & 22 & 68.75301 &  8.775325 & 0.8842629\\\\\n\t サンプル198 & Purple & Normal      &  7 & 38.77561 &  4.751376 & 0.6887839\\\\\n\t サンプル199 & Red    & Normal      & 15 & 67.75607 & 11.417932 & 1.0545072\\\\\n\t サンプル200 & Yellow & Normal      &  3 & 68.71653 & 11.187747 & 0.9340436\\\\\n\\end{tabular}\n",
            "text/plain": [
              "    X           Flower Resistance  Age Height   Leaf_length Leaf_width\n",
              "1   サンプル1   Yellow Normal       1  65.78827  7.834566   1.2310844 \n",
              "2   サンプル2   Purple Weak         1  26.70546  4.654080   0.6596468 \n",
              "3   サンプル3   Blue   Very strong 18  31.67394  6.657642   0.5777713 \n",
              "4   サンプル4   Blue   Very strong  2  41.59529  4.530526   1.0155126 \n",
              "5   サンプル5   Blue   Very strong  4  40.18388  6.621776   0.5938072 \n",
              "6   サンプル6   Blue   Very strong  4  28.85123  6.452588   0.3979530 \n",
              "7   サンプル7   Purple Weak        19  38.82291  4.279560   0.9062809 \n",
              "8   サンプル8   Blue   Very strong 23  30.98029  4.659435   0.5892911 \n",
              "9   サンプル9   Yellow Normal      16  48.80066  8.535383   0.7677384 \n",
              "10  サンプル10  Purple Weak         7  29.53996  3.477631   0.5385743 \n",
              "11  サンプル11  Yellow Normal      15  47.00730  8.951398   0.9601034 \n",
              "12  サンプル12  Red    Normal      17  53.56526  7.070920   0.6897565 \n",
              "13  サンプル13  Blue   Very strong 15  31.83995  5.873062   0.5740251 \n",
              "14  サンプル14  Red    Normal       3  57.23582 10.641621   1.0266159 \n",
              "15  サンプル15  Blue   Normal      21  37.34221  5.577850   0.4910724 \n",
              "16  サンプル16  Purple Weak        13  29.32653  4.846040   0.5706115 \n",
              "17  サンプル17  Yellow Normal      25  52.61834  6.664918   1.1178341 \n",
              "18  サンプル18  Yellow Normal      10  43.64418  6.137423   0.6880305 \n",
              "19  サンプル19  Red    Normal      24  59.90945 10.149776   0.9190133 \n",
              "20  サンプル20  Yellow Normal       3  52.29948 10.205240   1.0951992 \n",
              "21  サンプル21  Yellow Normal       4  71.59820 11.462912   1.1321516 \n",
              "22  サンプル22  Blue   Normal      18  40.34838  7.003064   0.5903145 \n",
              "23  サンプル23  Red    Normal      20  66.84285 10.286368   1.0218066 \n",
              "24  サンプル24  Red    Normal      25  50.39984  9.141129   0.6451531 \n",
              "25  サンプル25  Yellow Normal       5  62.03321  7.533771   0.8993173 \n",
              "26  サンプル26  Red    Normal      13  63.60514 10.040415   1.0591647 \n",
              "27  サンプル27  Red    Normal      15  65.38000  9.384388   1.2840807 \n",
              "28  サンプル28  Purple Weak         1  29.90585  3.294802   0.3962400 \n",
              "29  サンプル29  Red    Normal      11  60.19023  7.558168   1.1354616 \n",
              "30  サンプル30  Yellow Normal       9  66.46125  6.931840   0.9225667 \n",
              "⋮   ⋮           ⋮      ⋮           ⋮   ⋮        ⋮           ⋮         \n",
              "171 サンプル171 Blue   Very strong 19  22.60525  5.666858   0.5020847 \n",
              "172 サンプル172 Red    Normal      20  61.08874  7.684547   0.8189618 \n",
              "173 サンプル173 Purple Weak        23  26.80917  6.769459   0.3716374 \n",
              "174 サンプル174 Yellow Normal      21  56.89745  7.204118   0.9432215 \n",
              "175 サンプル175 Red    Normal      18  57.96699  9.646074   1.1210375 \n",
              "176 サンプル176 Red    Normal      19  66.12513 10.118793   0.9609095 \n",
              "177 サンプル177 Purple Weak         6  20.99969  6.299875   0.6934825 \n",
              "178 サンプル178 Purple Weak        17  31.66969  4.564230   0.6069522 \n",
              "179 サンプル179 Red    Normal      10  59.57610  6.709022   0.8978995 \n",
              "180 サンプル180 Blue   Normal       9  28.66669  5.161722   0.5359009 \n",
              "181 サンプル181 Purple Weak        21  25.78500  3.546704   0.6915299 \n",
              "182 サンプル182 Purple Weak        22  35.35861  7.235764   0.9136668 \n",
              "183 サンプル183 Purple Normal      25  40.67800  4.258611   0.6854165 \n",
              "184 サンプル184 Yellow Normal      10  62.71454  8.695516   0.8301335 \n",
              "185 サンプル185 Purple Weak         2  33.68824  6.615134   0.6216764 \n",
              "186 サンプル186 Red    Normal      11  56.44637  8.730434   1.0568722 \n",
              "187 サンプル187 Purple Weak         6  29.52112  4.966718   0.7449458 \n",
              "188 サンプル188 Red    Normal      22  62.61242  9.031238   0.8633003 \n",
              "189 サンプル189 Yellow Normal      20  58.81326  6.991399   1.1568745 \n",
              "190 サンプル190 Red    Normal       1  64.52315  9.342552   1.0034172 \n",
              "191 サンプル191 Blue   Very strong  4  27.70623  4.506814   0.8308974 \n",
              "192 サンプル192 Red    Normal      12  62.16707 10.141846   1.0515442 \n",
              "193 サンプル193 Red    Normal      21  63.54447 10.961013   0.8703741 \n",
              "194 サンプル194 Yellow Normal       2  61.38525  8.735638   0.8996846 \n",
              "195 サンプル195 Blue   Very strong 19  26.30057  5.154804   0.6980355 \n",
              "196 サンプル196 Yellow Normal      10  66.18592  7.352300   1.1494283 \n",
              "197 サンプル197 Yellow Normal      22  68.75301  8.775325   0.8842629 \n",
              "198 サンプル198 Purple Normal       7  38.77561  4.751376   0.6887839 \n",
              "199 サンプル199 Red    Normal      15  67.75607 11.417932   1.0545072 \n",
              "200 サンプル200 Yellow Normal       3  68.71653 11.187747   0.9340436 "
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "1. カテゴリ型データ\n",
        "  * 名義データ、nominal data\n",
        "    * 最も単純なデータの一つ。データの属性を表すカテゴリーを示す。\n",
        "    * 例) 赤色or青色or白色, 男性or女性など。男性を0, 女性を1とおくなど数値に変換することもあるが、**値の間に優劣は無い。**\n",
        "    * 特に二つの属性(男or女やはいorいいえ)しか存在しない場合、binary data(2値データ)と呼びます。\n",
        "  * 順序データ、ordinal data\n",
        "    * カテゴリー間に**順序や優劣関係がある**場合のデータ。\n",
        "    * 例) 致死・重度・中程度・軽度など。これも4, 3, 2, 1などの数値で表すこともあるが、値自体に意味があるわけではない。\n",
        "  * 順位データ、ranked data\n",
        "    * ある規則に基づいて観測データを並び替え、数値を割り当てたもの。\n",
        "    * 偏差値の高い大学の順位や、食堂での販売順位など。実際の観測値よりも相対的な順位が重視される際に用いられる。\n",
        "1. 数値型データ\n",
        "  * 離散データ、discrete data\n",
        "    * 観測値が**整数**となり、数値の大きさと順位が共に重要な場合に用いられる。\n",
        "    * 例) 年齢や顧客数、台風の数など。\n",
        "    * 観測値自体が中間値をとることはないが、平均値を求める等の算術処理が可能であり、その結果台風の数は年平均10.5回来る、等の様に整数とならないこともある。\n",
        "  * 連続データ、continuous data\n",
        "    * 多くの測定可能な観測値のデータタイプ。連続した無数の値のうちの一つの値を取ることができる。\n",
        "    * 例) イネの草丈や収穫量、人の身長など。生物の実験で扱うほとんどの観測値が連続データとなる。\n",
        "    * 連続データは離散データや順序データ・2値データに変換することも可能だが、情報量が落ちることもあるため、適切な変換を行う必要がある。"
      ],
      "metadata": {
        "id": "fIn3hqQm_D2c"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### データの要約・視覚的表現\n",
        "\n",
        "調査や実験を行いデータが得られた際に、データの要約をするために度数分布表を作成することがあります。\n",
        "\n",
        "1点1点のデータを見るのではなく、全体の分布を捉えることが目的です。\n",
        "\n",
        "まずは、先ほどのデータセットで`Flower`というカテゴリ型データの列があったかと思います。\n",
        "\n",
        "このデータを度数分布表にしてみます。`table`関数で行うことが出来ます。\n",
        "\n",
        "`table(データセットからFlowerの列のデータを取り出す)`"
      ],
      "metadata": {
        "id": "1okpAvBukOX0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Flowerの度数をtable関数で表示\n",
        "table(df$Flower)"
      ],
      "metadata": {
        "id": "sj2I0xoYHnmj",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 73
        },
        "outputId": "8c24f666-a61a-47d5-e9b4-dc6986c1ff74"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "  Blue Purple    Red Yellow \n",
              "    38     55     59     48 "
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "この様に、各カテゴリ毎のデータ数のことを**度数**と呼びます。\n",
        "\n",
        "全てのカテゴリの度数をまとめたものを**度数分布**と呼び、これを表にしたものが**度数分布表**です。\n",
        "\n",
        "今回の結果だと、青色の花が比較的少なく、他の色は同程度の数あることが分かります。\n",
        "\n",
        "抵抗性の強さ(Resistance)についても度数分布表を作成してみましょう。\n",
        "\n",
        "`table(Resistanceの列データ)`"
      ],
      "metadata": {
        "id": "FFX1ee9CIJWL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Resistanceの度数分布表を表示\n",
        "table(df$Resistance)"
      ],
      "metadata": {
        "id": "irFrm2zbLD5X",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 73
        },
        "outputId": "82ad732a-2321-4b1f-b168-8872221776bb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "     Normal Very strong        Weak \n",
              "        131          27          42 "
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "では続いて、量的なデータの年齢`Age`の度数分布表を作成してみます。"
      ],
      "metadata": {
        "id": "8swvwdx-La9S"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Ageの度数分布表を表示\n",
        "table(df$Age)"
      ],
      "metadata": {
        "id": "BIDAxSn4MYJ_",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 73
        },
        "outputId": "e16be1ae-a3bb-444a-8d3b-f7d18e47fbfc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              " 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 \n",
              " 7  8  9 10  5  7 10  7 12 13  8  5  6  5  7  7  8 11  7 10  6  8  6  8 10 "
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "花の色や抵抗性など、質的なデータはカテゴリ数が少なかったので見やすかったですが、\n",
        "\n",
        "量的なデータの場合、数が多すぎてあまりよくわかりません。\n",
        "\n",
        "この様な場合はヒストグラムとして表示する場合が多いです。\n",
        "\n",
        "Rでは`hist`関数でヒストグラムを描くことが出来ます。\n",
        "\n",
        "`hist(Ageの列のデータ)`"
      ],
      "metadata": {
        "id": "ps7g0qYjMaod"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Ageのヒストグラムをhist関数で描写\n",
        "hist(df$Age)"
      ],
      "metadata": {
        "id": "NUHoOmJEM3l5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "b17f50c0-a751-4019-f4d5-c7fe65e888f9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Histogram of df$Age”"
            ],
            "image/png": 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RIsQvJESLAIyRMhwSIkT4QEi5A8ERIs\nQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIk\nT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJE\nSLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QE\ni5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAI\nyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8\nERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMh\nwSIkT4QEi5A8ERIsQvJESLAIyRMhwfIJqWXp/HvvXfDSh4wiJEKqAaWHtHL6QJM1/NK1hcYR\nEiHVgJJDem07s9PEmXPmXDB+sNl1ZYGBhERINaDkkCZn7swvNc+tm1ZgICERUg0oOaRBk9qX\nTxpWYCAhEVINKDmkzOXtyxf3KDCQkAipBpQc0ogT25fHbVtgICERUg0oOaRpdVeszy29d5GZ\nUWAgIRFSDSg5pFW7mz4HTzzzjAljepnRqwsMJCRCqgGlv4+04aqR9fZtpMze85oLjSMkQqoB\nXh8RWvfCU08t+aBMVk45rc04QiKk6hfks3Yr/+6eQUiEVFtKD+mZI0fsPzf3oG5GoWvhoR0h\n1YCSQ3q0wfTKmAOzHw4iJEKqdSWHNDZzX8v6qzJ7vhcREiGh5JCGfdEeLuhxZDMhERJK/4jQ\nRdmjH5uphERIKDmkocfkjs81cwiJkGpeySFNrbtuoz1umWDOPouQCKnGlRzSW8PNIdmFlqnG\nEBIh1bjS30daMeXs/NI9OxASIdU4/oqQJ0KCRUieCAkWIXkiJFiE5ImQYBGSJ0KCRUieCAkW\nIXkiJFiE5ImQYBGSJ0KCRUieCAkWIXkiJFiE5ImQYFVUSM/8a7Embgw1d2eqIqRriv7B/iDt\nTe5qKiqkeX0nFed480aouTtTFSHts0eRP9hPHpX2Jnc1lRXSiCJvtPcTkso+04rciYmE5CAk\nT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJE\nSLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QE\ni5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAI\nyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8\nERIsQvJESLAISTpxVJGaajKkA5qK/TmdmPY+lhkhSf1Omlmc3jUZ0i47FfljOqlf2vtYZoQk\n9bumyCk+UpshHVjkCtcQki9CkgipKhGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmE\npEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQX\nIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJS\nISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQ\nJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCcvmGtGHRQ8sKjyAkiZCqUskhXfaQ\nPbyhnzFm1NOFBhKSREhVqeSQzIz44AHTcNzp+5mmFwsMJCSJkKqSX0g7NS2OD++pO6XAQEKS\nCKkqeYX0pjkvu3zskAIDCUkipKrkFdJL5tbs8gWZAgMJSSKkquQVUnPT7OzypK0KDCQkiZCq\nUukhjX9iyYpzd1wTLz7f++gCAwlJIqSqVHpIOXdH0W29uy0qMJCQJEKqSiWHdPPVM6dNOHbM\ngiiaO+QXhQYSkkRIVSnAR4RWb9rsrGUD+rXpY9Z3suLMfkXqRUjlQUjegnzW7q0lzhmbHp7f\n5ppO75Em7ntjcfYmpPIgJG9BQppR6Fo6f2g3cVyR/xpHE1J5EJI3QpIISYWQXIQkEZIKIblK\nDmlUB4MISY+QqlLJIXXr1tCmnpD0CKkqlRzSjD7tL9Xx0K4IhFSVSg5p4257bGxdJqQiEFJV\nKv3FhsWN57QuElIRCKkqebxq987brUsLZxcYRkgSIVWljiHtfcM/yzADIUmEVJU6htTdNI5/\ncPMPznkiJImQqlLHkN76/sH1Ztj57gfnPBGSREhVyXmO9Ob1B3Uz+//g3YAzEJJESFVp8xcb\nXrt6V9PrK38LNgMhSYRUlTYLae1dJzSa4ZnMxS2BZiAkiZCqkhPSo6f2NY1feDh66QQzM9AM\nhCQRUlXqGNJL39rJmN2+u8outxwyMNAMhCQRUlXqGFI30/SVJ1tPfLcu0AyEJBFSVeoY0uhb\n1rafWHJvoBkISSKkqiSfIz27wh78T9AZCEkipKrUMaSNk8zD8dF1ZmJzwBkISSKkqtQxpCvN\nWPulYX89yVwTcAZCksofUkt/U6yyhzS16E0q3n3l/sEW0jGkTx6VXzhyx4AzEJJU/pA2mYt/\nWpyeZQ9p0hZFbtKV5soi1xg0r9w/2EI6htR4ZX5hTqFvlygWIUlJhHRLkdvUu/wh9S1yhfvN\n/UWuMaLLhLT1WfmFKVsHnIGQJEJSqeSQJvX6pT3aOK/7lwLOQEgSIalUckivbWOGf/ao/bcy\n2/wj4AyEJBGSSiWHFC3/ykeMMQP+7ZWQMxCSREgqFR1SFLW8+uJ7gWcgJImQVCo8pDIgJImQ\nVCo5pJY7jxr5iZyAMxCSREgqlRzSFcb0asoJOAMhSYSkUskhDT1saRlmICSJkFQqOaTMH8sx\nAyFJhKRSySENfbwcMxCSREgqlRzSN6aUYwZCkghJpZJDWn3Yyb9ZvCQr4AyEJBGSSiWH1OFX\nOwLOQEgSIalUckjjJ0xuFXAGQpIISaWSQyoPQpIISaXCQ3r32VWhZyAkiZBUKjqkhaOM+XUU\nHf3bkDMQkkRIKpUc0p969DksDunNQT2e7HR88QhJIiSVSg5p7PCXX7f3SG8MHxdwBkKSpu25\nskhritwHQkpBx5A+MjvKhhTNCvlHyAhJOqjoPzPVp8gvBiGkFIivvvxJPqSb+StCakWHtO/H\nf12cOabIryMlpBSIz9qdnw/plBEBZyAkad9di1zhFkJS6TohndbvKRvSyvNMyA/dEZJESCqV\nHNLrw7rvbkaObDDDlwecgZAkQlKp5JCiN75q/4pQ/68We+sriJAkQlKp6JCiqGX5kpD3RhYh\nSYSkUuEhlQEhSYSkUskhHdxmdMAZCEkiJJVKDqn9HcDBAWcgJImQVCo5pPez1jx7zgHvBJyB\nkCRCUqnkkNp88ysBZyAkiZBUqiKkx3lop0ZIKrUZ0oO9As5ASBIhqVRySKty3nx4JH/7W42Q\nVGoqpPYP7t8acAZCkghJpZJDGptz7Ff5VXM9QlKpqZDKg5AkQlIhJBchSYSkUskh7frpvToK\nNAMhSYSkUskhbd1ojKmL/2ustwLNQEgSIalUckgr9z/jf9ZF7/zu+EP5iJAaIanUVEinTMwv\nHH5qwBnSDWnR0uI0EZIGIbk6hjTgpvzCfwwMOEOaIX2/rui/fUVIGoTk6hhSw+X5hX9vCDhD\nmiFdZx74Q3HqCEmDkFwdQ9ptcO5LZB/tv2vAGdIN6XdFrkFIKoTk6hjSz+rNdoccfcj2pu7u\ngDMQkkRIKpUcUrTwsJ7xs4Qen5kfcgZCkghJpaJDiv8NXnnh5eawMxCSREgqFR5SlX3RGCHp\nEJK36v6iMULSISRv1f1FY4SkQ0jeqvuLxghJh5C8VfcXjRGSDiF5q+4vGiMkHULyVt1fNEZI\nOoTkrbq/aIyQdAjJW3V/0Rgh6RCSt+r+ojFC0iEkb9X9RWOEpENI3sSnv58txwyEJBGSSiWH\n1PPb5ZiBkCRCUqnkkA45osh/MRVCkghJpZJDWj7+8NufXJIVcAZCkghJpZJD6vAnQALOQEgS\nIalUckgnfWnS5LyAMxCSVHRIN5tFTxZlESElr7r/9ndVhHRh0X9SjJCS1xbSdY9kj55+JfQM\nhCQVHdK55pniVniakJLXFpKZljs6I/QMhCQRkgohuQhJIiQVQnIRkkRIKoTkIiSJkFQIyUVI\nEiGpEJKLkCRCUiEkFyFJhKRSuSHtNdMye2aPAs5ASBIhqVRuSELAGQhJIiSVig3pViHgDIQk\nEZJKxYZUgpal8++9d8FLHzKKkCRCUqmdkFZOH5h7GDj80rWFxhGSREgqNRPSa9uZnSbOnDPn\ngvGDza4rCwwkJImQVGompMmZO/NLzXPrphUYSEgSIanUTEiDJrUvnzSswEBCkghJpWZCylze\nvnxxjwIDCUkiJJWaCWnEie3L47YtMJCQJEJSqZmQptVdsT639N5FZkaBgYQkEZJKzYS0anfT\n5+CJZ54xYUwvM3p1gYGEJBGSSs2EFG24amS9fRsps/e85kLjCEkiJJXaCSm27oWnnlryQZls\nenh+m2sISSAkleJDGvy1+UV6zefG7wjy8dS33L/MumxAvzZ9zPpOViMkFULSyfTsW5xMyD/f\nGCSkGYWuhYd2EiGpFB9S95lFrjBuYogbfx4hSYSkQkguQpIISYWQXCWHNKqDQYSkR0gqNRNS\nt24NbeoJSY+QVGompBl92l+q46FdEQhJpWZC2rjbHhtblwmpCISkUjMhRYsbz2ldJKQiEJJK\n7YQUvfN269LC2QWGEZJESCo1FJISIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgq\nhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGS\nREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVC\nchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEki\nJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5\nCEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGS\nCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyE\nJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmF\nkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKS\nCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJI\nLkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmE\npEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQX\nIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJS\nISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJJVaC2nDooeWFR5BSBIhqdRMSJc9ZA9v6GeM\nGfV0oYGEJBGSSs2EZGbEBw+YhuNO3880vVhgICFJhKRSWyHt1LQ4Pryn7pQCAwlJIiSVmgrp\nTXNedvnYIc6FK6ec1mYcIQmEpFJTIb1kbs0uX5BxLiSkzhGSSk2F1Nw0O7s8aasCA3loJxGS\nSu2ENP6JJSvO3XFNvPh876MLDCQkiZBUaieknLuj6Lbe3RYVGEhIEiGp1ExIN189c9qEY8cs\niKK5Q35RaCAhSYSkUjMhtVu9qeDFhCQRkkoNhvQhCEkiJBVCchGSREgqhOQiJImQVAjJRUgS\nIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJ\nRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQ\nVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQi\nJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgq\nhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGS\nREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVC\nchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEki\nJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5\nCEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGS\nCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyE\nJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmF\nkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKS\nCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJI\nLkKSCEmllkJqWTr/3nsXvGAm18wAAAktSURBVPQhowhJIiSV2glp5fSBJmv4pWsLjSMkiZBU\naiak17YzO02cOWfOBeMHm11XFhhISBIhqdRMSJMzd+aXmufWTSswkJAkQlKpmZAGTWpfPmlY\ngYGEJBGSSs2ElLm8ffniHs6Fywb0a9PHbOzkKiZn+hYn063IFXqZPkWuYXoVuUJdQ5ErdK8v\ncoWepsgV+preRa5Q9E7Udy9yhYa6IlfYwmxR5BqmZ5ErZCaXeuP/ACWHNOLE9uVx2zoXbnp4\nfpsHf9LZVbw2v0gP3FTsGt8rdoV5vy5yhZ/cXeQK9/+oyBUevKHIFebf8GCRK/zo/iJXuPsn\nRa7w63lFrlD8P91NDxS7xmul3vg/QMkhTau7Yn1u6b2LzIxQmwNUppJDWrW76XPwxDPPmDCm\nlxm9OuQmAZWn9PeRNlw1st6+jZTZe15zwA0CKpHXR4TWvfDUU0s6e00OqCHl/6wdUAMICQiA\nkIAACAkIgJCAAAgJCICQgAAICQiAkIAACAkIgJCAAAgJCICQgAAICQiAkIAACAkIgJCAANIM\naW8DlF+3lgRuzGmGdPLRT6blS6NTm/qMT6U29fnDU5v6ir6pTT3PbErgxpxmSBND/qXL4pxz\nVGpTz9ontann7ZTa1Pf2S23q3xFS+RBSwgipjAgpYYRUPoSUNEJKGCGVESEljJDKiJASRkjl\nQ0hJI6SEEVIZEVLCCKmMCClhhFQ+hJQ0QkpY9Yd02mmpTX3e8alN/R8Hpjb1LZ9IbeoHtk5t\n6scz1f5Zu5UrU5v63TdTm3ptyC9cLM7Gl1Kbuvn/Upu6ZVkSs/BrFEAAhAQEQEhAAIQEBEBI\nQACEBARASEAAhAQEQEhAAIQEBEBIQACEBARASEAAhAQEQEhAAIQEBJBeSKumjchsMzmN33K7\nOf8tBZclO+3Gb3YblVtKfNfbpk5811dOH95j23GP28Wk97p96iT2OrWQNuxuTrh8Uma7FH5L\n9mozfob1UKKzLt69T/7WnPiut0+d9K6/va0Ze+EXuvf83+T3usPUSex1aiFdZb4TH/7UTE9+\n6pnmieQnfadxjyUNuVtz0rveYeqkd/0Mc118eI85Mvm97jB1EnudWkgj+6y3RzsOTOIvU0jT\nzJLE54zenr4xyt+ak971DlMnvetnH7wxPmxpHJH8XneYOom9TiukdfUHZ48nmqWJzz3BrGh+\neUXi00b5W3Mqu54PKZ1dX5/ZL61/cDt1InudVkgvmNwftZtp5ic+97Hm/H7GfPS2xCfO3ZpT\n2fV8SOns+rXxo6yU/sHt1InsdVohPWXOyB5fYe5NfO4xZvvZPz63r7kh6Ylzt+ZUdj0fUiq7\nvrDH/u+n9A+enTqRvU4vpDOzx3PMfYnPveDu9+LD5xq22pDwxK0hpbDr+ZDS2PXbG3Z/O6W9\nzk2dyF6nFdISMyF7fIH5bUpbEB1nFiU8Y+7WnMqu50PKS3DXWy4yh78bpbLXrVO3KutepxXS\nhu5jssfjzT9S2oLodJPsG0mtt+ZUdl2GlNyut0wyZzXbheT3um3qVmXd69Re/t6r15r4cNPg\nYYnPvPp7t2eP90/8BcP8rTmNXc9NnfyuTzOz8kuJ73Xb1InsdWohzTMXx4fXm0sSn3nTkC2e\nj4/uN7slPXM+pDR2PTd14rt+j5nWupj0XrdPnchepxZS82gz7pLP131yTfJT/6yu9+QLj6vr\n+1SSky6cMWNG/aD44K3Ed73D1Env+g7mrOyHc2asTHyvO0ydxF6n96HV1eeMyAw54+00pn7s\niC27D/5ysu/xz85/cNK+yZ7wrnecOuFdb53Z/D3xve44dQJ7za9RAAEQEhAAIQEBEBIQACEB\nARASEAAhAQEQEhAAIQEBEBIQACEBARASEAAhAQEQEhAAIQEBEBIQACEBARASEAAhAQEQEhAA\nIQEBEBIQACEBARASEAAhAQEQEhAAIQEBEBIQACEBARASEAAhAQEQEhAAIQEBEFIlqN8rPrht\nSP052VNN89PdGnwAQqoENqR/NjbNigv66ej+pvv2s9blLphumtamu2nIIaRKYEN6wkyJ7PfB\n7n1p48R9zOez52/o3838KN1NQw4hVQIb0iNmRhStadivxT60O948Yc+/3Uyp2z/tjYNFSF3b\nL3fvOWDyqjikw+wXdJ++1JydfY707FUv2kvHmBdGm8XZgQ/s2bj11LVDd4sXl08Znuk/blGa\nm117CKlLe7R+8Kwbvzg6s1f02Cxz/H1/XtOwy9r2Fxv+ZvaNbjRft4u/qx90ydwxxzTFd11v\njmiaceusoQ0LU9zu2kNIXdoRxt6xTDGtD+2ii8zO3+3dGtJ0c2P0bq/+G+LFz9rHes0H2YFf\n7W4f9r3UZ4/UtroWEVJXtqlxB3v0dHtILddubcygCQ/bs9f3b3wnir5k7oiXe37MnvObeGBL\n/91ftw4zq1Pb7hpESF3ZK+az9mhde0jx3c7Cxu27mRPju6HbzBfj0w+ZQ6JolTnKXvZuPHC5\nafVcehteewipK3vBHJ09rusQkn2x4f+OMNdG0YHmB0uWLHlh67ql0YvmxOxF9XtFS8zIX+es\nSmmraxIhdWUv5+6RVhsnpOid+iOjv7bd9ZwX/cMcYy9Zk71HGpna9tYwQurK3u+xoz36Q1tI\nFw9alfuIUNP+0dfNqXdZt9Zv8/6GbrvagQ/Zgf17Zu+K3kxzw2sPIXVpY7Kv2p3cFtIt5vTs\nG7J3munrP9KQb+UEc3/06brn46dPh2VftYvvoeKOBh2V5obXHELq0n5VN/CbVxz1mabWkJoP\nN7t+vefJx9QNW36bOSU/aKEZG91ltrvi+6MnNMQD3xhuTrll1vDMg6luea0hpK7tjk/2GDBp\n1bDdWp8jrb92VD/TfcQZy6MDzJ9bB32y/uXopp17jDh/Y49945Ovf3VY9y2P+VN6G12LCKny\ndP5rFO/kXnNA8gip8sxeuvl5PzzwyfjwWjMn8a1BFiFVhz82DLrkxindh/PeUUoIqUo8esTA\nzJBJr6a9GTWLkIAACAkIgJCAAAgJCICQgAAICQiAkIAACAkIgJCAAAgJCICQgAAICQiAkIAA\nCAkIgJCAAAgJCICQgAAICQiAkIAACAkIgJCAAAgJCICQgAAICQiAkIAACAkIgJCAAP4fcFBv\nXfcRLegAAAAASUVORK5CYII="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "ヒストグラムは、取りうる値をいくつかの**階級**に分割し、各階級ごとに**度数**を数えて図にしたものになります。\n",
        "\n",
        "この様に、量的なデータの場合は、階級毎に度数分布表やグラフを作成します。\n",
        "\n",
        "また、細かくは説明しませんが、Rの`hist`関数を使用することで、各階級毎の度数を求め表にすることも出来ます。"
      ],
      "metadata": {
        "id": "LvtvvzYTNh3F"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 描いたヒストグラムの各範囲の度数を表示\n",
        "h <- hist(df$Age)\n",
        "n <- length(h$counts) # 階級の数\n",
        "class_names <- NULL # 階級の名前格納用\n",
        "for(i in 1:n) {\n",
        "  class_names[i] <- paste(h$breaks[i], \"～\", h$breaks[i+1])\n",
        "}\n",
        "frequency_table <- data.frame(class=class_names, frequency=h$counts)\n",
        "frequency_table"
      ],
      "metadata": {
        "id": "Kqg6nFAWM_xa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 925
        },
        "outputId": "59a100fb-ddf6-456e-f7a0-dc2d612b4244"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A data.frame: 13 × 2</caption>\n",
              "<thead>\n",
              "\t<tr><th scope=col>class</th><th scope=col>frequency</th></tr>\n",
              "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><td>0 ～ 2  </td><td>15</td></tr>\n",
              "\t<tr><td>2 ～ 4  </td><td>19</td></tr>\n",
              "\t<tr><td>4 ～ 6  </td><td>12</td></tr>\n",
              "\t<tr><td>6 ～ 8  </td><td>17</td></tr>\n",
              "\t<tr><td>8 ～ 10 </td><td>25</td></tr>\n",
              "\t<tr><td>10 ～ 12</td><td>13</td></tr>\n",
              "\t<tr><td>12 ～ 14</td><td>11</td></tr>\n",
              "\t<tr><td>14 ～ 16</td><td>14</td></tr>\n",
              "\t<tr><td>16 ～ 18</td><td>19</td></tr>\n",
              "\t<tr><td>18 ～ 20</td><td>17</td></tr>\n",
              "\t<tr><td>20 ～ 22</td><td>14</td></tr>\n",
              "\t<tr><td>22 ～ 24</td><td>14</td></tr>\n",
              "\t<tr><td>24 ～ 26</td><td>10</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ],
            "text/markdown": "\nA data.frame: 13 × 2\n\n| class &lt;chr&gt; | frequency &lt;int&gt; |\n|---|---|\n| 0 ～ 2   | 15 |\n| 2 ～ 4   | 19 |\n| 4 ～ 6   | 12 |\n| 6 ～ 8   | 17 |\n| 8 ～ 10  | 25 |\n| 10 ～ 12 | 13 |\n| 12 ～ 14 | 11 |\n| 14 ～ 16 | 14 |\n| 16 ～ 18 | 19 |\n| 18 ～ 20 | 17 |\n| 20 ～ 22 | 14 |\n| 22 ～ 24 | 14 |\n| 24 ～ 26 | 10 |\n\n",
            "text/latex": "A data.frame: 13 × 2\n\\begin{tabular}{ll}\n class & frequency\\\\\n <chr> & <int>\\\\\n\\hline\n\t 0 ～ 2   & 15\\\\\n\t 2 ～ 4   & 19\\\\\n\t 4 ～ 6   & 12\\\\\n\t 6 ～ 8   & 17\\\\\n\t 8 ～ 10  & 25\\\\\n\t 10 ～ 12 & 13\\\\\n\t 12 ～ 14 & 11\\\\\n\t 14 ～ 16 & 14\\\\\n\t 16 ～ 18 & 19\\\\\n\t 18 ～ 20 & 17\\\\\n\t 20 ～ 22 & 14\\\\\n\t 22 ～ 24 & 14\\\\\n\t 24 ～ 26 & 10\\\\\n\\end{tabular}\n",
            "text/plain": [
              "   class    frequency\n",
              "1  0 ～ 2   15       \n",
              "2  2 ～ 4   19       \n",
              "3  4 ～ 6   12       \n",
              "4  6 ～ 8   17       \n",
              "5  8 ～ 10  25       \n",
              "6  10 ～ 12 13       \n",
              "7  12 ～ 14 11       \n",
              "8  14 ～ 16 14       \n",
              "9  16 ～ 18 19       \n",
              "10 18 ～ 20 17       \n",
              "11 20 ～ 22 14       \n",
              "12 22 ～ 24 14       \n",
              "13 24 ～ 26 10       "
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Histogram of df$Age”"
            ],
            "image/png": 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RIsQvJESLAIyRMhwSIkT4QEi5A8ERIs\nQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIk\nT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJE\nSLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QE\ni5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAI\nyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8\nERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMh\nwSIkT4QEi5A8ERIsQvJESLAIyRMhwfIJqWXp/HvvXfDSh4wiJEKqAaWHtHL6QJM1/NK1hcYR\nEiHVgJJDem07s9PEmXPmXDB+sNl1ZYGBhERINaDkkCZn7swvNc+tm1ZgICERUg0oOaRBk9qX\nTxpWYCAhEVINKDmkzOXtyxf3KDCQkAipBpQc0ogT25fHbVtgICERUg0oOaRpdVeszy29d5GZ\nUWAgIRFSDSg5pFW7mz4HTzzzjAljepnRqwsMJCRCqgGlv4+04aqR9fZtpMze85oLjSMkQqoB\nXh8RWvfCU08t+aBMVk45rc04QiKk6hfks3Yr/+6eQUiEVFtKD+mZI0fsPzf3oG5GoWvhoR0h\n1YCSQ3q0wfTKmAOzHw4iJEKqdSWHNDZzX8v6qzJ7vhcREiGh5JCGfdEeLuhxZDMhERJK/4jQ\nRdmjH5uphERIKDmkocfkjs81cwiJkGpeySFNrbtuoz1umWDOPouQCKnGlRzSW8PNIdmFlqnG\nEBIh1bjS30daMeXs/NI9OxASIdU4/oqQJ0KCRUieCAkWIXkiJFiE5ImQYBGSJ0KCRUieCAkW\nIXkiJFiE5ImQYBGSJ0KCRUieCAkWIXkiJFiE5ImQYFVUSM/8a7Embgw1d2eqIqRriv7B/iDt\nTe5qKiqkeX0nFed480aouTtTFSHts0eRP9hPHpX2Jnc1lRXSiCJvtPcTkso+04rciYmE5CAk\nT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJE\nSLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QE\ni5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAI\nyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8\nERIsQvJESLAISTpxVJGaajKkA5qK/TmdmPY+lhkhSf1Omlmc3jUZ0i47FfljOqlf2vtYZoQk\n9bumyCk+UpshHVjkCtcQki9CkgipKhGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmE\npEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQX\nIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJS\nISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQ\nJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCcvmGtGHRQ8sKjyAkiZCqUskhXfaQ\nPbyhnzFm1NOFBhKSREhVqeSQzIz44AHTcNzp+5mmFwsMJCSJkKqSX0g7NS2OD++pO6XAQEKS\nCKkqeYX0pjkvu3zskAIDCUkipKrkFdJL5tbs8gWZAgMJSSKkquQVUnPT7OzypK0KDCQkiZCq\nUukhjX9iyYpzd1wTLz7f++gCAwlJIqSqVHpIOXdH0W29uy0qMJCQJEKqSiWHdPPVM6dNOHbM\ngiiaO+QXhQYSkkRIVSnAR4RWb9rsrGUD+rXpY9Z3suLMfkXqRUjlQUjegnzW7q0lzhmbHp7f\n5ppO75Em7ntjcfYmpPIgJG9BQppR6Fo6f2g3cVyR/xpHE1J5EJI3QpIISYWQXIQkEZIKIblK\nDmlUB4MISY+QqlLJIXXr1tCmnpD0CKkqlRzSjD7tL9Xx0K4IhFSVSg5p4257bGxdJqQiEFJV\nKv3FhsWN57QuElIRCKkqebxq987brUsLZxcYRkgSIVWljiHtfcM/yzADIUmEVJU6htTdNI5/\ncPMPznkiJImQqlLHkN76/sH1Ztj57gfnPBGSREhVyXmO9Ob1B3Uz+//g3YAzEJJESFVp8xcb\nXrt6V9PrK38LNgMhSYRUlTYLae1dJzSa4ZnMxS2BZiAkiZCqkhPSo6f2NY1feDh66QQzM9AM\nhCQRUlXqGNJL39rJmN2+u8outxwyMNAMhCQRUlXqGFI30/SVJ1tPfLcu0AyEJBFSVeoY0uhb\n1rafWHJvoBkISSKkqiSfIz27wh78T9AZCEkipKrUMaSNk8zD8dF1ZmJzwBkISSKkqtQxpCvN\nWPulYX89yVwTcAZCksofUkt/U6yyhzS16E0q3n3l/sEW0jGkTx6VXzhyx4AzEJJU/pA2mYt/\nWpyeZQ9p0hZFbtKV5soi1xg0r9w/2EI6htR4ZX5hTqFvlygWIUlJhHRLkdvUu/wh9S1yhfvN\n/UWuMaLLhLT1WfmFKVsHnIGQJEJSqeSQJvX6pT3aOK/7lwLOQEgSIalUckivbWOGf/ao/bcy\n2/wj4AyEJBGSSiWHFC3/ykeMMQP+7ZWQMxCSREgqFR1SFLW8+uJ7gWcgJImQVCo8pDIgJImQ\nVCo5pJY7jxr5iZyAMxCSREgqlRzSFcb0asoJOAMhSYSkUskhDT1saRlmICSJkFQqOaTMH8sx\nAyFJhKRSySENfbwcMxCSREgqlRzSN6aUYwZCkghJpZJDWn3Yyb9ZvCQr4AyEJBGSSiWH1OFX\nOwLOQEgSIalUckjjJ0xuFXAGQpIISaWSQyoPQpIISaXCQ3r32VWhZyAkiZBUKjqkhaOM+XUU\nHf3bkDMQkkRIKpUc0p969DksDunNQT2e7HR88QhJIiSVSg5p7PCXX7f3SG8MHxdwBkKSpu25\nskhritwHQkpBx5A+MjvKhhTNCvlHyAhJOqjoPzPVp8gvBiGkFIivvvxJPqSb+StCakWHtO/H\nf12cOabIryMlpBSIz9qdnw/plBEBZyAkad9di1zhFkJS6TohndbvKRvSyvNMyA/dEZJESCqV\nHNLrw7rvbkaObDDDlwecgZAkQlKp5JCiN75q/4pQ/68We+sriJAkQlKp6JCiqGX5kpD3RhYh\nSYSkUuEhlQEhSYSkUskhHdxmdMAZCEkiJJVKDqn9HcDBAWcgJImQVCo5pPez1jx7zgHvBJyB\nkCRCUqnkkNp88ysBZyAkiZBUqiKkx3lop0ZIKrUZ0oO9As5ASBIhqVRySKty3nx4JH/7W42Q\nVGoqpPYP7t8acAZCkghJpZJDGptz7Ff5VXM9QlKpqZDKg5AkQlIhJBchSYSkUskh7frpvToK\nNAMhSYSkUskhbd1ojKmL/2ustwLNQEgSIalUckgr9z/jf9ZF7/zu+EP5iJAaIanUVEinTMwv\nHH5qwBnSDWnR0uI0EZIGIbk6hjTgpvzCfwwMOEOaIX2/rui/fUVIGoTk6hhSw+X5hX9vCDhD\nmiFdZx74Q3HqCEmDkFwdQ9ptcO5LZB/tv2vAGdIN6XdFrkFIKoTk6hjSz+rNdoccfcj2pu7u\ngDMQkkRIKpUcUrTwsJ7xs4Qen5kfcgZCkghJpaJDiv8NXnnh5eawMxCSREgqFR5SlX3RGCHp\nEJK36v6iMULSISRv1f1FY4SkQ0jeqvuLxghJh5C8VfcXjRGSDiF5q+4vGiMkHULyVt1fNEZI\nOoTkrbq/aIyQdAjJW3V/0Rgh6RCSt+r+ojFC0iEkb9X9RWOEpENI3sSnv58txwyEJBGSSiWH\n1PPb5ZiBkCRCUqnkkA45osh/MRVCkghJpZJDWj7+8NufXJIVcAZCkghJpZJD6vAnQALOQEgS\nIalUckgnfWnS5LyAMxCSVHRIN5tFTxZlESElr7r/9ndVhHRh0X9SjJCS1xbSdY9kj55+JfQM\nhCQVHdK55pniVniakJLXFpKZljs6I/QMhCQRkgohuQhJIiQVQnIRkkRIKoTkIiSJkFQIyUVI\nEiGpEJKLkCRCUiEkFyFJhKRSuSHtNdMye2aPAs5ASBIhqVRuSELAGQhJIiSVig3pViHgDIQk\nEZJKxYZUgpal8++9d8FLHzKKkCRCUqmdkFZOH5h7GDj80rWFxhGSREgqNRPSa9uZnSbOnDPn\ngvGDza4rCwwkJImQVGompMmZO/NLzXPrphUYSEgSIanUTEiDJrUvnzSswEBCkghJpWZCylze\nvnxxjwIDCUkiJJWaCWnEie3L47YtMJCQJEJSqZmQptVdsT639N5FZkaBgYQkEZJKzYS0anfT\n5+CJZ54xYUwvM3p1gYGEJBGSSs2EFG24amS9fRsps/e85kLjCEkiJJXaCSm27oWnnlryQZls\nenh+m2sISSAkleJDGvy1+UV6zefG7wjy8dS33L/MumxAvzZ9zPpOViMkFULSyfTsW5xMyD/f\nGCSkGYWuhYd2EiGpFB9S95lFrjBuYogbfx4hSYSkQkguQpIISYWQXCWHNKqDQYSkR0gqNRNS\nt24NbeoJSY+QVGompBl92l+q46FdEQhJpWZC2rjbHhtblwmpCISkUjMhRYsbz2ldJKQiEJJK\n7YQUvfN269LC2QWGEZJESCo1FJISIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgq\nhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGS\nREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVC\nchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEki\nJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5\nCEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGS\nCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyE\nJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmF\nkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKS\nCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJI\nLkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmE\npEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQX\nIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJS\nISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJJVaC2nDooeWFR5BSBIhqdRMSJc9ZA9v6GeM\nGfV0oYGEJBGSSs2EZGbEBw+YhuNO3880vVhgICFJhKRSWyHt1LQ4Pryn7pQCAwlJIiSVmgrp\nTXNedvnYIc6FK6ec1mYcIQmEpFJTIb1kbs0uX5BxLiSkzhGSSk2F1Nw0O7s8aasCA3loJxGS\nSu2ENP6JJSvO3XFNvPh876MLDCQkiZBUaieknLuj6Lbe3RYVGEhIEiGp1ExIN189c9qEY8cs\niKK5Q35RaCAhSYSkUjMhtVu9qeDFhCQRkkoNhvQhCEkiJBVCchGSREgqhOQiJImQVAjJRUgS\nIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJ\nRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQ\nVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQi\nJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgq\nhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGS\nREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVC\nchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEki\nJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5\nCEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGS\nCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyE\nJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmF\nkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKS\nCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJI\nLkKSCEmllkJqWTr/3nsXvGAm18wAAAktSURBVPQhowhJIiSV2glp5fSBJmv4pWsLjSMkiZBU\naiak17YzO02cOWfOBeMHm11XFhhISBIhqdRMSJMzd+aXmufWTSswkJAkQlKpmZAGTWpfPmlY\ngYGEJBGSSs2ElLm8ffniHs6Fywb0a9PHbOzkKiZn+hYn063IFXqZPkWuYXoVuUJdQ5ErdK8v\ncoWepsgV+preRa5Q9E7Udy9yhYa6IlfYwmxR5BqmZ5ErZCaXeuP/ACWHNOLE9uVx2zoXbnp4\nfpsHf9LZVbw2v0gP3FTsGt8rdoV5vy5yhZ/cXeQK9/+oyBUevKHIFebf8GCRK/zo/iJXuPsn\nRa7w63lFrlD8P91NDxS7xmul3vg/QMkhTau7Yn1u6b2LzIxQmwNUppJDWrW76XPwxDPPmDCm\nlxm9OuQmAZWn9PeRNlw1st6+jZTZe15zwA0CKpHXR4TWvfDUU0s6e00OqCHl/6wdUAMICQiA\nkIAACAkIgJCAAAgJCICQgAAICQiAkIAACAkIgJCAAAgJCICQgAAICQiAkIAACAkIgJCAANIM\naW8DlF+3lgRuzGmGdPLRT6blS6NTm/qMT6U29fnDU5v6ir6pTT3PbErgxpxmSBND/qXL4pxz\nVGpTz9ontann7ZTa1Pf2S23q3xFS+RBSwgipjAgpYYRUPoSUNEJKGCGVESEljJDKiJASRkjl\nQ0hJI6SEEVIZEVLCCKmMCClhhFQ+hJQ0QkpY9Yd02mmpTX3e8alN/R8Hpjb1LZ9IbeoHtk5t\n6scz1f5Zu5UrU5v63TdTm3ptyC9cLM7Gl1Kbuvn/Upu6ZVkSs/BrFEAAhAQEQEhAAIQEBEBI\nQACEBARASEAAhAQEQEhAAIQEBEBIQACEBARASEAAhAQEQEhAAIQEBJBeSKumjchsMzmN33K7\nOf8tBZclO+3Gb3YblVtKfNfbpk5811dOH95j23GP28Wk97p96iT2OrWQNuxuTrh8Uma7FH5L\n9mozfob1UKKzLt69T/7WnPiut0+d9K6/va0Ze+EXuvf83+T3usPUSex1aiFdZb4TH/7UTE9+\n6pnmieQnfadxjyUNuVtz0rveYeqkd/0Mc118eI85Mvm97jB1EnudWkgj+6y3RzsOTOIvU0jT\nzJLE54zenr4xyt+ak971DlMnvetnH7wxPmxpHJH8XneYOom9TiukdfUHZ48nmqWJzz3BrGh+\neUXi00b5W3Mqu54PKZ1dX5/ZL61/cDt1InudVkgvmNwftZtp5ic+97Hm/H7GfPS2xCfO3ZpT\n2fV8SOns+rXxo6yU/sHt1InsdVohPWXOyB5fYe5NfO4xZvvZPz63r7kh6Ylzt+ZUdj0fUiq7\nvrDH/u+n9A+enTqRvU4vpDOzx3PMfYnPveDu9+LD5xq22pDwxK0hpbDr+ZDS2PXbG3Z/O6W9\nzk2dyF6nFdISMyF7fIH5bUpbEB1nFiU8Y+7WnMqu50PKS3DXWy4yh78bpbLXrVO3KutepxXS\nhu5jssfjzT9S2oLodJPsG0mtt+ZUdl2GlNyut0wyZzXbheT3um3qVmXd69Re/t6r15r4cNPg\nYYnPvPp7t2eP90/8BcP8rTmNXc9NnfyuTzOz8kuJ73Xb1InsdWohzTMXx4fXm0sSn3nTkC2e\nj4/uN7slPXM+pDR2PTd14rt+j5nWupj0XrdPnchepxZS82gz7pLP131yTfJT/6yu9+QLj6vr\n+1SSky6cMWNG/aD44K3Ed73D1Env+g7mrOyHc2asTHyvO0ydxF6n96HV1eeMyAw54+00pn7s\niC27D/5ysu/xz85/cNK+yZ7wrnecOuFdb53Z/D3xve44dQJ7za9RAAEQEhAAIQEBEBIQACEB\nARASEAAhAQEQEhAAIQEBEBIQACEBARASEAAhAQEQEhAAIQEBEBIQACEBARASEAAhAQEQEhAA\nIQEBEBIQACEBARASEAAhAQEQEhAAIQEBEBIQACEBARASEAAhAQEQEhAAIQEBEFIlqN8rPrht\nSP052VNN89PdGnwAQqoENqR/NjbNigv66ej+pvv2s9blLphumtamu2nIIaRKYEN6wkyJ7PfB\n7n1p48R9zOez52/o3838KN1NQw4hVQIb0iNmRhStadivxT60O948Yc+/3Uyp2z/tjYNFSF3b\nL3fvOWDyqjikw+wXdJ++1JydfY707FUv2kvHmBdGm8XZgQ/s2bj11LVDd4sXl08Znuk/blGa\nm117CKlLe7R+8Kwbvzg6s1f02Cxz/H1/XtOwy9r2Fxv+ZvaNbjRft4u/qx90ydwxxzTFd11v\njmiaceusoQ0LU9zu2kNIXdoRxt6xTDGtD+2ii8zO3+3dGtJ0c2P0bq/+G+LFz9rHes0H2YFf\n7W4f9r3UZ4/UtroWEVJXtqlxB3v0dHtILddubcygCQ/bs9f3b3wnir5k7oiXe37MnvObeGBL\n/91ftw4zq1Pb7hpESF3ZK+az9mhde0jx3c7Cxu27mRPju6HbzBfj0w+ZQ6JolTnKXvZuPHC5\nafVcehteewipK3vBHJ09rusQkn2x4f+OMNdG0YHmB0uWLHlh67ql0YvmxOxF9XtFS8zIX+es\nSmmraxIhdWUv5+6RVhsnpOid+iOjv7bd9ZwX/cMcYy9Zk71HGpna9tYwQurK3u+xoz36Q1tI\nFw9alfuIUNP+0dfNqXdZt9Zv8/6GbrvagQ/Zgf17Zu+K3kxzw2sPIXVpY7Kv2p3cFtIt5vTs\nG7J3munrP9KQb+UEc3/06brn46dPh2VftYvvoeKOBh2V5obXHELq0n5VN/CbVxz1mabWkJoP\nN7t+vefJx9QNW36bOSU/aKEZG91ltrvi+6MnNMQD3xhuTrll1vDMg6luea0hpK7tjk/2GDBp\n1bDdWp8jrb92VD/TfcQZy6MDzJ9bB32y/uXopp17jDh/Y49945Ovf3VY9y2P+VN6G12LCKny\ndP5rFO/kXnNA8gip8sxeuvl5PzzwyfjwWjMn8a1BFiFVhz82DLrkxindh/PeUUoIqUo8esTA\nzJBJr6a9GTWLkIAACAkIgJCAAAgJCICQgAAICQiAkIAACAkIgJCAAAgJCICQgAAICQiAkIAA\nCAkIgJCAAAgJCICQgAAICQiAkIAACAkIgJCAAAgJCICQgAAICQiAkIAACAkIgJCAAP4fcFBv\nXfcRLegAAAAASUVORK5CYII="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "同じように量的データである草丈(Height)についてもヒストグラムを作成してみましょう。\n",
