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{
"cells": [
{
"cell_type": "markdown",
"id": "0a11e40c",
"metadata": {},
"source": [
"### Задача 1"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "0ec1f0ef",
"metadata": {},
"outputs": [],
"source": [
"# Список\n",
"new_list = [100, 80, 75, 77, 89, 33, 45, 25, 65, 17, 30, 230, 24, 57, 55, 70, 75, 65, 84, 90, 150]\n",
"\n",
"def sum_list(list):\n",
" \"\"\"Суммирование всех элементов списка\"\"\"\n",
" n_sum = 0\n",
" for i in list:\n",
" n_sum += i\n",
" return n_sum"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "ad23c3f3",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Ответ: 47.34795213553139\n"
]
}
],
"source": [
"def get_dis(list):\n",
" \"\"\" Нахождение результата по формуле квадратичного отклонения \"\"\"\n",
" d_sum = 0\n",
" result = 0\n",
" # Нахождение среднего значения списка\n",
" list_aver = sum_list(list) / len(list)\n",
" for i in list:\n",
" d_sum += (i - list_aver)**2\n",
" # Результат - корень из полученного значения \n",
" return (d_sum / (len(list) - 1))**0.5\n",
" \n",
"answ = get_dis(new_list)\n",
"print(\"Ответ: \", answ)"
]
},
{
"cell_type": "markdown",
"id": "d332c51e",
"metadata": {},
"source": [
"### Задача 2"
]
},
{
"cell_type": "markdown",
"id": "41a15c9d",
"metadata": {},
"source": [
"Задача 2\n",
"Найдите число выбросов в выборке из задачи 1. Для определения выбросов используйте методику как при построении “усов” в boxplot, однако, как и в задаче 1, пользоваться можно только встроенными функциями и структурами данных.\n"
]
},
{
"cell_type": "code",
"execution_count": 65,
"id": "27ee281e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[17, 24, 25, 30, 33, 45, 55, 57, 65, 65, 70, 75, 75, 77, 80, 84, 89, 90, 100, 150, 230]\n"
]
}
],
"source": [
"# Для начала упорядочим список по возрастанию\n",
"def sort_list(list):\n",
" i = 0\n",
" a = 0\n",
" while i < (len(list) - 1):\n",
" if list[i+1] < list[i]:\n",
" a = list[i]\n",
" list[i] = list[i+1]\n",
" list[i+1] = a\n",
" i = 0\n",
" else:\n",
" i += 1\n",
" return list\n",
"sorted_list = sort_list(new_list)\n",
"print([elem for elem in sorted_list]) "
]
},
{
"cell_type": "code",
"execution_count": 79,
"id": "306e95a5",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(70, 45, 84)"
]
},
"execution_count": 79,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Вычислим медиану\n",
"list_m = sorted_list[len(sorted_list) // 2]\n",
"\n",
"# Вычислим нижний квантиль\n",
"def get_q1(list):\n",
" list_q1 = [elem for elem in list if elem < list[len(list) // 2]]\n",
" i = len(list_q1) // 2\n",
" result = list_q1[i] \n",
" return result\n",
"\n",
"# Вычислим верхний квантиль\n",
"def get_q3(list):\n",
" list_q3 = [elem for elem in list if elem > list[len(list) // 2]]\n",
" i = len(list_q3) // 2\n",
" result = list_q3[i-1]\n",
" return result\n",
"\n",
"list_q1 = get_q1(sorted_list)\n",
"list_q3 = get_q3(sorted_list)\n",
"list_m, list_q1, list_q3"
]
},
{
"cell_type": "code",
"execution_count": 90,
"id": "7d709283",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(58.5, -26.25, 155.25)"
]
},
"execution_count": 90,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Вычислим межквантильный диапазон\n",
"q_d = 1.5 * (list_q3 - list_q1)\n",
"\n",
"# Найдем внутренние границы значений\n",
"x1 = list_q1 - q_n\n",
"x2 = list_q3 + q_n\n",
"\n",
"q_d, x1, x2"
]
},
{
"cell_type": "code",
"execution_count": 91,
"id": "42faac62",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"([230], 1)"
]
},
"execution_count": 91,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Выведем элементы, которые не входят во внутренние границы и количество\n",
"main_res = [elem for elem in new_list if (elem <= x1) or (elem >= x2)]\n",
"main_res, len(main_res)"
]
},
{
"cell_type": "code",
"execution_count": 86,
"id": "6e5e8bad",
"metadata": {},
"outputs": [],
"source": [
"# Ответ не совпал, выполню проверку"
]
},
{
"cell_type": "code",
"execution_count": 87,
"id": "81063bf8",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 88,
"id": "978fb76a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(70.0, 45.0, 84.0)"
]
},
"execution_count": 88,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.quantile(sorted_list, 0.5), np.quantile(sorted_list, 0.25), np.quantile(sorted_list, 0.75)"
]
},
{
"cell_type": "code",
"execution_count": 89,
"id": "d20c8300",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.boxplot(sorted_list)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 92,
"id": "59c9ff7d",
"metadata": {},
"outputs": [],
"source": [
"# BoxPlot показывает два выброса, у меня получился один, значение 150 почему-то\n",
"# не захвачено, жду проверки :)"
]
},
{
"cell_type": "markdown",
"id": "03516c35",
"metadata": {},
"source": [
"### Задача 3"
]
},
{
"cell_type": "markdown",
"id": "4c549a57",
"metadata": {},
"source": [
"В университет на факультет A поступило 100 человек, на факультет B - 90 человек и на факультет C - 45 человек. Вероятность того, что студент с факультета A сдаст первую сессию, равна 0.6. Для студента с факультета B эта вероятность равна 0.7, а для студента с факультета C - 0.8. Случайным образом выбирается студент, сдавший первую сессию. Какое событие наиболее вероятно:\n",
"\n",
"студент учится на факультете A,\n",
"студент учится на факультете B,\n",
"студент учится на факультете C?"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "71f5cce9",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.425531914893617 0.3829787234042553 0.19148936170212766\n"
]
}
],
"source": [
"# Вероятности для каждого факультета\n",
"A1 = 0.6\n",
"A2 = 0.7\n",
"A3 = 0.8\n",
"\n",
"# количество учащихся в каждом факультете\n",
"A_n = 100\n",
"B_n = 90\n",
"C_n = 45\n",
"\n",
"# общее количество учащихся\n",
"N = 100 + 90 + 45\n",
"\n",
"# Вероятности для каждого факультета, что случайно выбранный студент именно с него\n",
"Xn_A = A_n / N\n",
"Xn_B = B_n / N\n",
"Xn_C = C_n / N\n",
"print(Xn_A, Xn_B, Xn_C)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "057c3c29",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"25.53 26.81 15.32\n"
]
}
],
"source": [
"# Так как наши вероятности зависимы, найдем искомую вероятность, перемножив их друг \n",
"# на друга\n",
"P_a = round((Xn_A * A1) * 100, 2)\n",
"P_b = round((Xn_B * A2) * 100, 2)\n",
"P_c = round((Xn_C * A3) * 100, 2)\n",
"print(P_a, P_b, P_c)"
]
},
{
"cell_type": "markdown",
"id": "345e6c71",
"metadata": {},
"source": [
"#### Наиболее вероятно событие №2"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.8.8"
}
},
"nbformat": 4,
"nbformat_minor": 5
}