{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9PP0UCeGztkS"
      },
      "source": [
        "# <a href=\"https://thetahat.ru/courses/ad\" target=\"_top\">Введение в анализ данных</a>\n",
        "\n",
        "## Что такое среднее и как с ним правильно работать."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-06T12:51:48.836506Z",
          "start_time": "2021-03-06T12:51:48.082486Z"
        },
        "id": "Dd2PKAtHztkU"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "from random import choices, shuffle\n",
        "import scipy.stats as sps\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "import seaborn as sns\n",
        "\n",
        "sns.set(style=\"whitegrid\", font_scale=1.3, palette=\"Set2\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kj68YNruztkV"
      },
      "source": [
        "### 1. Кошачий университет\n",
        "\n",
        "Пусть у нас есть 20 групп котиков-студентов.\n",
        "\n",
        "**Вопрос:** сколько котиков в среднем в группе?\n",
        "\n",
        "**Ответ деканата:** посчитать количество котиков в каждой группе и взять среднее арифметическое полученных чисел.\n",
        "\n",
        "Проведем эксперимент. Сгенерируем 20 групп, причем в каждой будет от 10 до 30 котиков."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-06T12:51:48.847433Z",
          "start_time": "2021-03-06T12:51:48.838315Z"
        },
        "id": "2PD1h3OvztkW",
        "outputId": "29ea0875-1055-4a50-82e0-3d5d4a529071"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([11, 26, 18, 17, 11, 13, 12, 27, 13, 26, 19, 19, 17, 26, 26, 10, 16,\n",
              "       29, 17, 19])"
            ]
          },
          "execution_count": 2,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "groups_count = 20\n",
        "\n",
        "groups_size = sps.randint(low=10, high=30).rvs(size=groups_count)\n",
        "groups_size"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YwXQvF9NztkW"
      },
      "source": [
        "Ответ получить очень просто:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-06T12:51:48.973743Z",
          "start_time": "2021-03-06T12:51:48.967741Z"
        },
        "id": "fc4w4zWqztkX",
        "outputId": "33945ab1-acaa-479d-c103-aa7d635ecedf"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "18.6"
            ]
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "groups_size.mean()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_uqqpaOoztkX"
      },
      "source": [
        "Теперь предположим, что мы хотим провести эксперимент согласно тому, как учат в анализе данных:\n",
        "* возьмем случайную выборку котиков,\n",
        "* спросим у них, сколько котиков в их группе,\n",
        "* усредним полученные ответы.\n",
        "\n",
        "*Замечание.* Следующие операции с точки зрения кода можно сделать более эффективно, однако приведенный код повышает эффектность изложения материала.\n",
        "\n",
        "Для начала давайте создадим список всех студентов-котиков, каждому из которых присвоим номер группы."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-06T12:51:50.057491Z",
          "start_time": "2021-03-06T12:51:50.051055Z"
        },
        "id": "lVVduBJMztkX"
      },
      "outputs": [],
      "source": [
        "students_group = []\n",
        "\n",
        "for i in range(groups_count):\n",
        "    students_group += [i] * groups_size[i]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ImpMS7TVztkX"
      },
      "source": [
        "Возьмем 30 случайных котиков, спросим их и усредним ответы"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-06T12:51:50.779224Z",
          "start_time": "2021-03-06T12:51:50.772840Z"
        },
        "id": "O2Zk3brsztkX",
        "outputId": "7dd38722-8587-421f-c095-bf4c043eedaf"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "20.7"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "random_indexes = np.array(choices(students_group, k=30))\n",
        "groups_size[random_indexes].mean()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8yIf9ovqztkY"
      },
      "source": [
        "Хм, среднее получилось больше, чем ответ деканата. Может случайно так получилось? Ведь эксперимент случайный.\n",
        "\n",
        "Давайте повторим эксперимент 10 раз."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-06T12:51:54.372502Z",