        "\n",
        "`hist(Heightの列データ)`"
      ],
      "metadata": {
        "id": "uE3WKsoXOb_M"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Heightのヒストグラムを描写\n",
        "hist(df$Height)"
      ],
      "metadata": {
        "id": "sR0jwsM8OhME",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "3af9c3f6-a0ab-4e56-b5f0-4c28faf830aa"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Histogram of df$Height”"
            ],
            "image/png": 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AMhSS0xpJdvjelQQlJ4r51UmCEdWN47nhQhKYQkFWZI+4+PuU+7E5JCSBIhmRCS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\nAA8ICfDg/wGbjMUhiGtV4wAAAABJRU5ErkJggg=="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "今回の場合は峰が２つありそうです。\n",
        "\n",
        "この様な場合、性質の異なるデータが混ざっている可能性が高いと考えられます。\n",
        "\n",
        "例:男女が混ざった身長のデータ\n",
        "\n",
        "混ざったデータを適切にグループ分けすることを**層別**と呼んだりします。\n",
        "\n",
        "例えば、今回の草丈のデータは花の色(青・紫 or 赤・黄色)で**層別化**すると峰１つのヒストグラムになります。"
      ],
      "metadata": {
        "id": "6WdNAT-yQa8b"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 花の色(Flower)が青(Blue)か紫(Purple)のデータ\n",
        "df_Blue_Purple_Height <- df[(df$Flower == \"Blue\") | (df$Flower == \"Purple\"), \"Height\"]\n",
        "hist(df_Blue_Purple_Height)"
      ],
      "metadata": {
        "id": "IL6dWoYKesAs",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "92c7a34d-5ec6-48a1-ac08-6b55697d95a2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Histogram of df_Blue_Purple_Height”"
            ],
            "image/png": 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PbOdWuyPouyPqBNiPQSoQ2vL1tWv6mF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\nAAAASUVORK5CYII="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# 花の色(Flower)が赤(Red)か黄色(Yellow)のデータ\n",
        "df_Blue_Purple_Height <- df[(df$Flower == \"Red\") | (df$Flower == \"Yellow\"), \"Height\"]\n",
        "hist(df_Blue_Purple_Height)"
      ],
      "metadata": {
        "id": "Sp536nzbfXwI",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "9ae72f9a-1c11-46ea-b449-def6b2c43835"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Histogram of df_Blue_Purple_Height”"
            ],
            "image/png": 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B8aa2+EJHkZEn9orL0RkuRlSPyhsfZGSJKXIfGHxtobIUlehsQfGmtvhCR5GRJ/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\nSUVORK5CYII="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "※今回の様に花の色によって上手く層別化できると分かっていれば話は簡単ですが、\n",
        "\n",
        "　実際に解析では何の要因によって層別化出来そうか色々試して探索する必要があります。\n",
        "\n",
        "また、ヒストグラムを描く際の注意点として、階級の数と階級の幅には気を付ける必要があります。\n",
        "\n",
        "先ほどのデータを少ない階級の数でヒストグラムを描いてみましょう。\n",
        "\n",
        "`hist`関数では`breaks`オプションで階級の数を変更することが出来ます。\n",
        "\n",
        "`hist(data, breaks = ?)`\n"
      ],
      "metadata": {
        "id": "LYqCTvwufwTt"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "hist(df$Height, breaks=4)"
      ],
      "metadata": {
        "id": "elMcERc8gO3w",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "cde02173-763f-4567-9805-28f4d904e354"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Histogram of df$Height”"
            ],
            "image/png": 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          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "この様に、あまり階級の幅が広すぎると、見えていたはずの2つの峰が見えなくなってしまいます。\n",
        "\n",
        "階級の数をどのようにとるかはデータ毎に異なってくるので、試行錯誤を繰り返して、データの特徴を上手く表現できる階級数・幅を探す必要があります。"
      ],
      "metadata": {
        "id": "MD4yGyGSgwM3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### データの代表値\n",
        "\n",
        "代表値とは、データの分布を代表する値のことを指します。\n",
        "\n",
        "先ほどまで扱っていたヒストグラムや度数分布は視覚的な感覚(=個人的な感覚)でデータを把握することになりますが、代表値は数量の概念として捉えることが可能です。\n",
        "\n",
        "代表値はデータの情報量を減らす場合もありますが、計算したり他者に伝達する際に客観的な値として使用することが可能になります。\n",
        "\n",
        "平均値や中央値、最頻値といった値が代表値に当たります。\n",
        "\n"
      ],
      "metadata": {
        "id": "Ni1MDdu7kSc0"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### ■ 平均値 (mean)\n",
        "\n",
        "もっともよく使用される代表値が平均値です。特に**算術平均**はよく用いられます。\n",
        "\n",
        "算術平均$\\bar{x}$は観測値 $x_1, x_2, x_3, \\cdots, x_n$の和を観測値の総数$n$でわったものになります。\n",
        "\n",
        "$\\bar{x} = \\dfrac{x_1+x_2+x_3+\\cdots+x_n}{n}$\n",
        "\n",
        "Rでは`mean`関数で簡単に算術平均を求めることが出来ます。\n",
        "\n",
        "例えば先ほどのサンプルデータ`df`の草丈`Height`の平均値を求めると\n",
        "\n",
        "`mean(Heightの列データ)`"
      ],
      "metadata": {
        "id": "uxAFOIUZxqLZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Height列の平均値を求める\n",
        "mean(df$Height)"
      ],
      "metadata": {
        "id": "1Ja2nTd_pE_L",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "de386ab7-928d-4145-b3b2-ee1a953c1030"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "46.42607590325"
            ],
            "text/markdown": "46.42607590325",
            "text/latex": "46.42607590325",
            "text/plain": [
              "[1] 46.42608"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### 他の平均\n",
        "\n",
        "平均には算術平均以外にも、**幾何平均** (geometric mean)や**調和平均** (harmonic mean)などがあります。\n",
        "\n",
        "**幾何平均**$x_G$は$x_G = \\sqrt[n]{x_1x_2x_3\\cdots x_n}$ で定義される平均値になり、\n",
        "\n",
        "成長率や比率などの平均を扱う際に用いられます。\n",
        "\n",
        "例えば、植物の草丈が5日間の間にそれぞれ15%, 24%, 32%, 20%, 28%成長した場合、日毎の平均成長率は\n",
        "\n"
      ],
      "metadata": {
        "id": "E_YC4x3gpPkR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 算術平均の場合\n",
        "up_rate <- c(15,24,32,20,28)\n",
        "mean(up_rate)"
      ],
      "metadata": {
        "id": "jrxFHnrLr9rU",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "c62ea8c1-89d3-452e-f917-c7db794a8426"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "23.8"
            ],
            "text/markdown": "23.8",
            "text/latex": "23.8",
            "text/plain": [
              "[1] 23.8"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "で23.8%ではなく、幾何平均を用いる必要があります。\n",
        "\n",
        "$x_G = \\sqrt[5]{1.15\\times1.24\\times1.32\\times1.20\\times1.28} = \\sqrt[5]{2.89124352} = 1.23656495589664$\n",
        "\n",
        "ということで、23.66%が平均成長率となる。\n",
        "\n",
        "これは\"毎日同じ成長率が適用された場合\"という意味で、平均的な成長率と解釈します。"
      ],
      "metadata": {
        "id": "YsCMIEUssB_x"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 幾何平均の計算\n",
        "(1.15*1.24*1.32*1.20*1.28)**(1/5)"
      ],
      "metadata": {
        "id": "EtZd00yjD15K",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "7ad9a4df-a028-4221-eecb-f0f69296f828"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "1.23656495589664"
            ],
            "text/markdown": "1.23656495589664",
            "text/latex": "1.23656495589664",
            "text/plain": [
              "[1] 1.236565"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "幾何平均は対数をとるとRでより簡単に計算できます。\n",
        "\n",
        "$x_G = \\sqrt[5]{1.15\\times1.24\\times1.32\\times1.20\\times1.28}$\n",
        "\n",
        "$\\log x_G = \\dfrac{1}{5}(\\log 1.15+\\log 1.24 + ... + \\log 1.28)$\n",
        "\n",
        "$x_G = e^{\\frac{1}{5}(\\log 1.15+\\log 1.24 + ... + \\log 1.28)}$"
      ],
      "metadata": {
        "id": "8Y535tMAE7QZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 対数を用いて幾何平均を求める\n",
        "up_rate <- c(1.15, 1.24, 1.32, 1.20, 1.28)\n",
        "exp(mean(log(up_rate)))"
      ],
      "metadata": {
        "id": "X6-wBa7ZsQdW",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "c926cad0-7a9c-4656-f014-848f0e4387d9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "1.23656495589664"
            ],
            "text/markdown": "1.23656495589664",
            "text/latex": "1.23656495589664",
            "text/plain": [
              "[1] 1.236565"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "調和平均$x_H$は逆数同士の算術平均\n",
        "\n",
        "$\\dfrac{1}{x_H} = \\dfrac{1}{n}(\\dfrac{1}{x_1}+\\cdots+\\dfrac{1}{x_n})$\n",
        "\n",
        "を求め、そのまた逆数を求めた値になります。\n",
        "\n",
        "割合や速度などの平均を求める際に使用します。\n",
        "\n",
        "簡単な例だと行き時速40km、帰り時速20kmで移動した場合の平均速度は$(40+20)/2=30$だと正しくないので、調和平均で求める事が出来ます。"
      ],
      "metadata": {
        "id": "FxaExESNrz7_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 時速40kmと時速20kmの調和平均を求める\n",
        "1/((1/2)*(1/40+1/20))"
      ],
      "metadata": {
        "id": "mZdILd6EvL9V",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "3fdfa08d-09ce-480d-9c35-0fa0aa99e276"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "26.6666666666667"
            ],
            "text/markdown": "26.6666666666667",
            "text/latex": "26.6666666666667",
            "text/plain": [
              "[1] 26.66667"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 平均値を利用する際の注意点\n",
        "\n",
        "最初にも記述しましたが、代表値はデータの情報量を減らす可能性があります。\n",
        "\n",
        "例えば下はサンプルデータ`df`の草丈`Height`の平均値を求めてみると…"
      ],
      "metadata": {
        "id": "-XxnJsv8vrv2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 草丈(Height)の平均値\n",
        "mean(df$Height)"
      ],
      "metadata": {
        "id": "9Xivp-UFz_9l",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "abf5c718-eb64-4481-ed39-cadd64bf28a6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "46.42607590325"
            ],
            "text/markdown": "46.42607590325",
            "text/latex": "46.42607590325",
            "text/plain": [
              "[1] 46.42608"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "と一応平均値は求まります。\n",
        "\n",
        "ここで下はサンプルデータ`df`の草丈`Height`のヒストグラムと平均値を描くコードになりますが、\n",
        "\n",
        "この様な分布の場合安易に平均値を代表値としてしまって良いでしょうか？"
      ],
      "metadata": {
        "id": "GEmV7ybyz_kQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 草丈(Height)の分布と平均値を図示\n",
        "hist(df$Height)\n",
        "abline(v = mean(df$Height),col=\"red\",lty=1,lwd=2) # 平均値に赤線を引く\n",
        "mean(df$Height)"
      ],
      "metadata": {
        "id": "FFjBvbsawjtZ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 454
        },
        "outputId": "5452caaf-f973-42da-bfc6-63c8c7feaebc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "46.42607590325"
            ],
            "text/markdown": "46.42607590325",
            "text/latex": "46.42607590325",
            "text/plain": [
              "[1] 46.42608"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Histogram of df$Height”"
            ],
            "image/png": 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05ewLFixYojjjiib9++GzdufO2113r2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\nRU5ErkJggg=="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "この場合、平均値は46.4と計算されはしましたが、その値付近にデータは存在していません。\n",
        "\n",
        "この値を代表値として扱うことが正しいかは疑問符が付きます。\n",
        "\n",
        "また下記の新たなデータは、とある高校を卒業した学生の年収のサンプルデータになります。"
      ],
      "metadata": {
        "id": "4Kvgd8agIGhA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 新しいサンプルデータ\n",
        "sample_data <- read.csv(\"https://raw.githubusercontent.com/slt666666/biostatistics_text_wed/refs/heads/main/source/_static/data/chapter3_Hanamaki_higashi.csv\")\n",
        "sample_data"
      ],
      "metadata": {
        "id": "bttXN7JGIRjD",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "cbee3a2c-e15a-431a-e619-cbb2b4cbe0e9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A data.frame: 240 × 2</caption>\n",
              "<thead>\n",
              "\t<tr><th scope=col>X</th><th scope=col>Salary</th></tr>\n",
              "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><td>student1 </td><td>    138.3699</td></tr>\n",
              "\t<tr><td>student2 </td><td>    225.1977</td></tr>\n",
              "\t<tr><td>student3 </td><td>    327.0206</td></tr>\n",
              "\t<tr><td>student4 </td><td>    307.1165</td></tr>\n",
              "\t<tr><td>student5 </td><td>    363.0438</td></tr>\n",
              "\t<tr><td>student6 </td><td>    103.8047</td></tr>\n",
              "\t<tr><td>student7 </td><td>    412.3765</td></tr>\n",
              "\t<tr><td>student8 </td><td>    210.8079</td></tr>\n",
              "\t<tr><td>student9 </td><td>    291.5057</td></tr>\n",
              "\t<tr><td>student10</td><td>    194.8952</td></tr>\n",
              "\t<tr><td>student11</td><td>    299.2906</td></tr>\n",
              "\t<tr><td>student12</td><td>    387.5801</td></tr>\n",
              "\t<tr><td>student13</td><td>    271.0449</td></tr>\n",
              "\t<tr><td>student14</td><td>    385.0331</td></tr>\n",
              "\t<tr><td>student15</td><td>    382.7077</td></tr>\n",
              "\t<tr><td>student16</td><td>    358.4886</td></tr>\n",
              "\t<tr><td>student17</td><td>1000000.0000</td></tr>\n",
              "\t<tr><td>student18</td><td>    308.1741</td></tr>\n",
              "\t<tr><td>student19</td><td>    313.9527</td></tr>\n",
              "\t<tr><td>student20</td><td>    214.3619</td></tr>\n",
              "\t<tr><td>student21</td><td>    442.9607</td></tr>\n",
              "\t<tr><td>student22</td><td>    297.2510</td></tr>\n",
              "\t<tr><td>student23</td><td>    253.7788</td></tr>\n",
              "\t<tr><td>student24</td><td>    171.4676</td></tr>\n",
              "\t<tr><td>student25</td><td>    367.1616</td></tr>\n",
              "\t<tr><td>student26</td><td>    448.7010</td></tr>\n",
              "\t<tr><td>student27</td><td>    269.3509</td></tr>\n",
              "\t<tr><td>student28</td><td>    297.2861</td></tr>\n",
              "\t<tr><td>student29</td><td>    236.3801</td></tr>\n",
              "\t<tr><td>student30</td><td>    309.5516</td></tr>\n",
              "\t<tr><td>⋮</td><td>⋮</td></tr>\n",
              "\t<tr><td>student211</td><td>343.8213</td></tr>\n",
              "\t<tr><td>student212</td><td>266.0198</td></tr>\n",
              "\t<tr><td>student213</td><td>249.6514</td></tr>\n",
              "\t<tr><td>student214</td><td>263.4043</td></tr>\n",
              "\t<tr><td>student215</td><td>315.8730</td></tr>\n",
              "\t<tr><td>student216</td><td>207.3158</td></tr>\n",
              "\t<tr><td>student217</td><td>400.4940</td></tr>\n",
              "\t<tr><td>student218</td><td>199.6521</td></tr>\n",
              "\t<tr><td>student219</td><td>207.3640</td></tr>\n",
              "\t<tr><td>student220</td><td>483.9198</td></tr>\n",
              "\t<tr><td>student221</td><td>307.8051</td></tr>\n",
              "\t<tr><td>student222</td><td>225.6996</td></tr>\n",
              "\t<tr><td>student223</td><td>144.7991</td></tr>\n",
              "\t<tr><td>student224</td><td>417.6686</td></tr>\n",
              "\t<tr><td>student225</td><td>357.1344</td></tr>\n",
              "\t<tr><td>student226</td><td>249.2913</td></tr>\n",
              "\t<tr><td>student227</td><td>286.0981</td></tr>\n",
              "\t<tr><td>student228</td><td>230.8265</td></tr>\n",
