Lesson1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Импортируйте библиотеку Numpy и дайте ей псевдоним np. Создайте массив Numpy под названием a размером 5x2, то есть состоящий из 5 строк и 2 столбцов. Первый столбец должен содержать числа 1, 2, 3, 3, 1, а второй — числа 6, 8, 11, 10, 7. Будем считать, что каждый столбец — это признак, а строка — наблюдение. Затем найдите среднее значение по каждому признаку, используя метод mean массива Numpy. Результат запишите в массив mean_a, в нем должно быть 2 элемента."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([\n",
    "    [1, 6], \n",
    "    [2, 8], \n",
    "    [3, 11], \n",
    "    [3, 10], \n",
    "    [1, 7]\n",
    "])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  6],\n",
       "       [ 2,  8],\n",
       "       [ 3, 11],\n",
       "       [ 3, 10],\n",
       "       [ 1,  7]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2. , 8.4])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_a = np.mean(a, axis = 0)\n",
    "mean_a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Вычислите массив a_centered, отняв от значений массива а средние значения соответствующих признаков, содержащиеся в массиве mean_a. Вычисление должно производиться в одно действие. Получившийся массив должен иметь размер 5x2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1. , -2.4],\n",
       "       [ 0. , -0.4],\n",
       "       [ 1. ,  2.6],\n",
       "       [ 1. ,  1.6],\n",
       "       [-1. , -1.4]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_centered = np.subtract(\n",
    "    a,\n",
    "    np.append(\n",
    "        [mean_a], \n",
    "        [mean_a, mean_a, mean_a, mean_a], \n",
    "        axis = 0\n",
    "    )\n",
    ")\n",
    "a_centered"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. Найдите скалярное произведение столбцов массива a_centered. В результате должна получиться величина a_centered_sp. Затем поделите a_centered_sp на N-1, где N — число наблюдений."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_centered_sp = a_centered[0:, 0] @ a_centered[0:, 1]\n",
    "a_centered_sp / (a_centered[0:, 0].size - 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4. Число, которое мы получили в конце задания 3, является ковариацией двух признаков, содержащихся в массиве а. В задании 3 мы делили сумму произведений центрированных признаков на N-1, а не на N, поэтому полученная нами величина является несмещенной оценкой ковариации.\n",
    "\n",
    "В этом задании проверьте получившееся число, вычислив ковариацию еще одним способом — с помощью функции np.cov. В качестве аргумента m функция np.cov должна принимать транспонированный массив a. В получившейся ковариационной матрице (массив Numpy размером 2x2) искомое значение ковариации будет равно элементу в строке с индексом 0 и столбце с индексом 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1. , 2. ],\n",
       "       [2. , 4.3]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cov(a.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5. Импортируйте библиотеку Pandas и дайте ей псевдоним pd. Создайте датафрейм authors со столбцами author_id и author_name, в которых соответственно содержатся данные: [1, 2, 3] и ['Тургенев', 'Чехов', 'Островский']. Затем создайте датафрейм book cо столбцами author_id, book_title и price, в которых соответственно содержатся данные: [1, 1, 1, 2, 2, 3, 3], ['Отцы и дети', 'Рудин', 'Дворянское гнездо', 'Толстый и тонкий', 'Дама с собачкой', 'Гроза', 'Таланты и поклонники'], [450, 300, 350, 500, 450, 370, 290]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>author_id</th>\n",
       "      <th>author_name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>Тургенев</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>Чехов</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>Островский</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   author_id author_name\n",
       "0          1    Тургенев\n",
       "1          2       Чехов\n",
       "2          3  Островский"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "authors = pd.DataFrame(\n",
    "    {\n",
    "        'author_id': [1, 2, 3],\n",
    "        'author_name':['Тургенев', 'Чехов', 'Островский']\n",
    "    },\n",
    "    columns = ['author_id', 'author_name']\n",
    ")\n",
    "authors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>author_id</th>\n",
       "      <th>book_title</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>Отцы и дети</td>\n",
       "      <td>450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>Рудин</td>\n",
       "      <td>300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>Дворянское гнездо</td>\n",
       "      <td>350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>Толстый и тонкий</td>\n",
       "      <td>500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>Дама с собачкой</td>\n",
       "      <td>450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3</td>\n",
       "      <td>Гроза</td>\n",
       "      <td>370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3</td>\n",
       "      <td>Таланты и поклонники</td>\n",
       "      <td>290</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   author_id            book_title  price\n",
       "0          1           Отцы и дети    450\n",
       "1          1                 Рудин    300\n",
       "2          1     Дворянское гнездо    350\n",
       "3          2      Толстый и тонкий    500\n",
       "4          2       Дама с собачкой    450\n",
       "5          3                 Гроза    370\n",
       "6          3  Таланты и поклонники    290"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "books = pd.DataFrame(\n",
    "    {\n",
    "        'author_id': [1, 1, 1, 2, 2, 3, 3],\n",
    "        'book_title': ['Отцы и дети', 'Рудин', 'Дворянское гнездо', 'Толстый и тонкий', 'Дама с собачкой', 'Гроза', 'Таланты и поклонники'],\n",
    "        'price': [450, 300, 350, 500, 450, 370, 290]\n",
    "    },\n",
    "    columns = ['author_id', 'book_title', 'price']\n",
    ")\n",
    "books"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6. Получите датафрейм authors_price, соединив датафреймы authors и books по полю author_id."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>author_id</th>\n",