          "start_time": "2021-03-06T12:51:54.350280Z"
        },
        "id": "UAE20YtxztkY",
        "outputId": "84d69de0-4e49-4102-c5b0-dbab7a04cff8"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "21.67\n",
            "21.0\n",
            "20.67\n",
            "19.37\n",
            "21.33\n",
            "19.3\n",
            "20.6\n",
            "22.43\n",
            "21.43\n",
            "21.3\n"
          ]
        }
      ],
      "source": [
        "for _ in range(10):\n",
        "    random_indexes = np.array(choices(students_group, k=30))\n",
        "    print(np.round(groups_size[random_indexes].mean(), 2))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GYVmZCJjztkY"
      },
      "source": [
        "Что-то все равно не так...\n",
        "\n",
        "А что будет если опросить вообще всех котиков? Навернято хоть тут должен получиться тот же ответ.\n",
        "\n",
        "Попробуем"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-06T12:51:56.705167Z",
          "start_time": "2021-03-06T12:51:56.699454Z"
        },
        "id": "H4OD43JsztkY",
        "outputId": "88d93521-7fdb-46da-a3f5-5674ebe3f3b3"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "20.50537634408602"
            ]
          },
          "execution_count": 7,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "groups_size[np.array(students_group)].mean()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zqpOkL6NztkY"
      },
      "source": [
        "Хм, ответ все равно получился не тот, что сказали нам в деканате... В чем же дело?\n",
        "\n",
        "Оказывается, дело в том, что выбирая случайного котика мы чаще попадаем на котика из большей группы. В самом деле, если\n",
        "* $n$ &mdash; общее количество котиков,\n",
        "* $n_j$ &mdash; количество котиков в группе $j$,\n",
        "\n",
        "то вероятность того, что случайно выбранный котик учится в группе $j$ равна $n_j/n$.\n",
        "\n",
        "Посчитаем теперь средний ответ котика. Пусть $\\xi$ &mdash; количество студентов в группе у случайно выбранного котика. Тогда\n",
        "$$\\mathsf{E} \\xi = \\frac1n \\sum_{котик\\ i} \\sum_{j} n_j \\cdot I\\{котик\\ i\\ из\\ группы\\ j\\} = \\frac1n \\sum_{j} n_j^2.$$\n",
        "\n",
        "Проверим ответ:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-06T12:52:01.875384Z",
          "start_time": "2021-03-06T12:52:01.866131Z"
        },
        "id": "y4R53gsjztkY",
        "outputId": "e655739d-6ab9-404b-afb7-cd3a43501098"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "20.50537634408602"
            ]
          },
          "execution_count": 8,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "(groups_size**2).sum() / groups_size.sum()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cxvekYIAztkY"
      },
      "source": [
        "Это среднее можно посчитать другим способом:\n",
        "$$\\mathsf{E} \\xi = \\sum_j n_j \\cdot \\mathsf{P}(случайный\\ котик\\ из\\ группы\\ j).$$\n",
        "\n",
        "Если рассматривать в качестве данных сами группы, а не котиков, то такой тип усреднения называется **взвешенным средним**. Общая формула взвешенного среднего чисел $x_1, ..., x_n$ с неотрицательными весами $w_1, ..., w_n$, для которых выполнено $\\sum_{i=1}^n w_i=1$, имеет вид $$\\sum_{i=1}^n w_i x_i.$$\n",
        "\n",
        "**Выводы:**\n",
        "* Деканат в качестве объектов данных рассматривает группы и берет по ним арифметическое среднее.\n",
        "* При проведении опроса объектами данных выступают котики, и арифметическое среднее по котикам отличается от результата деканата.\n",
        "* Деканат может взять взвешенное среднее и получить тот же ответ, что при проведении опроса.\n",
        "\n",
        "Этот пример &mdash; частный случай **парадокса инспекции**, который можно охарактеризовать как непосредственную зависимость наблюдения количества с самим наблюдаемым количеством."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q6P6UjrWztkY"
      },
      "source": [
        "---\n",
        "### 2. Средняя зарплата\n",
        "\n",
        "**Вопрос:** какова средняя зарплата населения?\n",
        "\n",
        "Важно отличать разные \"виды средних\":\n",
        "* обычное **среднее арифметическое**,\n",
        "* **медиана** &mdash; значение, слева и справа от которого одинаковое количество элементов,\n",