              "\t<tr><td>student229</td><td>366.3081</td></tr>\n",
              "\t<tr><td>student230</td><td>200.5346</td></tr>\n",
              "\t<tr><td>student231</td><td>331.7983</td></tr>\n",
              "\t<tr><td>student232</td><td>358.5179</td></tr>\n",
              "\t<tr><td>student233</td><td>471.5199</td></tr>\n",
              "\t<tr><td>student234</td><td>308.4997</td></tr>\n",
              "\t<tr><td>student235</td><td>198.3318</td></tr>\n",
              "\t<tr><td>student236</td><td>131.4145</td></tr>\n",
              "\t<tr><td>student237</td><td>242.8344</td></tr>\n",
              "\t<tr><td>student238</td><td>225.7406</td></tr>\n",
              "\t<tr><td>student239</td><td>322.1616</td></tr>\n",
              "\t<tr><td>student240</td><td>232.4191</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ],
            "text/markdown": "\nA data.frame: 240 × 2\n\n| X &lt;chr&gt; | Salary &lt;dbl&gt; |\n|---|---|\n| student1  |     138.3699 |\n| student2  |     225.1977 |\n| student3  |     327.0206 |\n| student4  |     307.1165 |\n| student5  |     363.0438 |\n| student6  |     103.8047 |\n| student7  |     412.3765 |\n| student8  |     210.8079 |\n| student9  |     291.5057 |\n| student10 |     194.8952 |\n| student11 |     299.2906 |\n| student12 |     387.5801 |\n| student13 |     271.0449 |\n| student14 |     385.0331 |\n| student15 |     382.7077 |\n| student16 |     358.4886 |\n| student17 | 1000000.0000 |\n| student18 |     308.1741 |\n| student19 |     313.9527 |\n| student20 |     214.3619 |\n| student21 |     442.9607 |\n| student22 |     297.2510 |\n| student23 |     253.7788 |\n| student24 |     171.4676 |\n| student25 |     367.1616 |\n| student26 |     448.7010 |\n| student27 |     269.3509 |\n| student28 |     297.2861 |\n| student29 |     236.3801 |\n| student30 |     309.5516 |\n| ⋮ | ⋮ |\n| student211 | 343.8213 |\n| student212 | 266.0198 |\n| student213 | 249.6514 |\n| student214 | 263.4043 |\n| student215 | 315.8730 |\n| student216 | 207.3158 |\n| student217 | 400.4940 |\n| student218 | 199.6521 |\n| student219 | 207.3640 |\n| student220 | 483.9198 |\n| student221 | 307.8051 |\n| student222 | 225.6996 |\n| student223 | 144.7991 |\n| student224 | 417.6686 |\n| student225 | 357.1344 |\n| student226 | 249.2913 |\n| student227 | 286.0981 |\n| student228 | 230.8265 |\n| student229 | 366.3081 |\n| student230 | 200.5346 |\n| student231 | 331.7983 |\n| student232 | 358.5179 |\n| student233 | 471.5199 |\n| student234 | 308.4997 |\n| student235 | 198.3318 |\n| student236 | 131.4145 |\n| student237 | 242.8344 |\n| student238 | 225.7406 |\n| student239 | 322.1616 |\n| student240 | 232.4191 |\n\n",
            "text/latex": "A data.frame: 240 × 2\n\\begin{tabular}{ll}\n X & Salary\\\\\n <chr> & <dbl>\\\\\n\\hline\n\t student1  &     138.3699\\\\\n\t student2  &     225.1977\\\\\n\t student3  &     327.0206\\\\\n\t student4  &     307.1165\\\\\n\t student5  &     363.0438\\\\\n\t student6  &     103.8047\\\\\n\t student7  &     412.3765\\\\\n\t student8  &     210.8079\\\\\n\t student9  &     291.5057\\\\\n\t student10 &     194.8952\\\\\n\t student11 &     299.2906\\\\\n\t student12 &     387.5801\\\\\n\t student13 &     271.0449\\\\\n\t student14 &     385.0331\\\\\n\t student15 &     382.7077\\\\\n\t student16 &     358.4886\\\\\n\t student17 & 1000000.0000\\\\\n\t student18 &     308.1741\\\\\n\t student19 &     313.9527\\\\\n\t student20 &     214.3619\\\\\n\t student21 &     442.9607\\\\\n\t student22 &     297.2510\\\\\n\t student23 &     253.7788\\\\\n\t student24 &     171.4676\\\\\n\t student25 &     367.1616\\\\\n\t student26 &     448.7010\\\\\n\t student27 &     269.3509\\\\\n\t student28 &     297.2861\\\\\n\t student29 &     236.3801\\\\\n\t student30 &     309.5516\\\\\n\t ⋮ & ⋮\\\\\n\t student211 & 343.8213\\\\\n\t student212 & 266.0198\\\\\n\t student213 & 249.6514\\\\\n\t student214 & 263.4043\\\\\n\t student215 & 315.8730\\\\\n\t student216 & 207.3158\\\\\n\t student217 & 400.4940\\\\\n\t student218 & 199.6521\\\\\n\t student219 & 207.3640\\\\\n\t student220 & 483.9198\\\\\n\t student221 & 307.8051\\\\\n\t student222 & 225.6996\\\\\n\t student223 & 144.7991\\\\\n\t student224 & 417.6686\\\\\n\t student225 & 357.1344\\\\\n\t student226 & 249.2913\\\\\n\t student227 & 286.0981\\\\\n\t student228 & 230.8265\\\\\n\t student229 & 366.3081\\\\\n\t student230 & 200.5346\\\\\n\t student231 & 331.7983\\\\\n\t student232 & 358.5179\\\\\n\t student233 & 471.5199\\\\\n\t student234 & 308.4997\\\\\n\t student235 & 198.3318\\\\\n\t student236 & 131.4145\\\\\n\t student237 & 242.8344\\\\\n\t student238 & 225.7406\\\\\n\t student239 & 322.1616\\\\\n\t student240 & 232.4191\\\\\n\\end{tabular}\n",
            "text/plain": [
              "    X          Salary      \n",
              "1   student1       138.3699\n",
              "2   student2       225.1977\n",
              "3   student3       327.0206\n",
              "4   student4       307.1165\n",
              "5   student5       363.0438\n",
              "6   student6       103.8047\n",
              "7   student7       412.3765\n",
              "8   student8       210.8079\n",
              "9   student9       291.5057\n",
              "10  student10      194.8952\n",
              "11  student11      299.2906\n",
              "12  student12      387.5801\n",
              "13  student13      271.0449\n",
              "14  student14      385.0331\n",
              "15  student15      382.7077\n",
              "16  student16      358.4886\n",
              "17  student17  1000000.0000\n",
              "18  student18      308.1741\n",
              "19  student19      313.9527\n",
              "20  student20      214.3619\n",
              "21  student21      442.9607\n",
              "22  student22      297.2510\n",
              "23  student23      253.7788\n",
              "24  student24      171.4676\n",
              "25  student25      367.1616\n",
              "26  student26      448.7010\n",
              "27  student27      269.3509\n",
              "28  student28      297.2861\n",
              "29  student29      236.3801\n",
              "30  student30      309.5516\n",
              "⋮   ⋮          ⋮           \n",
              "211 student211 343.8213    \n",
              "212 student212 266.0198    \n",
              "213 student213 249.6514    \n",
              "214 student214 263.4043    \n",
              "215 student215 315.8730    \n",
              "216 student216 207.3158    \n",
              "217 student217 400.4940    \n",
              "218 student218 199.6521    \n",
              "219 student219 207.3640    \n",
              "220 student220 483.9198    \n",
              "221 student221 307.8051    \n",
              "222 student222 225.6996    \n",
              "223 student223 144.7991    \n",
              "224 student224 417.6686    \n",
              "225 student225 357.1344    \n",
              "226 student226 249.2913    \n",
              "227 student227 286.0981    \n",
              "228 student228 230.8265    \n",
              "229 student229 366.3081    \n",
              "230 student230 200.5346    \n",
              "231 student231 331.7983    \n",
              "232 student232 358.5179    \n",
              "233 student233 471.5199    \n",
              "234 student234 308.4997    \n",
              "235 student235 198.3318    \n",
              "236 student236 131.4145    \n",
              "237 student237 242.8344    \n",
              "238 student238 225.7406    \n",
              "239 student239 322.1616    \n",
              "240 student240 232.4191    "
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "このデータ(`sample_data`)の年収(`Salary`)のヒストグラムを描いてみると…"
      ],
      "metadata": {
        "id": "dWrXzgLu0xt1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# sample_dataの年収(Salary)のヒストグラムを描く\n",
        "hist(sample_data$Salary)"
      ],
      "metadata": {
        "id": "XNcdJ1zW0vtM",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "dcbc726a-8944-4832-e5dc-3ef916913519"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Histogram of sample_data$Salary”"
            ],
            "image/png": 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IACQgIUEBKggJAABekMaXNFkjanceMB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\n77YYFmcgI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CFBASoICQAAWEBCggJEAB\nIQEKCAlQQEiAAkICFBASoICQAAWEBCggJEABIQEKCAlQQEiAAkICFBASoICQAAWEBCggJEDB\n/wMTIbpcfvR32AAAAABJRU5ErkJggg=="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "極端に高い年収の人が混ざっています。\n",
        "\n",
        "この様に極端に大きな値や小さな値の様な異常な値(**外れ値**)がデータに含まれている場合は、外れ値を省いて平均値を計算する方が望ましい場合もあります。\n",
        "\n",
        "ただし、外れ値だと思っていた値が、実際に生じ得る観察結果である可能性も当然ありえるため、データを省く際には、種のレベルで個体差があった、ヒューマンエラー(肥料の量ミス、水やりを忘れていた等)があった等、極端な値が外れ値である可能性が高いという根拠があるほうが好ましいです。"
      ],
      "metadata": {
        "id": "f1yqGsEhwjN9"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### ■ 中央値 (median)\n",
        "\n",
        "先ほど説明した、外れ値が混ざっていた場合や、データの分布が偏っている場合には、平均値が代表値として適切ではないことがあります。\n",
        "\n",
        "この様な場合、ある観測地より小さい観測値の数と大きな観測値の数が等しくなる様な値の方が望ましいことがあります。このような値は**中央値**(median)と呼ばれます。\n",
        "\n",
        "有名な例として、「2013年に花巻東高校を卒業した生徒の平均年収が4000万円になる」というものがあります。\n",
        "\n",
        "花巻東高校は各学年が240人いるそうなので、某野球選手が100億円くらい貰っていたら計算が合います。\n",
        "\n",
        "(実際の年俸等は詳しくないので自分で調べてください。)\n",
        "\n",
        "* https://raw.githubusercontent.com/slt666666/biostatistics_text_wed/refs/heads/main/source/_static/data/chapter3_Hanamaki_higashi.csv\n",
        "\n",
        "上記URLに仮想の卒業生の年収データを入れてあるので、読み込んで平均値を求めてみましょう。\n",
        "\n",
        "```\n",
        "Hanamaki_df <- read.csv(ファイル名のURL)\n",
        "mean(平均値を求めるデータ)\n",
        "```"
      ],
      "metadata": {
        "id": "WxLnVo93xVLV"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 花巻東高校の仮想年収データの平均値\n",
        "Hanamaki_df <- read.csv(\"https://raw.githubusercontent.com/slt666666/biostatistics_text_wed/refs/heads/main/source/_static/data/chapter3_Hanamaki_higashi.csv\")\n",
        "mean(Hanamaki_df$Salary)\n",
        "hist(Hanamaki_df$Salary)"
      ],
      "metadata": {
        "id": "MrsEiLRuhoIo",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 454
        },
        "outputId": "f9b26efd-2cc0-451a-df89-f7cbb1e8cf8a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "4458.58559529342"
            ],
            "text/markdown": "4458.58559529342",
            "text/latex": "4458.58559529342",
            "text/plain": [
              "[1] 4458.586"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Histogram of Hanamaki_df$Salary”"
            ],
            "image/png": 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AFCAgQICRAgJECAkAABQgIECAkQICRA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"
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "また、外れ値を省いた(`Salalry`が1000000未満)データから平均値・ヒストグラムを描いてみると"
      ],
      "metadata": {
        "id": "sfxeuThmJ3aJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 外れ値を省いた結果\n",
        "Hanamaki_normal_df <- Hanamaki_df[Hanamaki_df$Salary < 1000000,]\n",
        "mean(Hanamaki_normal_df$Salary)\n",
        "hist(Hanamaki_normal_df$Salary)"
      ],
      "metadata": {
        "id": "fdR2IvnrJ8XP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 454
        },
        "outputId": "f1eaf0db-760e-4450-efa5-988ced0b9890"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "293.140346738159"
            ],
            "text/markdown": "293.140346738159",
            "text/latex": "293.140346738159",
            "text/plain": [
              "[1] 293.1403"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Histogram of Hanamaki_normal_df$Salary”"
            ],
            "image/png": 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iCAkAABhFQR/rawGKs7e9nQCKki9Om5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"
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "ある程度ばらつきが見えてきます。\n",
        "\n",
        "この様な、極端なデータの分布をしている場合は、平均値がデータの代表値としては不適切だと考えられるため、**中央値**を使用します。\n",
        "\n",
        "極端に大きい(小さい)観測値の影響を省いた、中心的な値の情報が手に入ります。\n",
        "\n",
        "Rでは`median`関数で求めることが出来ます。\n",
        "\n",
        "`median(中央値を求めるデータ)`"
      ],
      "metadata": {
        "id": "Oebx7X3fi6lM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Salary列データの中央値を求める\n",
        "median(Hanamaki_df$Salary)"
      ],
      "metadata": {
        "id": "r_IRSuQHjR5O",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "ff916095-b589-442c-a7a8-26f716b75487"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "291.79909825"
            ],
            "text/markdown": "291.79909825",
            "text/latex": "291.79909825",
            "text/plain": [
              "[1] 291.7991"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "この中央値の考え方を拡張したものに**分位点**があります。\n",
        "\n",
        "観測値を小さいものから並べたとき、全体の$100p\\%(0\\leqq p\\leqq1)$に位置する値を$100p\\%$**パーセンタイル**または**百分位点**と呼びます。\n",
        "\n",
        "特によく用いられるのは四分位点(quartile)で、25％ずつデータを分割した際の3つの分割点になります。\n",
        "\n",
        "**第1四分位点**$Q_1$は25％分位点、**第2四分位点**$Q_2$は50％分位点(**中央値**)、**第3四分位点**$Q_3$は75％分位点になります。\n",
        "\n",
        "箱ひげ図(boxplot)を描く際には、この四分位点を基準にBoxが描かれることが多いです。\n",
        "\n",
        "Rでは`boxplot`関数で簡単な箱ひげ図を描くことが出来ます。\n",
        "\n",
        "また、前回扱った`summary`関数でも四分位点を表示してくれます。"
      ],
      "metadata": {
        "id": "Bs28AbYajlG2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 1,2,3,...,99,100のデータに対し、summary関数の適用と箱ひげ図を描く\n",
        "sample_data <- seq(1,100) # 1~100までの数値\n",
        "summary(sample_data)\n",
        "boxplot(sample_data)"
      ],
      "metadata": {
        "id": "dYl6-7RflQT-",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 474
        },
        "outputId": "eb00f0d1-aa84-484f-bb71-3e4129dcfc17"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
              "   1.00   25.75   50.50   50.50   75.25  100.00 "
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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vFd+6bdu6ddf+PszDkhrSshLdjBB7L/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\nrkJggg=="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### ■ 最頻値 (mode)\n",
        "平均値、中央値と並んでよく用いられる代表値の一つに最頻値があります。\n",
        "\n",
        "ヒストグラムを描いた際に、分布の峰となっている部分の値になります。\n",
        "\n",
        "例えば最初のサンプルデータの年齢(Age)列のデータの場合、ヒストグラムと各範囲の度数分布表を描いてみると"
      ],
      "metadata": {
        "id": "LLHIXHV0x0DL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# ヒストグラムと度数分布表を描く\n",
        "h <- hist(df$Age)\n",
        "n <- length(h$counts) # 階級の数\n",
        "class_names <- NULL # 階級の名前格納用\n",
        "for(i in 1:n) {\n",
        "  class_names[i] <- paste(h$breaks[i], \"～\", h$breaks[i+1])\n",
        "}\n",
        "frequency_table <- data.frame(class=class_names, frequency=h$counts)\n",
        "frequency_table"
      ],
      "metadata": {
        "id": "lcu5s4eHmcga",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 925
        },
        "outputId": "825ba7f0-64b3-4f32-8ba4-99b61c2f2f67"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A data.frame: 13 × 2</caption>\n",
              "<thead>\n",
              "\t<tr><th scope=col>class</th><th scope=col>frequency</th></tr>\n",
              "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><td>0 ～ 2  </td><td>15</td></tr>\n",
              "\t<tr><td>2 ～ 4  </td><td>19</td></tr>\n",
              "\t<tr><td>4 ～ 6  </td><td>12</td></tr>\n",
              "\t<tr><td>6 ～ 8  </td><td>17</td></tr>\n",
              "\t<tr><td>8 ～ 10 </td><td>25</td></tr>\n",
              "\t<tr><td>10 ～ 12</td><td>13</td></tr>\n",
              "\t<tr><td>12 ～ 14</td><td>11</td></tr>\n",
              "\t<tr><td>14 ～ 16</td><td>14</td></tr>\n",
              "\t<tr><td>16 ～ 18</td><td>19</td></tr>\n",
              "\t<tr><td>18 ～ 20</td><td>17</td></tr>\n",
              "\t<tr><td>20 ～ 22</td><td>14</td></tr>\n",
              "\t<tr><td>22 ～ 24</td><td>14</td></tr>\n",
              "\t<tr><td>24 ～ 26</td><td>10</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ],