       "      <th>author_name</th>\n",
       "      <th>book_title</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>Тургенев</td>\n",
       "      <td>Отцы и дети</td>\n",
       "      <td>450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>Тургенев</td>\n",
       "      <td>Рудин</td>\n",
       "      <td>300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>Тургенев</td>\n",
       "      <td>Дворянское гнездо</td>\n",
       "      <td>350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>Чехов</td>\n",
       "      <td>Толстый и тонкий</td>\n",
       "      <td>500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>Чехов</td>\n",
       "      <td>Дама с собачкой</td>\n",
       "      <td>450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3</td>\n",
       "      <td>Островский</td>\n",
       "      <td>Гроза</td>\n",
       "      <td>370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3</td>\n",
       "      <td>Островский</td>\n",
       "      <td>Таланты и поклонники</td>\n",
       "      <td>290</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   author_id author_name            book_title  price\n",
       "0          1    Тургенев           Отцы и дети    450\n",
       "1          1    Тургенев                 Рудин    300\n",
       "2          1    Тургенев     Дворянское гнездо    350\n",
       "3          2       Чехов      Толстый и тонкий    500\n",
       "4          2       Чехов       Дама с собачкой    450\n",
       "5          3  Островский                 Гроза    370\n",
       "6          3  Островский  Таланты и поклонники    290"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "authors_price = pd.merge(authors, books, on = 'author_id', how = 'inner')\n",
    "authors_price"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "7. Создайте датафрейм top5, в котором содержатся строки из authors_price с пятью самыми дорогими книгами."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>author_id</th>\n",
       "      <th>author_name</th>\n",
       "      <th>book_title</th>\n",
       "      <th>price</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2</td>\n",
       "      <td>Чехов</td>\n",
       "      <td>Толстый и тонкий</td>\n",
       "      <td>500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>Тургенев</td>\n",
       "      <td>Отцы и дети</td>\n",
       "      <td>450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>Чехов</td>\n",
       "      <td>Дама с собачкой</td>\n",
       "      <td>450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>Островский</td>\n",
       "      <td>Гроза</td>\n",
       "      <td>370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>Тургенев</td>\n",
       "      <td>Дворянское гнездо</td>\n",
       "      <td>350</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   author_id author_name         book_title  price\n",
       "0          2       Чехов   Толстый и тонкий    500\n",
       "1          1    Тургенев        Отцы и дети    450\n",
       "2          2       Чехов    Дама с собачкой    450\n",
       "3          3  Островский              Гроза    370\n",
       "4          1    Тургенев  Дворянское гнездо    350"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top5 = authors_price.sort_values(by = ['price'], ascending=False).head(5)\n",
    "top5.reset_index(drop = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
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       "      <td>2</td>\n",
       "      <td>Чехов</td>\n",
       "      <td>Толстый и тонкий</td>\n",
       "      <td>500</td>\n",
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       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>Тургенев</td>\n",
       "      <td>Отцы и дети</td>\n",
       "      <td>450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>Чехов</td>\n",
       "      <td>Дама с собачкой</td>\n",
       "      <td>450</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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       "</div>"
      ],
      "text/plain": [
       "   author_id author_name        book_title  price\n",
       "3          2       Чехов  Толстый и тонкий    500\n",
       "0          1    Тургенев       Отцы и дети    450\n",
       "4          2       Чехов   Дама с собачкой    450"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top3 = authors_price.nlargest(3, 'price')\n",
    "top3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "8. Создайте датафрейм authors_stat на основе информации из authors_price. В датафрейме authors_stat должны быть четыре столбца: author_name, min_price, max_price и mean_price, в которых должны содержаться соответственно имя автора, минимальная, максимальная и средняя цена на книги этого автора."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"3\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>max</th>\n",
       "      <th>min</th>\n",
       "      <th>mean</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>author_name</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Островский</th>\n",
       "      <td>370</td>\n",
       "      <td>290</td>\n",
       "      <td>330.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Тургенев</th>\n",
       "      <td>450</td>\n",
       "      <td>300</td>\n",
       "      <td>366.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Чехов</th>\n",
       "      <td>500</td>\n",
       "      <td>450</td>\n",
       "      <td>475.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            price                 \n",
       "              max  min        mean\n",
       "author_name                       \n",
       "Островский    370  290  330.000000\n",
       "Тургенев      450  300  366.666667\n",
       "Чехов         500  450  475.000000"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "authors_stat = authors_price.groupby('author_name').agg({'price': ['max', 'min', 'mean']})\n",
    "authors_stat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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