        "* **мода** &mdash; самое частое значение.\n",
        "\n",
        "Разницу между ними наглядно показывает иллюстрация из книги *Huff D. How To Lie With Statistics. — New York: W.W. Norton & Company, 1954*.\n",
        "\n",
        "![](загруженное1.jpg)\n",
        "\n",
        "Посмотрим на численном примере. Сгенерируем зарплату 10 000 человек в соответствии с некоторым распределением."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-06T12:52:18.375632Z",
          "start_time": "2021-03-06T12:52:18.367762Z"
        },
        "id": "dJ5P0OfUztkY"
      },
      "outputs": [],
      "source": [
        "count = 10000\n",
        "salary = np.abs(sps.t(df=2, scale=100).rvs(size=count))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XnEdlMObztkY"
      },
      "source": [
        "Посмотрим на *описательные статистики*. Как мы видим, среднее достаточно сильно отличается от медианы."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-06T12:52:19.545372Z",
          "start_time": "2021-03-06T12:52:19.518971Z"
        },
        "id": "Q8loND5IztkY",
        "outputId": "3103758e-91e3-46ea-e48c-851e766bf3d3"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "count    10000.000000\n",
              "mean       143.361444\n",
              "std        274.727742\n",
              "min          0.014972\n",
              "25%         35.979807\n",
              "50%         81.488075\n",
              "75%        162.664021\n",
              "max       8320.602082\n",
              "dtype: float64"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "pd.Series(salary).describe()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GvV7W_M5ztkZ"
      },
      "source": [
        "Посмотрим на гистограмму распределения. Однако, в данном случае в выборке есть **выбросы** &mdash; сильно выделяющиеся по сравнению с остальными наблюдения. Видимо, выбросами у нас являются миллиардеры. В анализе данных существуют специальные методы для работы с выбросами, однако не редко их просто выбрасывают из анализа.\n",
        "\n",
        "Выбросы сильно влияют на вид гистограммы. В данном случае видна широкая часть графика справа, в которой скорее какая-то пустота. Для наглядности стоит рисовать гистограмму в логарифмическом масштабе, на которой явно видно имеющиеся выбросы."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-06T12:52:25.290254Z",
          "start_time": "2021-03-06T12:52:24.284179Z"
        },
        "id": "YWtzrq0OztkZ",
        "outputId": "767cf223-ae4b-424e-98ad-4b8934cd5508"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1440x432 with 2 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.figure(figsize=(20, 6))\n",
        "\n",
        "plt.subplot(121)\n",
        "plt.hist(salary, bins=50)\n",
        "plt.xlabel(\"Зарплата\")\n",
        "plt.ylabel(\"Количество человек\")\n",
        "plt.title(\"Простая гистограмма\")\n",
        "\n",
        "plt.subplot(122)\n",
        "plt.hist(salary, bins=50, log=True)\n",
        "plt.xlabel(\"Зарплата\")\n",
        "plt.ylabel(\"Количество человек\")\n",
        "plt.title(\"Гистограмма в логарифмическом масштабе\")\n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5ykm7ylrztkZ"
      },
      "source": [
        "Попробуем убрать несколько выбросов и посчитать среднее по оставшимся элементам. Как видим, среднее достаточно сильно уменьшилось, хотя мы выкинули около 10 человек."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "ExecuteTime": {
          "end_time": "2021-03-06T12:52:34.238172Z",
          "start_time": "2021-03-06T12:52:34.219851Z"
        },
        "id": "bQ7_jWsWztkZ",
        "outputId": "686d2169-eb64-4ad9-f6a7-643739f609f7"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "137.01957408968383"
            ]
          },
          "execution_count": 12,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "salary[salary < 3300].mean()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yZ-XvYjVztkZ"
      },
      "source": [
        "Такой вид усреднения обычно называется **усеченное среднее**. Чаще усеченное среднее рассматривают для симметричных распределений, исключая одинаковое количество минимальных и максимальных значений."
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "hide_input": false,
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.11.6"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}