            "text/markdown": "\nA data.frame: 13 × 2\n\n| class &lt;chr&gt; | frequency &lt;int&gt; |\n|---|---|\n| 0 ～ 2   | 15 |\n| 2 ～ 4   | 19 |\n| 4 ～ 6   | 12 |\n| 6 ～ 8   | 17 |\n| 8 ～ 10  | 25 |\n| 10 ～ 12 | 13 |\n| 12 ～ 14 | 11 |\n| 14 ～ 16 | 14 |\n| 16 ～ 18 | 19 |\n| 18 ～ 20 | 17 |\n| 20 ～ 22 | 14 |\n| 22 ～ 24 | 14 |\n| 24 ～ 26 | 10 |\n\n",
            "text/latex": "A data.frame: 13 × 2\n\\begin{tabular}{ll}\n class & frequency\\\\\n <chr> & <int>\\\\\n\\hline\n\t 0 ～ 2   & 15\\\\\n\t 2 ～ 4   & 19\\\\\n\t 4 ～ 6   & 12\\\\\n\t 6 ～ 8   & 17\\\\\n\t 8 ～ 10  & 25\\\\\n\t 10 ～ 12 & 13\\\\\n\t 12 ～ 14 & 11\\\\\n\t 14 ～ 16 & 14\\\\\n\t 16 ～ 18 & 19\\\\\n\t 18 ～ 20 & 17\\\\\n\t 20 ～ 22 & 14\\\\\n\t 22 ～ 24 & 14\\\\\n\t 24 ～ 26 & 10\\\\\n\\end{tabular}\n",
            "text/plain": [
              "   class    frequency\n",
              "1  0 ～ 2   15       \n",
              "2  2 ～ 4   19       \n",
              "3  4 ～ 6   12       \n",
              "4  6 ～ 8   17       \n",
              "5  8 ～ 10  25       \n",
              "6  10 ～ 12 13       \n",
              "7  12 ～ 14 11       \n",
              "8  14 ～ 16 14       \n",
              "9  16 ～ 18 19       \n",
              "10 18 ～ 20 17       \n",
              "11 20 ～ 22 14       \n",
              "12 22 ～ 24 14       \n",
              "13 24 ～ 26 10       "
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Histogram of df$Age”"
            ],
            "image/png": 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RIsQvJESLAIyRMhwSIkT4QEi5A8ERIs\nQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIk\nT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJE\nSLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QE\ni5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAI\nyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8\nERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMh\nwSIkT4QEi5A8ERIsQvJESLAIyRMhwfIJqWXp/HvvXfDSh4wiJEKqAaWHtHL6QJM1/NK1hcYR\nEiHVgJJDem07s9PEmXPmXDB+sNl1ZYGBhERINaDkkCZn7swvNc+tm1ZgICERUg0oOaRBk9qX\nTxpWYCAhEVINKDmkzOXtyxf3KDCQkAipBpQc0ogT25fHbVtgICERUg0oOaRpdVeszy29d5GZ\nUWAgIRFSDSg5pFW7mz4HTzzzjAljepnRqwsMJCRCqgGlv4+04aqR9fZtpMze85oLjSMkQqoB\nXh8RWvfCU08t+aBMVk45rc04QiKk6hfks3Yr/+6eQUiEVFtKD+mZI0fsPzf3oG5GoWvhoR0h\n1YCSQ3q0wfTKmAOzHw4iJEKqdSWHNDZzX8v6qzJ7vhcREiGh5JCGfdEeLuhxZDMhERJK/4jQ\nRdmjH5uphERIKDmkocfkjs81cwiJkGpeySFNrbtuoz1umWDOPouQCKnGlRzSW8PNIdmFlqnG\nEBIh1bjS30daMeXs/NI9OxASIdU4/oqQJ0KCRUieCAkWIXkiJFiE5ImQYBGSJ0KCRUieCAkW\nIXkiJFiE5ImQYBGSJ0KCRUieCAkWIXkiJFiE5ImQYFVUSM/8a7Embgw1d2eqIqRriv7B/iDt\nTe5qKiqkeX0nFed480aouTtTFSHts0eRP9hPHpX2Jnc1lRXSiCJvtPcTkso+04rciYmE5CAk\nT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJE\nSLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QE\ni5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAI\nyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8ERIsQvJESLAIyRMhwSIkT4QEi5A8\nERIsQvJESLAISTpxVJGaajKkA5qK/TmdmPY+lhkhSf1Omlmc3jUZ0i47FfljOqlf2vtYZoQk\n9bumyCk+UpshHVjkCtcQki9CkgipKhGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmE\npEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQX\nIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJS\nISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQ\nJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCcvmGtGHRQ8sKjyAkiZCqUskhXfaQ\nPbyhnzFm1NOFBhKSREhVqeSQzIz44AHTcNzp+5mmFwsMJCSJkKqSX0g7NS2OD++pO6XAQEKS\nCKkqeYX0pjkvu3zskAIDCUkipKrkFdJL5tbs8gWZAgMJSSKkquQVUnPT7OzypK0KDCQkiZCq\nUukhjX9iyYpzd1wTLz7f++gCAwlJIqSqVHpIOXdH0W29uy0qMJCQJEKqSiWHdPPVM6dNOHbM\ngiiaO+QXhQYSkkRIVSnAR4RWb9rsrGUD+rXpY9Z3suLMfkXqRUjlQUjegnzW7q0lzhmbHp7f\n5ppO75Em7ntjcfYmpPIgJG9BQppR6Fo6f2g3cVyR/xpHE1J5EJI3QpIISYWQXIQkEZIKIblK\nDmlUB4MISY+QqlLJIXXr1tCmnpD0CKkqlRzSjD7tL9Xx0K4IhFSVSg5p4257bGxdJqQiEFJV\nKv3FhsWN57QuElIRCKkqebxq987brUsLZxcYRkgSIVWljiHtfcM/yzADIUmEVJU6htTdNI5/\ncPMPznkiJImQqlLHkN76/sH1Ztj57gfnPBGSREhVyXmO9Ob1B3Uz+//g3YAzEJJESFVp8xcb\nXrt6V9PrK38LNgMhSYRUlTYLae1dJzSa4ZnMxS2BZiAkiZCqkhPSo6f2NY1feDh66QQzM9AM\nhCQRUlXqGNJL39rJmN2+u8outxwyMNAMhCQRUlXqGFI30/SVJ1tPfLcu0AyEJBFSVeoY0uhb\n1rafWHJvoBkISSKkqiSfIz27wh78T9AZCEkipKrUMaSNk8zD8dF1ZmJzwBkISSKkqtQxpCvN\nWPulYX89yVwTcAZCksofUkt/U6yyhzS16E0q3n3l/sEW0jGkTx6VXzhyx4AzEJJU/pA2mYt/\nWpyeZQ9p0hZFbtKV5soi1xg0r9w/2EI6htR4ZX5hTqFvlygWIUlJhHRLkdvUu/wh9S1yhfvN\n/UWuMaLLhLT1WfmFKVsHnIGQJEJSqeSQJvX6pT3aOK/7lwLOQEgSIalUckivbWOGf/ao/bcy\n2/wj4AyEJBGSSiWHFC3/ykeMMQP+7ZWQMxCSREgqFR1SFLW8+uJ7gWcgJImQVCo8pDIgJImQ\nVCo5pJY7jxr5iZyAMxCSREgqlRzSFcb0asoJOAMhSYSkUskhDT1saRlmICSJkFQqOaTMH8sx\nAyFJhKRSySENfbwcMxCSREgqlRzSN6aUYwZCkghJpZJDWn3Yyb9ZvCQr4AyEJBGSSiWH1OFX\nOwLOQEgSIalUckjjJ0xuFXAGQpIISaWSQyoPQpIISaXCQ3r32VWhZyAkiZBUKjqkhaOM+XUU\nHf3bkDMQkkRIKpUc0p969DksDunNQT2e7HR88QhJIiSVSg5p7PCXX7f3SG8MHxdwBkKSpu25\nskhritwHQkpBx5A+MjvKhhTNCvlHyAhJOqjoPzPVp8gvBiGkFIivvvxJPqSb+StCakWHtO/H\nf12cOabIryMlpBSIz9qdnw/plBEBZyAkad9di1zhFkJS6TohndbvKRvSyvNMyA/dEZJESCqV\nHNLrw7rvbkaObDDDlwecgZAkQlKp5JCiN75q/4pQ/68We+sriJAkQlKp6JCiqGX5kpD3RhYh\nSYSkUuEhlQEhSYSkUskhHdxmdMAZCEkiJJVKDqn9HcDBAWcgJImQVCo5pPez1jx7zgHvBJyB\nkCRCUqnkkNp88ysBZyAkiZBUqiKkx3lop0ZIKrUZ0oO9As5ASBIhqVRySKty3nx4JH/7W42Q\nVGoqpPYP7t8acAZCkghJpZJDGptz7Ff5VXM9QlKpqZDKg5AkQlIhJBchSYSkUskh7frpvToK\nNAMhSYSkUskhbd1ojKmL/2ustwLNQEgSIalUckgr9z/jf9ZF7/zu+EP5iJAaIanUVEinTMwv\nHH5qwBnSDWnR0uI0EZIGIbk6hjTgpvzCfwwMOEOaIX2/rui/fUVIGoTk6hhSw+X5hX9vCDhD\nmiFdZx74Q3HqCEmDkFwdQ9ptcO5LZB/tv2vAGdIN6XdFrkFIKoTk6hjSz+rNdoccfcj2pu7u\ngDMQkkRIKpUcUrTwsJ7xs4Qen5kfcgZCkghJpaJDiv8NXnnh5eawMxCSREgqFR5SlX3RGCHp\nEJK36v6iMULSISRv1f1FY4SkQ0jeqvuLxghJh5C8VfcXjRGSDiF5q+4vGiMkHULyVt1fNEZI\nOoTkrbq/aIyQdAjJW3V/0Rgh6RCSt+r+ojFC0iEkb9X9RWOEpENI3sSnv58txwyEJBGSSiWH\n1PPb5ZiBkCRCUqnkkA45osh/MRVCkghJpZJDWj7+8NufXJIVcAZCkghJpZJD6vAnQALOQEgS\nIalUckgnfWnS5LyAMxCSVHRIN5tFTxZlESElr7r/9ndVhHRh0X9SjJCS1xbSdY9kj55+JfQM\nhCQVHdK55pniVniakJLXFpKZljs6I/QMhCQRkgohuQhJIiQVQnIRkkRIKoTkIiSJkFQIyUVI\nEiGpEJKLkCRCUiEkFyFJhKRSuSHtNdMye2aPAs5ASBIhqVRuSELAGQhJIiSVig3pViHgDIQk\nEZJKxYZUgpal8++9d8FLHzKKkCRCUqmdkFZOH5h7GDj80rWFxhGSREgqNRPSa9uZnSbOnDPn\ngvGDza4rCwwkJImQVGompMmZO/NLzXPrphUYSEgSIanUTEiDJrUvnzSswEBCkghJpWZCylze\nvnxxjwIDCUkiJJWaCWnEie3L47YtMJCQJEJSqZmQptVdsT639N5FZkaBgYQkEZJKzYS0anfT\n5+CJZ54xYUwvM3p1gYGEJBGSSs2EFG24amS9fRsps/e85kLjCEkiJJXaCSm27oWnnlryQZls\nenh+m2sISSAkleJDGvy1+UV6zefG7wjy8dS33L/MumxAvzZ9zPpOViMkFULSyfTsW5xMyD/f\nGCSkGYWuhYd2EiGpFB9S95lFrjBuYogbfx4hSYSkQkguQpIISYWQXCWHNKqDQYSkR0gqNRNS\nt24NbeoJSY+QVGompBl92l+q46FdEQhJpWZC2rjbHhtblwmpCISkUjMhRYsbz2ldJKQiEJJK\n7YQUvfN269LC2QWGEZJESCo1FJISIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgq\nhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGS\nREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVC\nchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEki\nJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5\nCEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGS\nCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyE\nJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmF\nkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKS\nCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJI\nLkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmE\npEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQX\nIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJS\nISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJJVaC2nDooeWFR5BSBIhqdRMSJc9ZA9v6GeM\nGfV0oYGEJBGSSs2EZGbEBw+YhuNO3880vVhgICFJhKRSWyHt1LQ4Pryn7pQCAwlJIiSVmgrp\nTXNedvnYIc6FK6ec1mYcIQmEpFJTIb1kbs0uX5BxLiSkzhGSSk2F1Nw0O7s8aasCA3loJxGS\nSu2ENP6JJSvO3XFNvPh876MLDCQkiZBUaieknLuj6Lbe3RYVGEhIEiGp1ExIN189c9qEY8cs\niKK5Q35RaCAhSYSkUjMhtVu9qeDFhCQRkkoNhvQhCEkiJBVCchGSREgqhOQiJImQVAjJRUgS\nIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJ\nRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQ\nVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQi\nJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGSREgq\nhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVCchGS\nREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEkiJBVC\nchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5CEki\nJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGSCiG5\nCEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyEJBGS\nCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmFkFyE\nJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKSCEmF\nkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJILkKS\nCEmFkFyEJBGSCiG5CEkiJBVCchGSREgqhOQiJImQVAjJRUgSIakQkouQJEJSISQXIUmEpEJI\nLkKSCEmllkJqWTr/3nsXvGAm18wAAAktSURBVPQhowhJIiSV2glp5fSBJmv4pWsLjSMkiZBU\naiak17YzO02cOWfOBeMHm11XFhhISBIhqdRMSJMzd+aXmufWTSswkJAkQlKpmZAGTWpfPmlY\ngYGEJBGSSs2ElLm8ffniHs6Fywb0a9PHbOzkKiZn+hYn063IFXqZPkWuYXoVuUJdQ5ErdK8v\ncoWepsgV+preRa5Q9E7Udy9yhYa6IlfYwmxR5BqmZ5ErZCaXeuP/ACWHNOLE9uVx2zoXbnp4\nfpsHf9LZVbw2v0gP3FTsGt8rdoV5vy5yhZ/cXeQK9/+oyBUevKHIFebf8GCRK/zo/iJXuPsn\nRa7w63lFrlD8P91NDxS7xmul3vg/QMkhTau7Yn1u6b2LzIxQmwNUppJDWrW76XPwxDPPmDCm\nlxm9OuQmAZWn9PeRNlw1st6+jZTZe15zwA0CKpHXR4TWvfDUU0s6e00OqCHl/6wdUAMICQiA\nkIAACAkIgJCAAAgJCICQgAAICQiAkIAACAkIgJCAAAgJCICQgAAICQiAkIAACAkIgJCAANIM\naW8DlF+3lgRuzGmGdPLRT6blS6NTm/qMT6U29fnDU5v6ir6pTT3PbErgxpxmSBND/qXL4pxz\nVGpTz9ontann7ZTa1Pf2S23q3xFS+RBSwgipjAgpYYRUPoSUNEJKGCGVESEljJDKiJASRkjl\nQ0hJI6SEEVIZEVLCCKmMCClhhFQ+hJQ0QkpY9Yd02mmpTX3e8alN/R8Hpjb1LZ9IbeoHtk5t\n6scz1f5Zu5UrU5v63TdTm3ptyC9cLM7Gl1Kbuvn/Upu6ZVkSs/BrFEAAhAQEQEhAAIQEBEBI\nQACEBARASEAAhAQEQEhAAIQEBEBIQACEBARASEAAhAQEQEhAAIQEBJBeSKumjchsMzmN33K7\nOf8tBZclO+3Gb3YblVtKfNfbpk5811dOH95j23GP28Wk97p96iT2OrWQNuxuTrh8Uma7FH5L\n9mozfob1UKKzLt69T/7WnPiut0+d9K6/va0Ze+EXuvf83+T3usPUSex1aiFdZb4TH/7UTE9+\n6pnmieQnfadxjyUNuVtz0rveYeqkd/0Mc118eI85Mvm97jB1EnudWkgj+6y3RzsOTOIvU0jT\nzJLE54zenr4xyt+ak971DlMnvetnH7wxPmxpHJH8XneYOom9TiukdfUHZ48nmqWJzz3BrGh+\neUXi00b5W3Mqu54PKZ1dX5/ZL61/cDt1InudVkgvmNwftZtp5ic+97Hm/H7GfPS2xCfO3ZpT\n2fV8SOns+rXxo6yU/sHt1InsdVohPWXOyB5fYe5NfO4xZvvZPz63r7kh6Ylzt+ZUdj0fUiq7\nvrDH/u+n9A+enTqRvU4vpDOzx3PMfYnPveDu9+LD5xq22pDwxK0hpbDr+ZDS2PXbG3Z/O6W9\nzk2dyF6nFdISMyF7fIH5bUpbEB1nFiU8Y+7WnMqu50PKS3DXWy4yh78bpbLXrVO3KutepxXS\nhu5jssfjzT9S2oLodJPsG0mtt+ZUdl2GlNyut0wyZzXbheT3um3qVmXd69Re/t6r15r4cNPg\nYYnPvPp7t2eP90/8BcP8rTmNXc9NnfyuTzOz8kuJ73Xb1InsdWohzTMXx4fXm0sSn3nTkC2e\nj4/uN7slPXM+pDR2PTd14rt+j5nWupj0XrdPnchepxZS82gz7pLP131yTfJT/6yu9+QLj6vr\n+1SSky6cMWNG/aD44K3Ed73D1Env+g7mrOyHc2asTHyvO0ydxF6n96HV1eeMyAw54+00pn7s\niC27D/5ysu/xz85/cNK+yZ7wrnecOuFdb53Z/D3xve44dQJ7za9RAAEQEhAAIQEBEBIQACEB\nARASEAAhAQEQEhAAIQEBEBIQACEBARASEAAhAQEQEhAAIQEBEBIQACEBARASEAAhAQEQEhAA\nIQEBEBIQACEBARASEAAhAQEQEhAAIQEBEBIQACEBARASEAAhAQEQEhAAIQEBEFIlqN8rPrht\nSP052VNN89PdGnwAQqoENqR/NjbNigv66ej+pvv2s9blLphumtamu2nIIaRKYEN6wkyJ7PfB\n7n1p48R9zOez52/o3838KN1NQw4hVQIb0iNmRhStadivxT60O948Yc+/3Uyp2z/tjYNFSF3b\nL3fvOWDyqjikw+wXdJ++1JydfY707FUv2kvHmBdGm8XZgQ/s2bj11LVDd4sXl08Znuk/blGa\nm117CKlLe7R+8Kwbvzg6s1f02Cxz/H1/XtOwy9r2Fxv+ZvaNbjRft4u/qx90ydwxxzTFd11v\njmiaceusoQ0LU9zu2kNIXdoRxt6xTDGtD+2ii8zO3+3dGtJ0c2P0bq/+G+LFz9rHes0H2YFf\n7W4f9r3UZ4/UtroWEVJXtqlxB3v0dHtILddubcygCQ/bs9f3b3wnir5k7oiXe37MnvObeGBL\n/91ftw4zq1Pb7hpESF3ZK+az9mhde0jx3c7Cxu27mRPju6HbzBfj0w+ZQ6JolTnKXvZuPHC5\nafVcehteewipK3vBHJ09rusQkn2x4f+OMNdG0YHmB0uWLHlh67ql0YvmxOxF9XtFS8zIX+es\nSmmraxIhdWUv5+6RVhsnpOid+iOjv7bd9ZwX/cMcYy9Zk71HGpna9tYwQurK3u+xoz36Q1tI\nFw9alfuIUNP+0dfNqXdZt9Zv8/6GbrvagQ/Zgf17Zu+K3kxzw2sPIXVpY7Kv2p3cFtIt5vTs\nG7J3munrP9KQb+UEc3/06brn46dPh2VftYvvoeKOBh2V5obXHELq0n5VN/CbVxz1mabWkJoP\nN7t+vefJx9QNW36bOSU/aKEZG91ltrvi+6MnNMQD3xhuTrll1vDMg6luea0hpK7tjk/2GDBp\n1bDdWp8jrb92VD/TfcQZy6MDzJ9bB32y/uXopp17jDh/Y49945Ovf3VY9y2P+VN6G12LCKny\ndP5rFO/kXnNA8gip8sxeuvl5PzzwyfjwWjMn8a1BFiFVhz82DLrkxindh/PeUUoIqUo8esTA\nzJBJr6a9GTWLkIAACAkIgJCAAAgJCICQgAAICQiAkIAACAkIgJCAAAgJCICQgAAICQiAkIAA\nCAkIgJCAAAgJCICQgAAICQiAkIAACAkIgJCAAAgJCICQgAAICQiAkIAACAkIgJCAAP4fcFBv\nXfcRLegAAAAASUVORK5CYII="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "この場合は8~10が最頻値となります。\n",
        "\n",
        "当然ながら、最頻値は階級の取り方によって変化します。\n",
        "\n",
        "もっとたくさんの階級でヒストグラムを描いてみると、"
      ],
      "metadata": {
        "id": "piZ5w1xBop_L"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# breaksの数値を増やしてより細かい階級でのヒストグラムを描く\n",
        "hist(df$Age, breaks=20)"
      ],
      "metadata": {
        "id": "QpzOpJH3o0Cx",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "1bf929c2-ed8c-4835-de33-eacc39033474"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Histogram of df$Age”"
            ],
            "image/png": 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cwjpM4fGO0nFiElMI+QOn9gtJ9YhJTAPFUhrXvmsVfL34KQIswjpATm6Qjp4se8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\nRU5ErkJggg=="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "例えば`breaks=20`にした場合は、1~2が最頻値となります。\n",
        "\n",
        "実際の解析では、この様に最頻値になりうる値が複数ある(峰がいくつかありそうな)分布では最頻値は有効な値とは言えません。\n",
        "\n",
        "階級の取り方を変えてもそれほど大きく最頻値の位置が変わらない様な分布を示す場合に、有効な代表値となります。"
      ],
      "metadata": {
        "id": "DhCs_xMEpR8h"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 散らばりの尺度\n",
        "\n",
        "代表値はあくまでも分布の中心的な位置を示す値であり、それだけでデータを説明出来る訳ではありません。\n",
        "\n",
        "例えば下記のA, B, Cそれぞれのデータについて、`mean`関数で平均値を、`median`関数で中央値を求めてみましょう。\n"
      ],
      "metadata": {
        "id": "4079iTuLx9H-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 各データの平均値と中央値を求める\n",
        "A <- c(0,0,30,30,60,78,78,140,142,150,150)\n",
        "B <- c(10,30,50,60,70,78,80,100,120,120,140)\n",
        "C <- c(60,70,70,70,70,78,80,80,90,90,100)\n",
        "\n",
        "mean(A)\n",
        "mean(B)\n",
        "mean(C)\n",
        "median(A)\n",
        "median(B)\n",
        "median(C)"
      ],
      "metadata": {
        "id": "HWOFg7jxrDgv",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 121
        },
        "outputId": "5b93e5c9-e541-4440-8c17-5504c9a9a770"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "78"
            ],
            "text/markdown": "78",
            "text/latex": "78",
            "text/plain": [
              "[1] 78"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "78"
            ],
            "text/markdown": "78",
            "text/latex": "78",
            "text/plain": [
              "[1] 78"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "78"
            ],
            "text/markdown": "78",
            "text/latex": "78",
            "text/plain": [
              "[1] 78"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "78"
            ],
            "text/markdown": "78",
            "text/latex": "78",
            "text/plain": [
              "[1] 78"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "78"
            ],
            "text/markdown": "78",
            "text/latex": "78",
            "text/plain": [
              "[1] 78"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "78"
            ],
            "text/markdown": "78",
            "text/latex": "78",
            "text/plain": [
              "[1] 78"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "A,B,Cのデータセットはいずれも平均値、中央値が78のデータセットになっています。\n",
        "\n",
        "しかし、`hist`関数で分布をみると大きく異なっています。"
      ],
      "metadata": {
        "id": "-7O7Sbzptupe"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# A, B, Cそれぞれのヒストグラムを描く\n",
        "hist(A)\n",
        "hist(B)\n",
        "hist(C)"
      ],
      "metadata": {
        "id": "KXhzDLIYsVi1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "40eb737a-11de-4dda-ab03-3eb179616388"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Histogram of A”"
            ],
            "image/png": 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qVbVz635cGD5yfJ48Om9LEiIUWAkPL0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\nQmCC"
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Histogram of B”"
            ],
            "image/png": 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iHlhJDCIqScEFJYhJQTQgqLkHJCSGER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\nCm4WgwEQAAAAAElFTkSuQmCC"
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Histogram of C”"
            ],
            "image/png": 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4QkIyR4IyQZIcEbIckICd4ISUZI8EZI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"
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "ということで、A,B,Cのデータの分布の違いを説明する値が必要になります。\n",
        "\n",
        "この様な場合、データの分布の形状を示す指標として、代表値だけではなく散らばり具合を示す尺度が用いられます。"
      ],
      "metadata": {
        "id": "XvF4mzd2t5hX"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### ■ レンジ\n",
        "\n",
        "散らばり具合を表すもっとも簡単な指標がレンジになり、分布の存在する範囲を示します。\n",
        "\n",
        "レンジ$R$は、$R=max(x_1,x_2,\\cdots,x_n) - min(x_1,x_2,\\cdots,x_n)$で定義されます。\n",
        "\n",
        "Rでは`range`関数で最小値と最大値を表示できるのでその差をとればレンジ$R$が計算できます。\n"
      ],
      "metadata": {
        "id": "Q65CAEtvuH-s"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 各データのrangeを求める\n",
        "range(A)\n",
        "range(B)\n",
        "range(C)"
      ],
      "metadata": {
        "id": "p4AR90Z2u1Kq",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "outputId": "57ac3f7c-0d02-46d3-da85-0c32d8d7c604"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<style>\n",
              ".list-inline {list-style: none; margin:0; padding: 0}\n",
              ".list-inline>li {display: inline-block}\n",
              ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
              "</style>\n",
              "<ol class=list-inline><li>0</li><li>150</li></ol>\n"
            ],
            "text/markdown": "1. 0\n2. 150\n\n\n",
            "text/latex": "\\begin{enumerate*}\n\\item 0\n\\item 150\n\\end{enumerate*}\n",
            "text/plain": [
              "[1]   0 150"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<style>\n",
              ".list-inline {list-style: none; margin:0; padding: 0}\n",
              ".list-inline>li {display: inline-block}\n",
              ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
              "</style>\n",
              "<ol class=list-inline><li>10</li><li>140</li></ol>\n"
            ],
            "text/markdown": "1. 10\n2. 140\n\n\n",
            "text/latex": "\\begin{enumerate*}\n\\item 10\n\\item 140\n\\end{enumerate*}\n",
            "text/plain": [
              "[1]  10 140"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<style>\n",
              ".list-inline {list-style: none; margin:0; padding: 0}\n",
              ".list-inline>li {display: inline-block}\n",
              ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
              "</style>\n",
              "<ol class=list-inline><li>60</li><li>100</li></ol>\n"
            ],
            "text/markdown": "1. 60\n2. 100\n\n\n",
            "text/latex": "\\begin{enumerate*}\n\\item 60\n\\item 100\n\\end{enumerate*}\n",
            "text/plain": [
              "[1]  60 100"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "レンジは簡単に計算できますが、最大値・最小値という２つのデータポイントのみに依存するので、\n",
        "\n",
        "散らばり具合を説明するには粗く、あまり用いられません。\n",
        "\n",
        "(先ほどの花巻東高校の例だとレンジがかなり広くなることになります。)\n",
        "\n",
        "そこで、最小値・最大値のデータだけでなく、すべてのデータを用いて散らばり具合を表す尺度が次に説明する**偏差**になります。"
      ],
      "metadata": {
        "id": "RZ32ISSJvcLI"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### ■ 偏差\n",
        "\n",
        "**偏差**(deviation)は、すべてのデータを用いて計算する散らばり具合を表す尺度で、各観測値と平均との隔たりをもとに計算します。\n",
        "\n",
        "偏差には標準偏差や平均偏差がありますが、理論的な性質等が理由で通常は標準偏差が使用されます。\n",
        "\n",
        "#### (参考)平均偏差\n",
        "\n",
        "各観測値$x_i$が平均$\\bar{x}$からどれだけ離れているかの平均を求めたものが**平均偏差**(mean deviation)になります。\n",
        "\n",
        "平均偏差$d$は、$d=\\dfrac{1}{n}\\lbrace|x_1 - \\bar{x}|+|x_2 - \\bar{x}|+\\cdots+|x_n - \\bar{x}|\\rbrace$ で求められます。\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "EHa05KKbwDwx"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### ■ 分散と標準偏差\n",
        "\n",
        "観測値を平均の差を、2乗することで符号を消し、平均を求めたものを**分散**(variance)と呼びます。\n",
        "\n",
        "分散は$S^2$という記号で表され、\n",
        "\n",
        "$S^2=\\dfrac{1}{n}\\lbrace(x_1 - \\bar{x})^2+(x_2 - \\bar{x})^2+\\cdots+(x_n - \\bar{x})^2\\rbrace$\n",
        "\n",
        "と定義されます。\n",
        "\n",
        "観測値が$cm$だった場合、分散はこのままでは測定単位が変わってしまう($cm^2$)ので、\n",
        "\n",
        "観測値と単位を揃える際には、分散の平方根をとった$\\sqrt{S^2}=S$が用いられます。\n",
        "\n",
        "この$S$を**標準偏差**(standard deviation)と呼びます。\n",
        "\n",
        "先ほどのAのデータセットを用いて分散を計算してみましょう"
      ],
      "metadata": {
        "id": "Q_mCgy7pyOnc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A <- c(0,0,30,30,60,78,78,140,142,150,150)"
      ],
      "metadata": {
        "id": "8OFscp_hzh2W"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "まずは平均値$\\bar{x} = \\dfrac{1}{n}(x_1+...+x_n)$を計算します。`mean`関数で計算可能です。"
      ],
      "metadata": {
        "id": "92EkjPtG0ejU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 平均値を求める\n",
        "mean_A <- mean(A)\n",
        "mean_A"
      ],
      "metadata": {
        "id": "9HdmWOGx0esu",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "fd433376-4ab2-49aa-aa71-fa63137ace87"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "78"
            ],
            "text/markdown": "78",
            "text/latex": "78",
            "text/plain": [
              "[1] 78"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "次にAの各値$x_1, ..., x_n$から平均値$\\bar{x}$を引き、平均からの**偏差**を求めます。\n",
        "\n",
        "$(x_1 - \\bar{x})+(x_2 - \\bar{x})+\\cdots+(x_n - \\bar{x})$"
      ],
      "metadata": {
        "id": "B8Z831_L0e0j"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 平均値からの差である偏差を求める\n",
        "A_deviation <- A - mean_A\n",
        "A_deviation"
      ],
      "metadata": {
        "id": "IYsugRj_0e9T",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "ddf2fe88-24fc-47a5-8e6d-bbcdd4fb654f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<style>\n",
              ".list-inline {list-style: none; margin:0; padding: 0}\n",
              ".list-inline>li {display: inline-block}\n",
              ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
              "</style>\n",
              "<ol class=list-inline><li>-78</li><li>-78</li><li>-48</li><li>-48</li><li>-18</li><li>0</li><li>0</li><li>62</li><li>64</li><li>72</li><li>72</li></ol>\n"
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            "text/markdown": "1. -78\n2. -78\n3. -48\n4. -48\n5. -18\n6. 0\n7. 0\n8. 62\n9. 64\n10. 72\n11. 72\n\n\n",
            "text/latex": "\\begin{enumerate*}\n\\item -78\n\\item -78\n\\item -48\n\\item -48\n\\item -18\n\\item 0\n\\item 0\n\\item 62\n\\item 64\n\\item 72\n\\item 72\n\\end{enumerate*}\n",
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              " [1] -78 -78 -48 -48 -18   0   0  62  64  72  72"
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    },
    {
      "cell_type": "markdown",
      "source": [
        "これで各データが平均からどれだけ離れているかが計算できた訳ですが、正負が混ざっているのでそのまま平均を計算してしまうと、散らばり具合が0になってしまいます。\n",
        "\n",
        "そこで、各偏差を2乗して符号を消します。\n",
        "\n",
        "$(x_1 - \\bar{x})^2+(x_2 - \\bar{x})^2+\\cdots+(x_n - \\bar{x})^2$\n",
        "\n",
        "Rでは累乗の計算は`^`で行うことが出来ます。\n",
        "\n",
        "例)2の10乗は`2^10`。`^`をベクトルに適用すると、各要素が累乗されます。"
      ],
      "metadata": {
        "id": "BdLv96AX0fF9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 偏差を二乗する\n",
        "A_deviation^2"
      ],
      "metadata": {
        "id": "H2jUsFOx0fOX",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "5e499afb-3cbc-44e3-fee8-eacd250dea30"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<style>\n",
              ".list-inline {list-style: none; margin:0; padding: 0}\n",
              ".list-inline>li {display: inline-block}\n",
              ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
              "</style>\n",
              "<ol class=list-inline><li>6084</li><li>6084</li><li>2304</li><li>2304</li><li>324</li><li>0</li><li>0</li><li>3844</li><li>4096</li><li>5184</li><li>5184</li></ol>\n"
            ],
            "text/markdown": "1. 6084\n2. 6084\n3. 2304\n4. 2304\n5. 324\n6. 0\n7. 0\n8. 3844\n9. 4096\n10. 5184\n11. 5184\n\n\n",
            "text/latex": "\\begin{enumerate*}\n\\item 6084\n\\item 6084\n\\item 2304\n\\item 2304\n\\item 324\n\\item 0\n\\item 0\n\\item 3844\n\\item 4096\n\\item 5184\n\\item 5184\n\\end{enumerate*}\n",
            "text/plain": [
              " [1] 6084 6084 2304 2304  324    0    0 3844 4096 5184 5184"
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          "metadata": {}
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    },
    {
      "cell_type": "markdown",
      "source": [
        "この値の平均値が**分散**になります。\n",
        "\n",
        "$S^2 = \\dfrac{1}{n}\\lbrace(x_1 - \\bar{x})^2+(x_2 - \\bar{x})^2+\\cdots+(x_n - \\bar{x})^2\\rbrace$"
      ],
      "metadata": {
        "id": "xpeAvp8p1wHj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 偏差の二乗の平均値を求める\n",
        "sum_squared_deviation <- sum(A_deviation^2)\n",
        "variance <- sum_squared_deviation / length(A) # length関数でデータの数をカウント出来る\n",
        "variance"
      ],
      "metadata": {
        "id": "qkSDIf951wQz",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "ad8c9353-2447-40e5-e96c-635b29286611"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "3218.90909090909"
            ],
            "text/markdown": "3218.90909090909",
            "text/latex": "3218.90909090909",
            "text/plain": [
              "[1] 3218.909"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "次にこの分散の値の平方根をとったものが**標準偏差**です。\n",
        "\n",
        "$\\sqrt{S^2} = S$\n",
        "\n",
        "Rでは平方根は`sqrt`関数で計算できます。"
      ],
      "metadata": {
        "id": "CCFXdyDs2Ww3"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 分散の平方根を求める\n",
        "sqrt(variance)"
      ],
      "metadata": {
        "id": "RQ828Q1a2dTF",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "dbfea6e6-d363-4ff3-b1ee-91ec9108bf43"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "56.7354306488379"
            ],
            "text/markdown": "56.7354306488379",
            "text/latex": "56.7354306488379",
            "text/plain": [
              "[1] 56.73543"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "こうして分散が3218.9090..., 標準偏差が56.7354....と求まりましや。\n",
        "\n",
        "今回はちゃんと計算しましたが、Rには分散や標準偏差を求める関数があります。\n",
        "\n",
        "分散は`var`、標準偏差は`sd`という関数で求めることが出来ます。"
      ],
      "metadata": {
        "id": "tw7ZfW0O5uLy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 分散\n",
        "var(A)\n",
        "# 標準偏差\n",
        "sd(A)"
      ],
      "metadata": {
        "id": "bpMPFTzW2tNP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "934f4855-2248-42fc-a414-f42ac78a3126"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "3540.8"
            ],
            "text/markdown": "3540.8",
            "text/latex": "3540.8",
            "text/plain": [
              "[1] 3540.8"
            ]
          },
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        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "59.5046216692452"
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              "[1] 59.50462"
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    },
    {
      "cell_type": "markdown",
      "source": [
        "Rの関数で計算した分散や標準偏差は、今回計算で求めた値と一致しません。\n",
        "\n",
        "これはRの関数で計算される値は**不偏分散**と呼ばれるものでで、私達の計算してきた値は**不偏でない分散**と呼ばれる値になるからです。\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "6HCFZ5tj6Kot"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### **不偏でない分散と不偏分散**\n",
        "\n",
        "分散には**不偏でない分散**$S^2$と**不偏分散**$s^2$と呼ばれるものがあります。\n",
        "\n",
        "不偏でない分散は先ほど説明した$S^2$で、\n",
        "\n",
        "$S^2=\\dfrac{1}{n}\\lbrace(x_1 - \\bar{x})^2+(x_2 - \\bar{x})^2+\\cdots+(x_n - \\bar{x})^2\\rbrace$\n",
        "\n",
        "一方、不偏分散$s^2$は、\n",
        "\n",
        "$s^2=\\dfrac{1}{n-1}\\lbrace(x_1 - \\bar{x})^2+(x_2 - \\bar{x})^2+\\cdots+(x_n - \\bar{x})^2\\rbrace$\n",
        "\n",
        "で表されます。\n",
        "\n",
        "違いは平均値を求める際に$n$で割っているか$n-1$で割っているかになります。\n",
        "\n",
        "実際に先ほど求めた偏差の2乗和を$n-1$でを割ってみると`var`関数と同じ結果になります。"
      ],
      "metadata": {
        "id": "eBfA7ilR68tI"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 不偏分散を求める\n",
        "sum_squared_deviation / (11 - 1)\n",
        "var(A)"
      ],
      "metadata": {
        "id": "-b0wvwbr9IrN",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "2d24eba2-687e-4026-d76f-afd5d5dd6bd1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "3540.8"
            ],
            "text/markdown": "3540.8",
            "text/latex": "3540.8",
            "text/plain": [
              "[1] 3540.8"
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        {
          "output_type": "display_data",
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            "text/html": [
              "3540.8"
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            "text/plain": [
              "[1] 3540.8"
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    },
    {
      "cell_type": "markdown",
      "source": [
        "不偏でない分散は得られた観測データ自体の分散を表しており、不偏分散は得られた観測データから推測される母集団の分散を表します。\n",
        "\n",
        "標本数が少ないときに、標本分散は母集団の分散よりも小さくなる傾向にあるため、補正したものが不偏分散です。\n",
        "\n",
        "逆に標本数が多くなるほど、$S^2$と$s^2$は近くなります。\n",
        "\n",
        "通常は統計学で**分散**というとこの**不偏分散**を指すことが多いです。\n",
        "\n",
        "この**母集団**や**不偏推定量**という概念はまた第5回あたりの講義で扱うことになるので、その際に説明します。"
      ],
      "metadata": {
        "id": "I3M3SIGc9YV-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "最初の話に戻りますが、A, B, C各データセットの散らばり具合として、標準偏差を求めてみましょう。\n",
        "\n",
        "今回は`sd`関数を使用して標準偏差を求めてみます。\n",
        "\n",
        "`sd(データセット)`"
      ],
      "metadata": {
        "id": "wtYPz6q_9wuF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# A, B, Cそれぞれについて(不偏分散に基づく)標準偏差を求める\n",
        "A <- c(0,0,30,30,60,78,78,140,142,150,150)\n",
        "B <- c(10,30,50,60,70,78,80,100,120,120,140)\n",
        "C <- c(60,70,70,70,70,78,80,80,90,90,100)\n",
        "\n",
        "sd(A)\n",
        "sd(B)\n",
        "sd(C)"
      ],
      "metadata": {
        "id": "kXHBKQPC9pO3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "outputId": "39ee460e-8dfc-4384-c2fe-245dfcae5276"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "59.5046216692452"
            ],
            "text/markdown": "59.5046216692452",
            "text/latex": "59.5046216692452",
            "text/plain": [
              "[1] 59.50462"
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          "metadata": {}
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        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "39.9499687108764"
            ],
            "text/markdown": "39.9499687108764",
            "text/latex": "39.9499687108764",
            "text/plain": [
              "[1] 39.94997"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "11.6619037896906"
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            "text/markdown": "11.6619037896906",
            "text/latex": "11.6619037896906",
            "text/plain": [
              "[1] 11.6619"
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          },
          "metadata": {}
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      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "こうして結果を見ると、A, B, Cいずれも平均値・中央値は78で一致していましたが、\n",
        "\n",
        "標準偏差は59, 39, 11と大きく異なっており、Aが最もばらついているデータだということが分かります。\n",
        "\n"
      ],
      "metadata": {
        "id": "qdVd0D4B-EO1"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### ■ 標準化\n",
        "\n",
        "平均値や中央値でデータの代表値が、標準偏差や分散という指標で、データのばらつき具合が計算できました。\n",
        "\n",
        "この時、各データを平均$\\bar{z}=0$、標準偏差${S_Z=1}$になるように変換することを**標準化**と呼びます。\n",
        "\n",
        "平均値やばらつきが異なるデータにおける位置を比較したい時に用いられます。\n",
        "\n",
        "例えば、あるクラスの試験の結果が\n",
        "* 数学 ... 平均点:40、標準偏差:15\n",
        "* 理科 ... 平均点:70、標準偏差:10\n",
        "\n",
        "であった際に、そのクラスにおける数学の50点と理科の50点が同じ位置かというと、恐らく違うだろうと考えられます。\n",
        "\n",
        "そこで、数学と理科のデータをそれぞれ標準化し、同じ平均値・標準偏差に揃えることで、数学と理科を比較出来る値に変換する形になります。\n",
        "\n",
        "標準化は $z_i=\\dfrac{x_i-\\bar{x}}{s_x}$ で行い、標準化された値を**Z得点、Zスコア**と呼びます。\n",
        "\n",
        "($\\bar{x}$は平均値、$s_x$は標準偏差)\n",
        "\n",
        "数学、理科それぞれの50点を標準化してみると…"
      ],
      "metadata": {
        "id": "BVzSUYgzyA1U"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 数学・英語の50点を標準化した場合のZスコアを求める\n",
        "Math <- c(20, 20, 30, 40, 50, 50, 50, 60)\n",
        "Science <- c(50, 65, 65, 70, 75, 75, 80, 80)\n",
        "\n",
        "print(\"数学50点のZ得点\")\n",
        "(50 - mean(Math)) / sd(Math)\n",
        "print(\"理科50点のZ得点\")\n",
        "(50 - mean(Science)) / sd(Science)"
      ],
      "metadata": {
        "id": "73Qthlhzfzv9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 89
        },
        "outputId": "eb2ac85c-c8cc-4b57-d24c-e0fc8b6e1205"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1] \"数学50点のZ得点\"\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
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              "0.661437827766148"
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              "[1] 0.6614378"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1] \"理科50点のZ得点\"\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "-2"
            ],
            "text/markdown": "-2",
            "text/latex": "-2",
            "text/plain": [
              "[1] -2"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "ということで、Z得点で考えてみると、数学の50点は0.66、理科の50点は-2ということになりました。\n",
        "\n",
        "平均0標準偏差1の分布になっているので、数学は平均より少し高め、理科は平均よりかなり低い位置にいると比較できます。\n",
        "\n",
        "また、皆さんに馴染み深い**偏差値**という値は、この変換をするときに、\n",
        "\n",
        "平均$\\bar{z}=50$、標準偏差${s_Z=10}$になるように変換された値になります。\n",
        "\n",
        "偏差値$T_i$はZ得点から$T_i=10z_i+50$で計算できます。"
      ],
      "metadata": {
        "id": "6z9abfdPjcxc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Z得点から偏差値を求める\n",
        "print(\"数学の50点の偏差値\")\n",
        "0.661437827766148 * 10 + 50\n",
        "print(\"理科の50点の偏差値\")\n",
        "-2 * 10 + 50"
      ],
      "metadata": {
        "id": "SBZ7ntP7mIAI",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 89
        },
        "outputId": "3012d05f-9412-40be-a672-2cc7033bcda4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1] \"数学の50点の偏差値\"\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "56.6143782776615"
            ],
            "text/markdown": "56.6143782776615",
            "text/latex": "56.6143782776615",
            "text/plain": [
              "[1] 56.61438"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1] \"理科の50点の偏差値\"\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "30"
            ],
            "text/markdown": "30",
            "text/latex": "30",
            "text/plain": [
              "[1] 30"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 2次元のデータ\n",
        "\n",
        "ここまで１つの変数の観測値に関する記述統計を扱ってきました。\n",
        "\n",
        "次は２つ以上の変数の観測値があった際に、変数間の関係性を表す記述統計学の方法を扱います。"
      ],
      "metadata": {
        "id": "N2XCN-1PARo2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# サンプルデータの読み込み\n",
        "df <- read.csv(\"https://raw.githubusercontent.com/slt666666/biostatistics_text_wed/refs/heads/main/source/_static/data/chapter3_data.csv\")\n",
        "head(df) # 頭から一部のみ表示"
      ],
      "metadata": {
        "id": "7Dx4cGNBu-0m",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "b839b42a-5378-4dd6-c5af-a8c208665b87"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A data.frame: 6 × 7</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>X</th><th scope=col>Flower</th><th scope=col>Resistance</th><th scope=col>Age</th><th scope=col>Height</th><th scope=col>Leaf_length</th><th scope=col>Leaf_width</th></tr>\n",
              "\t<tr><th></th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>1</th><td>サンプル1</td><td>Yellow</td><td>Normal     </td><td> 1</td><td>65.78827</td><td>7.834566</td><td>1.2310844</td></tr>\n",
              "\t<tr><th scope=row>2</th><td>サンプル2</td><td>Purple</td><td>Weak       </td><td> 1</td><td>26.70546</td><td>4.654080</td><td>0.6596468</td></tr>\n",
              "\t<tr><th scope=row>3</th><td>サンプル3</td><td>Blue  </td><td>Very strong</td><td>18</td><td>31.67394</td><td>6.657642</td><td>0.5777713</td></tr>\n",
              "\t<tr><th scope=row>4</th><td>サンプル4</td><td>Blue  </td><td>Very strong</td><td> 2</td><td>41.59529</td><td>4.530526</td><td>1.0155126</td></tr>\n",
              "\t<tr><th scope=row>5</th><td>サンプル5</td><td>Blue  </td><td>Very strong</td><td> 4</td><td>40.18388</td><td>6.621776</td><td>0.5938072</td></tr>\n",
              "\t<tr><th scope=row>6</th><td>サンプル6</td><td>Blue  </td><td>Very strong</td><td> 4</td><td>28.85123</td><td>6.452588</td><td>0.3979530</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ],
            "text/markdown": "\nA data.frame: 6 × 7\n\n| <!--/--> | X &lt;chr&gt; | Flower &lt;chr&gt; | Resistance &lt;chr&gt; | Age &lt;int&gt; | Height &lt;dbl&gt; | Leaf_length &lt;dbl&gt; | Leaf_width &lt;dbl&gt; |\n|---|---|---|---|---|---|---|---|\n| 1 | サンプル1 | Yellow | Normal      |  1 | 65.78827 | 7.834566 | 1.2310844 |\n| 2 | サンプル2 | Purple | Weak        |  1 | 26.70546 | 4.654080 | 0.6596468 |\n| 3 | サンプル3 | Blue   | Very strong | 18 | 31.67394 | 6.657642 | 0.5777713 |\n| 4 | サンプル4 | Blue   | Very strong |  2 | 41.59529 | 4.530526 | 1.0155126 |\n| 5 | サンプル5 | Blue   | Very strong |  4 | 40.18388 | 6.621776 | 0.5938072 |\n| 6 | サンプル6 | Blue   | Very strong |  4 | 28.85123 | 6.452588 | 0.3979530 |\n\n",
            "text/latex": "A data.frame: 6 × 7\n\\begin{tabular}{r|lllllll}\n  & X & Flower & Resistance & Age & Height & Leaf\\_length & Leaf\\_width\\\\\n  & <chr> & <chr> & <chr> & <int> & <dbl> & <dbl> & <dbl>\\\\\n\\hline\n\t1 & サンプル1 & Yellow & Normal      &  1 & 65.78827 & 7.834566 & 1.2310844\\\\\n\t2 & サンプル2 & Purple & Weak        &  1 & 26.70546 & 4.654080 & 0.6596468\\\\\n\t3 & サンプル3 & Blue   & Very strong & 18 & 31.67394 & 6.657642 & 0.5777713\\\\\n\t4 & サンプル4 & Blue   & Very strong &  2 & 41.59529 & 4.530526 & 1.0155126\\\\\n\t5 & サンプル5 & Blue   & Very strong &  4 & 40.18388 & 6.621776 & 0.5938072\\\\\n\t6 & サンプル6 & Blue   & Very strong &  4 & 28.85123 & 6.452588 & 0.3979530\\\\\n\\end{tabular}\n",
            "text/plain": [
              "  X         Flower Resistance  Age Height   Leaf_length Leaf_width\n",
              "1 サンプル1 Yellow Normal       1  65.78827 7.834566    1.2310844 \n",
              "2 サンプル2 Purple Weak         1  26.70546 4.654080    0.6596468 \n",
              "3 サンプル3 Blue   Very strong 18  31.67394 6.657642    0.5777713 \n",
              "4 サンプル4 Blue   Very strong  2  41.59529 4.530526    1.0155126 \n",
              "5 サンプル5 Blue   Very strong  4  40.18388 6.621776    0.5938072 \n",
              "6 サンプル6 Blue   Very strong  4  28.85123 6.452588    0.3979530 "
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "最初に扱ったデータの場合、\n",
        "\n",
        "植物の葉身長`Leaf_length`と草丈`Height`の関係性であったり、\n",
        "\n",
        "花の色`Flower`と抵抗性`Resistance`の関係性などを記述する方法になります。"
      ],
      "metadata": {
        "id": "B3WZcO87vGxA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 散布図\n",
        "\n",
        "1次元のデータの時と同じく、まずは視覚的に表現して捉えることが一番重要です。\n",
        "\n",
        "まず、一組のデータ$(x_i, y_i)$が得られ、両方とも量的なデータである場合(草丈と葉身長、等)、\n",
        "\n",
        "縦軸に$y$、横軸に$x$をとり、各観察値をプロットすることで$x$と$y$の関係を把握することが出来ます。\n",
        "\n",
        "この図は**散布図**(Scatter plot)と呼ばれ、2次元データを手に入れたときに最初に描くことが多いグラフになります。\n",
        "\n",
        "Rでは`plot`関数で散布図を描くことが出来ます。\n",
        "\n",
        "今回は先ほどのデータ`df`の草丈`Height`と葉身長`Leaf_length`の関係性を確認してみましょう。\n",
        "\n",
        "`plot(Heightの列のデータ, Leaf_lengthの列のデータ)`"
      ],
      "metadata": {
        "id": "xiyQOzXLtpHh"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# データフレームdfのHeightとLeaf_lengthの散布図を描く\n",
        "plot(df$Height, df$Leaf_length)"
      ],
      "metadata": {
        "id": "DH5ovt7E7sgJ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "d4e7c25c-7084-49e4-ef6e-8d433b8ce781"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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yqOrrRuqbOpICRAQRfXJR4F542xyS3WdjMOT8hyjqTKxEIDM5wpPpwuN9uymTqc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          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "散布図では、各ドットが各個体の観察値を示しています。\n",
        "\n",
        "散布図を描いてみると、草丈が高い個体は葉身長も長い傾向にあることが分かります。\n",
        "\n",
        "(葉身長が長い個体は草丈が高い傾向にある、とも言えます。)\n",
        "\n",
        "この様な、2変数の間に関係性があることを**相関**があると言います。\n",
        "\n",
        "特に今回の様に変数$x$が大きいほど変数$y$が大きくなる傾向にある場合、**正の相関**があると言います。\n",
        "\n",
        "逆に、変数$x$が大きいほど変数$y$が小さくなる傾向にある場合、**負の相関**があると言います。\n",
        "\n",
        "また、変数$x$の大小と変数$y$の大小の間に関係がない場合、**無相関**と言います。\n",
        "\n",
        "例えば草丈`Height`と年齢`Age`の散布図を描いてみると、これら2つの変数は無相関であることが分かります。"
      ],
      "metadata": {
        "id": "-3loH5rT9hDX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# データフレームdfのHeightとAgeの散布図を描く\n",
        "plot(df$Height, df$Age)"
      ],
      "metadata": {
        "id": "n4b2FRBg-ylg",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "07cfe672-2c55-4961-f22b-6ef88120e60b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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ZuPvOfZOOLyvuecT5tbEKqX+y/+SLko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\nIIAgARD4P3Y7TvWUUbh0AAAAAElFTkSuQmCC"
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "また、草丈(Height)と葉身幅(Leaf_width)についても散布図を描いてみると、葉身長の時と同じ様に正の相関があることが分かります。"
      ],
      "metadata": {
        "id": "Ph5HESiccXg0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# データフレームdfのHeightとLeaf_widthの散布図を描く\n",
        "plot(df$Height, df$Leaf_width)"
      ],
      "metadata": {
        "id": "ZPqHfWW9ck3T",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "e63c4d6b-674c-4fd1-9e6b-3a3ddd6ced57"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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lhWmKlMLp/uaISImeXe66TPi8f5NY5R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\nG+I+0qk5v+UP0s2hIYZyHYQZw8V9pI0NTRVeT61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          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 相関係数\n",
        "\n",
        "散布図を描くことで、相関がありそうかを視覚的に捉えることが出来ました。\n",
        "\n",
        "次にこの相関の強さを数値として表しことにします。\n",
        "\n",
        "相関の強さを表す指標として**相関係数**(correlation coefficient)があります。\n",
        "\n",
        "相関係数には多くの定義がありますが、ここでは最も有名な**ピアソンの積率相関係数**を扱います。\n",
        "\n",
        "相関係数と言うときには基本的にはこれを指すことが多いです。\n",
        "\n",
        "2つの変数$x, y$のデータが$(x_1, y_1), (x_2, y_2), \\cdots, (x_n, y_n)$で与えられたとき、変数$x$と変数$y$の間の相関係数$r_{xy}$は\n",
        "\n",
        "$r_{xy}=\\dfrac{\\sum (x_i-\\bar{x})(y_i-\\bar{y})/n}{\\sqrt{\\sum (x_i-\\bar{x})^2/n}\\sqrt{\\sum (y_i-\\bar{y})^2/n}}=\\dfrac{\\sum (x_i-\\bar{x})(y_i-\\bar{y})}{\\sqrt{\\sum (x_i-\\bar{x})^2}\\sqrt{\\sum (y_i-\\bar{y})^2}}$\n",
        "\n",
        "で定義されます。\n",
        "\n",
        "分母の、$\\sqrt{\\sum (x_i-\\bar{x})^2/n}$, $\\sqrt{\\sum (y_i-\\bar{y})^2/n}$は、$x, y$の標準偏差$s_x, s_y$を表しており、\n",
        "\n",
        "分子の、$C_{xy}=\\sum (x_i-\\bar{x})(y_i-\\bar{y})/n$は偏差の積の平均で、**共分散**と呼びます。\n",
        "\n",
        "まずはこの共分散から見ていきましょう。"
      ],
      "metadata": {
        "id": "dSJHLE_uGC-2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 各変数の平均値より大きいか小さいかで色分けした散布図を描く\n",
        "tmp_df <- df[(df$Height >= mean(df$Height)) & (df$Leaf_length >= mean(df$Leaf_length)),]\n",
        "plot(tmp_df$Height, tmp_df$Leaf_length, xlim=range(df$Height), ylim=range(df$Leaf_length), col=\"red\")\n",
        "par(new=T)\n",
        "tmp_df <- df[(df$Height < mean(df$Height)) & (df$Leaf_length >= mean(df$Leaf_length)),]\n",
        "plot(tmp_df$Height, tmp_df$Leaf_length, xlim=range(df$Height), ylim=range(df$Leaf_length), col=\"blue\")\n",
        "par(new=T)\n",
        "tmp_df <- df[(df$Height >= mean(df$Height)) & (df$Leaf_length < mean(df$Leaf_length)),]\n",
        "plot(tmp_df$Height, tmp_df$Leaf_length, xlim=range(df$Height), ylim=range(df$Leaf_length), col=\"blue\")\n",
        "par(new=T)\n",
        "tmp_df <- df[(df$Height < mean(df$Height)) & (df$Leaf_length < mean(df$Leaf_length)),]\n",
        "plot(tmp_df$Height, tmp_df$Leaf_length, xlim=range(df$Height), ylim=range(df$Leaf_length), col=\"red\")\n",
        "abline(v=mean(df$Height))\n",
        "abline(h=mean(df$Leaf_length))\n",
        "text(mean(df$Height), 3, 'mean(Height)')\n",
        "text(20, mean(df$Leaf_length), 'mean(Leaf_length)')"
      ],
      "metadata": {
        "id": "vRp887B0M4g9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "accb579d-7dfd-4c1b-e437-1ff20faef039"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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Q791UFERCSFHDpEgwbY2yduz5ePihU5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Nk9zcpPfvVR2oIDt27Ji6urqqU+Q5Pj7S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\nbdu21XctBkyhUGRlZaWnp+u7EAN28+bNSpUqDRgw4KefftJ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            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "上のグラフは、草丈と葉身長の散布図を平均値より大きいか小さいかで色分けしたものになります。\n",
        "\n",
        "赤色の部分では、偏差の積$(x_i-\\bar{x})(y_i-\\bar{y}) > 0$で正となり、\n",
        "\n",
        "青色の部分では、偏差の積$(x_i-\\bar{x})(y_i-\\bar{y}) < 0$で負となります。\n",
        "\n",
        "つまり、共分散は赤色にくる観測値が増えるほど+に寄り、青色に来る観測値が増えるほど-に寄ることになります。\n",
        "\n",
        "どちらの領域にもまんべんなくデータが分布していれば、共分散は(結果的に相関係数も)0に近づきます。\n",
        "\n",
        "Rでは`cov`関数で共分散が計算できるので、\n",
        "\n",
        "* 草丈(Height)と葉身長(Leaf_length)\n",
        "* 草丈(Height)と葉身幅(Leaf_width)\n",
        "* 草丈(Height)と年齢(Age)\n",
        "\n",
        "それぞれの共分散を求めてみましょう。\n",
        "\n",
        "`cov(Height列のデータ, Leaf_length列のデータ)`"
      ],
      "metadata": {
        "id": "exLGXyeyUPsJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 各データの組み合わせごとに共分散を求める\n",
        "print(\"Height & Leaf length\")\n",
        "cov(df$Height, df$Leaf_length)\n",
        "print(\"Height & Leaf width\")\n",
        "cov(df$Height, df$Leaf_width)\n",
        "print(\"Height & Age\")\n",
        "cov(df$Height, df$Age)"
      ],
      "metadata": {
        "id": "4npj5Us9bU26",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 125
        },
        "outputId": "abb5af9f-5268-4f73-9edc-62f45d36d15b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1] \"Height & Leaf length\"\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "25.9178840692691"
            ],
            "text/markdown": "25.9178840692691",
            "text/latex": "25.9178840692691",
            "text/plain": [
              "[1] 25.91788"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1] \"Height & Leaf width\"\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "3.0242319891379"
            ],
            "text/markdown": "3.0242319891379",
            "text/latex": "3.0242319891379",
            "text/plain": [
              "[1] 3.024232"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1] \"Height & Age\"\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "-4.55270087700879"
            ],
            "text/markdown": "-4.55270087700879",
            "text/latex": "-4.55270087700879",
            "text/plain": [
              "[1] -4.552701"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "`cov`関数を使用すると共分散が求まりますが、この共分散の値だけでは、相関の強さがどの程度か、ということはよくわかりません。\n",
        "\n",
        "実際に草丈(Height)と葉身長(Leaf_length)、葉身幅(Leaf_width)のプロットを見てみると、むしろ共分散の小さい葉身幅の方が相関が強そうに見えます。"
      ],
      "metadata": {
        "id": "MJHggAmmeamG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Heightとleaf_length, HeightとLeaf_widthの散布図を並べて描く\n",
        "par(pin = c(2.5,2.5))\n",
        "par(mfrow=c(1, 2)) # 2つ並べて描く\n",
        "plot(df$Height, df$Leaf_length)\n",
        "plot(df$Height, df$Leaf_width)"
      ],
      "metadata": {
        "id": "NpJ5S12NeubO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "8f726eb2-bca3-4b57-dd5e-7893e32d21f4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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gM/rh86bpdWHFwOEFKukzg53M634Qlm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\nkptadJgzOVaWWRvikKLzhZtotltj2pgHZCb51b9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g02BeJ42ry24nCDnsQoRCWlQkFe+wiJ6+0soh8L7WPg0w/lNyEG9RvdN8VSLPhdbE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"
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "分散と標準偏差の時と同じ様に、データの単位やスケール等によって共分散の値は大きく変わってしまうためです。\n",
        "\n",
        "そこで、標準偏差を利用して、測定単位等の影響を受けない相関の指標にしたものが**相関係数**になります。\n",
        "\n",
        "相関係数は先ほども示した通り、$r_{xy}=\\dfrac{C_{xy}}{s_xs_y}$ で定義されます。\n",
        "\n",
        "共分散$C_{xy}$を標準偏差$s_x, s_y$の積で割ることで、測定単位の影響が無くなります。\n",
        "\n",
        "Rでは`cor`関数によって相関係数を計算できます。\n",
        "\n",
        "* 草丈(Height)と葉身長(Leaf_length)\n",
        "* 草丈(Height)と葉身幅(Leaf_width)\n",
        "* 草丈(Height)と年齢(Age)\n",
        "\n",
        "それぞれの相関係数を求めてみましょう。\n",
        "\n",
        "`cor(Height列のデータ, Leaf_length列のデータ)`"
      ],
      "metadata": {
        "id": "ExAqMfvMbnDF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 各変数間の相関係数を求める\n",
        "print(\"Height & Leaf length\")\n",
        "cor(df$Height, df$Leaf_length)\n",
        "print(\"Height & Leaf width\")\n",
        "cor(df$Height, df$Leaf_width)\n",
        "print(\"Height & Age\")\n",
        "cor(df$Height, df$Age)"
      ],
      "metadata": {
        "id": "Jt-XjFkzbmJO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 125
        },
        "outputId": "ea43c98e-b61a-4c05-a30a-6370e4be50bb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1] \"Height & Leaf length\"\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "0.76630905110646"
            ],
            "text/markdown": "0.76630905110646",
            "text/latex": "0.76630905110646",
            "text/plain": [
              "[1] 0.7663091"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1] \"Height & Leaf width\"\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "0.798735801134128"
            ],
            "text/markdown": "0.798735801134128",
            "text/latex": "0.798735801134128",
            "text/plain": [
              "[1] 0.7987358"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1] \"Height & Age\"\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "-0.0391864471450311"
            ],
            "text/markdown": "-0.0391864471450311",
            "text/latex": "-0.0391864471450311",
            "text/plain": [
              "[1] -0.03918645"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "相関係数は$-1\\leqq r_{xy}\\leqq1$の値の範囲をとり、1に近いほど相関が強く、-1に近いほど負の相関が強いことになります。\n",
        "\n",
        "そして0になると無相関です。\n",
        "\n",
        "今回の結果からは、草丈と葉身長・葉身幅は同じ程度に相関が強く、草丈と年齢は無相関だということが分かります。"
      ],
      "metadata": {
        "id": "taAM4rxHiqww"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "注意点として、よく統計の教科書では相関係数0.7以上だと\"強い相関\"等の基準が決められていたりします。\n",
        "\n",
        "しかし、相関係数はデータサイズや分布等によって大きく変化するため、その様な基準は参考程度にしましょう。\n",
        "\n",
        "また、線形的な関係性以外を捉えにくい指標でもあるので、散布図を確認するのが最重要です。\n",
        "\n",
        "下のサンプルデータで相関係数の計算と散布図の描写を実施し、役に立たない時の例を見てみましょう。"
      ],
      "metadata": {
        "id": "bUD1sPPin0-T"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 相関が役に立たない例1\n",
        "A <- seq(1,20)\n",
        "B <- c(10,9,8,7,6,5,4,3,2,1,1,2,3,4,5,6,7,8,9,10)\n",
        "plot(A, B)\n",
        "cor(A, B)"
      ],
      "metadata": {
        "id": "Xeu0pMBullEi",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 454
        },
        "outputId": "fcd93ba3-9251-4d15-ae8c-0aed3a6bad03"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "0"
            ],
            "text/markdown": "0",
            "text/latex": "0",
            "text/plain": [
              "[1] 0"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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8c0GjL6tPSclR4HxnVIZx6/I7RMz3jL\n9iSp4q2MGaFlx4/OtD1J7QINqW/rIsc5uOOW6u3SBoM8DoznkDaZyG8BPx1ld5DUMaq/u640\nm+wO4iHQkJpMdJwvzd3h/ahme33wq9/eVuOcOA5pbn5kM/VYq3OkkGPujGzy51qdw0ugITW8\n1nFK0uaF99fn7vXBLb2PrdHB7Iz2HL6b1S6yufcoq3OkkKPui2zazbI6h5dAQ+rV5SvHOXFi\naFvSvbvHgfH8rd3y9E/dzYiz7Q6SOs4e6a6fpi+3O4iHQEOab475W/mqtjO+Klv6E/OQx4Hx\nHFLlYZeG13UN5lieJGXMafBueL30sErLk9Qu2Je/H2loGhzR0WRkmLQrqzyOi+eQnH/kDl1Z\n8vFjrc/1+jeAUNU5rR/7uGTl0NzXbU9Su4B/IPvZ1P4dG+e0OHbcKs/D4jokZ3lPY0zTyWW2\n50gdZZObVl/ynvH7jR1vEYrO9iVFFbZnSC0VRUu2257BEyEBAoQECBASIEBIgAAhAQKEBAgQ\nEiBASIAAIQEChAQIEBIgQEiAACEBAoQECBASIEBIgAAhAQKEBAgQEiBASICAJKSSVYu/kkyz\nByEhwcQW0q6Z0/7hOK8daEzjGcqpCAkJJqaQth5qjLlke+v8wefmptf/fmpHSEgwMYU0wfS7\na1T6L9tsdpylmecLpyIkJJiYQjq6c4XjFKb9X2h/RhfhVISEBBNTSC1GVN8sN4+F9uP2/mta\nYkFISDAxhRT+WlRkwn8rQ6HyRXFCQoKJKSRT6BAS4BASIBFbSL0mT5481gypvp3ci5CQwmIL\n6XuEUxESEkxMIT3+PcKpCAkJhjetAgKEBAgQEiBASIAAIQEChAQIEBIgQEiAACEBAoQECBAS\nIEBIgAAhAQKEBAgQEiBASIAAIQEChAQIEBIgQEiAACH544M3PrM9QiL57I0PbI8QI0Lyw0Pt\njDGHzbc9RqJ4/rDqy9XuIdtjxISQfHB13tSNpesmZkr/8rXkNT1z4rrSjVPzJtkeJBaEpLc6\n/cXwelfTbZYnSQjbmtwVXl/IWG15klgQkt7Vvdy1ojVfkupgeusKd9PraruDxISQ9IaMiWz6\nXWt1jgTxm36RzeghVueIDSHpDR0R2fS60eocCeLGyBdw55ILrc4RG0LSm9a5PLxuy33B8iQJ\n4YVc96lk+cHTLE8SC0LS29os/M1+2ZDDy2yPkgjKDh8Suk5VVzX73PYoMSAkH7yY1/fuZ27v\n1uYd24MkhjWtj779mbtPznvR9iCxICQ/bBjVvflxE3lvQx19NvG45t1HbbA9RkwICRAgJECA\nkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQICRAgJECAkAABQgIECAkQICRAgJAA\nAUICBAgJECAkQICQAAFCAgQICRAgJECAkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFC\nAgQICRAgJECAkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQICRAgJECAkAABQgIE\nCAkQsBPSjsJ3PT+e/CGVLbhtylNf2p4iGF8+NeW2BWW2p/CZnZA+MvM9P570IS07OO+EU/Kb\nzrY9RxBmNc0/5YS8zstsz+GvQEMasUeB+emIER4HJntIm5oO21H9VWlq5gu2J/Hfgsyp1V+N\ndgxrtsn2JL4KNCTzPR4HJntIw/tUhtdfHWV5kAAc9avwUtnnEsuD+CvQkH6V0eOv20PWmie2\nb9/7ozuLa0xL8pAOmO6ua81mu4P470Ozzt1Mb2t3EJ8F+xxpRY+0y0LPsPf1HOn9tO9+udoZ\n9TkSQFX6K+5mt1ludxL/LTe73c0r6VV2J/FXwC82lN/WoN3cWl5s+NfKGpOS/CtSyz+76/tm\no91B/Ldxz7/i7JZ2B/FZ4K/avd/PDNqc6q/a/Wygu17f2e4cQeh8vbsO/JndOXxm4eXvx/Ib\nTU7xkNbkXlNevczO/pPtSfz3p+zQl9/ySblrbE/iKxs/R/rPz02Kh+QsaH7geUOPyLrT9hxB\nuDPziKHnHdh8ge05/GXnB7IvTFjn+fGkD8kpfvjyEdOS+ycrNTZNGzHmoWLbU/iM99oBAoQE\nCBASIEBIgAAhAQKEBAgQEiBASIAAIQEChAQIEBIgQEiAACEBAoQECBASIEBIgAAhAQKEBAgQ\nEiBASIAAIQEChAQIEBIgQEiAACEBAoQECBASIEBIgAAhAQKEBAgQEiBASIAAIQEChAQIEBIg\nQEiAACEBAoQECBASIEBIgAAhAQKEBAgQEiBASIAAIQEChAQIEBIgQEiAACEBAoQECBASIEBI\ngAAhAQKEFKcqZxf0OOWK9bbH2L/1V5zSo2B2pe0xbCOk+PR1/0bD77quT87jtgfZn5k5fa67\na3ij/l/bHsQyQopPozttCi33ZK6xPYm31Zn3hJZNnUbbnsQyQopL27Pmu5v+w+0Osj/D+7vr\n/KztdgexjZDi0ktZ5e7mvh/YHWR/Dr/PXcuyFtodxDZCikvPNY1sZnawOsd+tZ8Z2TR5zuoc\n1hFSXHrbfOJuru5jd5D96TPJXT82q+0OYhshxaWqrmPD69bWd1ueZD/ubv15eB3btcryJJYR\nUnxamDX+E6f8tSOPK7E9ibeS4458rdz5ZFyqP0UipHi1sItpmZ1+YbHtOfan+ML07JamS6p3\nREhxq3Lt3IVbbQ9RF1sXzl2b8m9sICRAgZAAAUICBAgJECAkQICQAAFCAgQICRAgJECAkAAB\nQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQICRAgJECAkAABQgIECAkQICRAgJAAAUIC\nBAgJECAkQICQAAFCAgQICRAgJECAkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQI\nCRAgJECAkAABQgIECAkQICRAgJAAAUICBAgJELAWUvG/PT5ISHVStrnc/5OUby7z/ySJL9iQ\nVg/o2Pv+ivC20OteCKkOFvbKNjl93/D3JG/0zTHZvV729yTJINCQ3sgxeVnm5OLQnpBi9MeM\nX7y88aWLMuf4eZKnMi9+aePLv8h4zM+TJIVAQxqY9UxVybSsH+12CClWH+fdF15vabbNv5N8\n0eyW8Hpf3if+nSQ5BBpS+wtDty9nD6ggpFj9tktVeC1v+6h/J3mkrfskrKrLNP9OkhwCDSnr\nuvAy04zbR0hfDB1S41izM9pzpIqRF0Y2g6707yRX/k9kM3SkfydJDoGGdFDkv8vV5o7/DunL\nsZfWGGBKoz1Hqhh1QWQzcKJ/J5lwZmRTcKl/J0kOgYY0Lu3e8EupVRebK8Z63ctiQtqfezq5\nr36Wtprh30mmt3L/O1R0vNe/kySHQEP6ooM5NbypGmcMIcVka5Obw2thqx3+nWRHq8LwenPT\nrf6dJDkE+3Okz0dfEdnNO4SQYjM3a8icFU8Oyn3Rz5O8mDvoyRVzhmTN9fMkSSE+3yJESHWw\nYlAL0+rcNf6eZPW5rUyLQSv8PUkyIKREtjtpTpLwCAkQICRAgJAAAUICBAgJECAkQICQAAFC\nAgQICRAgJECAkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQICRAgJECAkAABQgIE\nCAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQICRAgJECAkAABQgIECAkQICRAgJAAAUICBAgJ\nECAkQICQAAFCAgQICRAgJECAkAABQgIECAkQICRAgJAAAUICBAgpma194uHFnleydPHDT6wN\napqkRkjJ64O+5oAuGQctqP2IBQdldDnAnPJBcDMlLUJKWsUH933PcXYUZi2s7YiFWVftcJz3\n+h68Pci5khMhJa1JXb8Or5cfWdsRR14eXr7qek0wEyUzQkpaR9zprkVmw74P2GDedzd31poa\n6oqQklbT59y1KuOVfR/wSkaVu3m2aTATJTNCSloHPeauxWblvg9YaSLPjf7YPoh5khshJa2C\nQe76aLNaLmZpsz+4mzMvCGaiZEZISeutrPCTpOX5N9V2xI35y0PLnVlvBTVT8iKk5PXnvB7j\nJg3MGFlZ2wGVIzMHXjOuR94TQU6VpAgpiX0w5dxTx7/qdcSr4089dwo/jxUgJECAkAABQgIE\nCAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQICRAgJECAkAABQgIECAkQICRAID5DWmGABLOi\n3g9z/0Ny3l4Z31r98vGEcP6htieom0fMDbZHqJuTTq/tIfF2/R/lAYQU79rPtD1B3dza0/YE\ndbMrit/PrRg2THhnhERIYoSUoghJi5BSFCFpEVKKIiQtQkpRhKRFSCmKkLQIKUURkhYhpShC\n0iKkFEVIWoSUog5JkL8J5bcn2Z6gbr5JX217hLq59FLhnRGS82G57Qnq5usttieoo422B6ij\n4mLhnRESIEBIgAAhAQKEBAgQEiBASIAAIQEChAQIEBIgQEiAACEBAoQECBASIEBIgAAhAQKE\nBAikeEiPRf72gRttD+Kl7Kr0Y93d9vEds9qOiNv/wa9m0Pi+rMUTOmR3Ouufoa3ugqZ4SHeZ\ngsKQV2wP4mHdMY0jj8/SY8zgmy/JOlj5f3YKfTtoXF/WbZ3MwGuHZuaukV7QFA9pcvz/QR07\nGhxXlOM+PqeZ26tvnzQT7E5Ui+8MGteXdYy5t/p2nhkgvaApHtJ4U2R7hP3ZNqHMiTw+ezQu\nCS2Htq6yOlEtvjNoXF/WK/qVVd9WNegovaApHtLF5vOKjz63PcV+uY/PbzL6hX81zMTtHy8S\nCSkBLmtJVi/pBU3xkM421zQ3puss23Psh/v43GDcP4htsnnJ6jQeIiElwGW9u/obPOUFTfGQ\n+prOt868uol50PYg3tzH5yozJvyrqeZpq9N4iIQU/5d1UXbvcukFTfGQXp67u/p2bU5+fP/N\n63tCujz8qzvMM1an8RAJKe4v6+ycY7ZpL2iKhxRxjlluewRP7uOzyFwc/tVvzEKbw3iJhBQR\nr5e16jpz+k5He0EJKeQXJi5/4lHDfXyWZvYN/6rAfGh1Gg/fDylOL2vVJWZsRWijvKCpHdKu\nB2aH197x+zpYWOTxeULeV9W3le3a253GgztonF/W8eaWyE54QVM7pMoDG71bvTxrfmh7Em+R\nkB42U6pvf2+utzuNB3fQ+L6s88z4PVvhBU3tkJzn0hqOuPactCarbA9Su0WFhYUZB1TffOFU\n9DFnXf/ztG5f2Z5pn74zaFxf1kPM2PD7lwqLlRc0xUNylpzRLLPdRXH8c3jn1sgbQENvFtg1\nsWPWgWO22R5p3747aDxf1j1jmn8rL2iqhwRIEBIgQEiAACEBAoQECBASIEBIgAAhAQKEBAgQ\nEiBASIAAIQEChAQIEBIgQEiAACEBAoQECBASIEBIgAAhAQKEBAgQEiBASIAAIQEChAQIEBIg\nQEiAACEBAoQECBASIEBIgAAhAQKEBAgQEiBASIlrgmn6te0ZEEFICau0ZbqZYXsIRBBSwppt\nRqf1tj0EIggpYfU1G/qYdbangIuQEtV75kTnEXOl7THgIqRENcE84uzMa1lqew6EEVKCKmnZ\nYIfj/K95wvYgCCOkBDXLXFh9+4o51fYgCCOkBHWyebSoqGhDm7SNtidBCCElpvVmj0m2R0EI\nISWmK83IOSGPZ7Qttz0LHEJKUCUtcra6u8HmWbujIIyQEtIsMzyyW2QGWp0ELkJKSCeZt/ds\nu2V8ZHMSuAgJECAkQICQAAFCAgQICRAgJECAkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQ\nAAFCAgQICRAgJECAkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQICRAgJECAkACB\n/werFoo97BHMgAAAAABJRU5ErkJggg=="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "AとBの間には明らかな関係性がありそうですが、相関係数で見てしまうと0になってしまいます。"
      ],
      "metadata": {
        "id": "wdwDZ_8JnZqJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 相関が役に立たない例2\n",
        "C <- seq(1,12)\n",
        "D <- c(4,3,2,1,8,7,6,5,12,11,10,9)\n",
        "plot(C, D)\n",
        "cor(C, D)"
      ],
      "metadata": {
        "id": "tXZftj_6m7Bi",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 454
        },
        "outputId": "fa051455-05f2-417a-aa47-b336d1911a06"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "0.79020979020979"
            ],
            "text/markdown": "0.79020979020979",
            "text/latex": "0.79020979020979",
            "text/plain": [
              "[1] 0.7902098"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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BAgJAjod0h/uOQzn7si/ZaEQqLJ9DOk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\n6SAmAAAAAElFTkSuQmCC"
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "こちらは逆に、4つずつデータを見ると負の相関にあるのに、データ全体で見た結果、強い正の相関として判断されてしまう例です。\n",
        "\n",
        "これらの例の様に、2変数の関係性は、相関係数という数字のみで判断するのではなく、散布図も必ず描いて確認する必要があります。"
      ],
      "metadata": {
        "id": "G3qG5M7AlkSl"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 因果関係\n",
        "\n",
        "しばしば勘違いする人がいるのが、ある2つのデータの相関係数が高い(=強い相関関係がある)というのは、因果関係があるという訳では**無い**です。\n",
        "\n",
        "* 強い相関であっても因果関係ではない例\n",
        "\n",
        "例えば草丈と葉身長は基本的に高い相関にあると思われますが、どちらかが原因で、もう片方に影響を与えている訳ではなく、単にデカく育った植物が全部デカい・長い・重いだけの話になります。\n",
        "\n",
        "* 因果関係にはあっても強い相関関係にはならない例\n",
        "\n",
        "肥料を与えると基本的に植物は大きく育ちますが、与えすぎると栄養過多となり枯れてしまう場合があります。この場合、肥料の量と植物の大きさは因果関係にはありますが、相関係数という面では直線的な関係で無いため、それほど高くならないはずです。"
      ],
      "metadata": {
        "id": "tdjmONtvply4"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 見かけ上の相関\n",
        "\n",
        "また、よく判断を誤らせる相関関係として**見かけ上の相関**というものがあります。\n",
        "\n",
        "例えば\"大学受験の成績\"と\"ピアノを習っていた時間\"に強い相関があり、「ピアノを習えば、成績が良くなる」と宣伝する人達がいたとします。\n",
        "\n",
        "しかし、実際には\"親の年収\"が\"大学受験の成績\"につながっており、年収が高い親はピアノを習わせる余裕がある家が多かっただけ、の可能性もあります。\n",
        "\n",
        "この時、\"大学受験の成績\"と\"ピアノを習っていた時間\"の間の見かけの相関にはあまり意味はありません。\n",
        "\n",
        "※この様な場合、年収の影響を省いた上で、ピアノ時間と成績の相関係数を求める様な、**偏相関係数**という指標もあります。\n",
        "\n"
      ],
      "metadata": {
        "id": "E9jz28oPu6yL"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 回帰\n",
        "\n",
        "散布図を描く際に、$x, y$の関係性を直線に当てはめて、回帰直線を描く場合があります。\n",
        "\n",
        "これは、$y$が$x$によって左右もしくは決定されている様な関係性だった場合、**回帰**という方法で$x, y$の関係性を見ている形になります。\n",
        "\n",
        "回帰分析についてはまた後半の講義で扱うので、その際に詳しく説明したいと思います。\n",
        "\n"
      ],
      "metadata": {
        "id": "DYZFPKikoMs9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# 散布図に回帰直線を描く例\n",
        "plot(df$Height,df$Leaf_length)\n",
        "lm.obj<-lm(df$Leaf_length~df$Height)\n",
        "abline(lm.obj,col=2)"
      ],
      "metadata": {
        "id": "_6s-_A9goM3-",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "3bbe4411-ca05-4fab-d4c3-0ef6c21df2ce"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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PC6FgAA6DBGRkZ6enqXL19uutXI69ev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\nACATBDsAAACZINgBAADIxP8A/iJOx3MSqqwAAAAASUVORK5CYII="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 分割表\n",
        "\n",
        "ここまでの説明は2つの変数が量的なデータの時に、データを説明する方法でした。\n",
        "\n",
        "では次に、2つの変数に質的なデータが含まれている場合を見ていきます。\n",
        "\n",
        "質的なデータの場合は散布図等のグラフは作成しづらいので、**分割表**(クロス集計表とも呼ぶ)という表を作成します。\n",
        "\n",
        "Rでは`table`関数でクロス集計表を作成可能です。\n",
        "\n",
        "例えば、花の色(Flower)と抵抗性(Resistance)から表を作成すると\n",
        "\n",
        "`table(Flowerの列データ, Resistanceの列データ)`"
      ],
      "metadata": {
        "id": "rjx990qeztqU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Flower列とResistance列の分割表\n",
        "table(df$Flower, df$Resistance)"
      ],
      "metadata": {
        "id": "kCQ9_Vc-5FSk",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 129
        },
        "outputId": "45486861-29f9-4f84-ff63-51436748d064"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "        \n",
              "         Normal Very strong Weak\n",
              "  Blue       11          27    0\n",
              "  Purple     13           0   42\n",
              "  Red        59           0    0\n",
              "  Yellow     48           0    0"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "こうして見ると、抵抗性の強い個体は全て青い花をしていて、弱い個体は全て紫色の花だとわかります。\n",
        "\n",
        "また、2つの変数のうち片方が量的データ、もう片方が質的データの場合には、量的データの方を適当な階級に分けて項目化することで、分割表を作成出来ます。\n",
        "\n",
        "デフォルトのRにはちょうど良い関数が無いので少しコードを書くことになりますが、\n",
        "\n",
        "例えば、花の色(Flower)と草丈(Height)から表を作成すると"
      ],
      "metadata": {
        "id": "eRePi3xr5EN8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Flowerと階級分けした草丈`Height`の分割表\n",
        "breaks <- c(0, 10, 20, 30, 40, 50, 60, 70, 80)  # 例：0-29, 30-39, 40-49, 50以上\n",
        "labels <- c(\"0-9\", \"10-19\", \"20-29\", \"30-39\", \"40-49\", \"50-59\", \"60-69\", \"70+\")\n",
        "df$Height_group <- cut(df$Height, breaks = breaks, labels = labels, right = FALSE)\n",
        "table(df$Flower, df$Height_group)"
      ],
      "metadata": {
        "id": "tZzVyxQH1qnz",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 129
        },
        "outputId": "d999309f-ffaa-4499-a771-a7a990814514"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "        \n",
              "         0-9 10-19 20-29 30-39 40-49 50-59 60-69 70+\n",
              "  Blue     0     2    13    19     4     0     0   0\n",
              "  Purple   0     2    26    25     2     0     0   0\n",
              "  Red      0     0     0     0     3    31    25   0\n",
              "  Yellow   0     0     0     0     4    12    28   4"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "この様に見ると、花の色と草丈に強い相関があることが分かります。\n",
        "\n",
        "2つの変数の中に質的なデータが含まれていても、分割表を作成することで変数の間に相関があるかどうか確認できました。\n",
        "\n",
        "この相関の強さを数値的に表す方法としては、**ファイ係数**と呼ばれるものがあります。\n",
        "\n",
        "ファイ係数は分割表における行の変数と列の変数の関連の強さを示す指標にはなりますが、使える状況が限られていたり、あまり用いられる指標ではありません。\n",
        "\n",
        "相関係数と散布図の時と同じ様に、質的データに関しても、ファイ係数の様な数値の大小ではなく、分割表を見てデータを捉える方が良いでしょう。\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "aKwXmcuD59hc"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 課題\n",
        "\n",
        "今回の課題は下の課題ページを実施し、Pandaの**テスト・クイズ**に記述してください。\n",
        "\n",
        "[課題のノートブックへのリンク](https://colab.research.google.com/github/slt666666/biostatistics_text_wed/blob/main/source/_static/colab_notebook/chapter3_homework.ipynb)"
      ],
      "metadata": {
        "id": "XNkYbmjfhYvY"
      }
    }
  ]
}