CriticalOlymp/statistics.ipynb

## statistics.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0faed474",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = [10,20,40,40,40,60,70,20,40,40,40,40,40,60,10,20,30,40,50,60,70,70,20,30,40,50,70,20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "59b167f0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x =  [10, 20, 40, 40, 40, 60, 70, 20, 40, 40, 40, 40, 40, 60, 10, 20, 30, 40, 50, 60, 70, 70, 20, 30, 40, 50, 70, 20]\n",
      "\n",
      "N =  28\n"
     ]
    }
   ],
   "source": [
    "print('x = ', x)\n",
    "print()\n",
    "print('N = ', len(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "83538a3e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10, 10, 20, 20, 20, 20, 20, 30, 30, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 50, 50, 60, 60, 60, 70, 70, 70, 70]\n"
     ]
    }
   ],
   "source": [
    "y = sorted(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a1327486",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "range = 60\n"
     ]
    }
   ],
   "source": [
    "rng = y[-1] - y[0]\n",
    "print('range =', rng)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2b148b60",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "range = 10\n"
     ]
    }
   ],
   "source": [
    "rng = x[-1] - x[0]\n",
    "print('range =', rng)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "dc76a1ea",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10, 20, 40, 40, 40, 60, 70, 20, 40, 40, 40, 40, 40, 60, 10, 20, 30, 40, 50, 60, 70, 70, 20, 30, 40, 50, 70, 20]\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "76b91b41",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mid value = 35.0\n"
     ]
    }
   ],
   "source": [
    "mid = (x[13]+x[14])/2\n",
    "print('mid value =', mid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "43d14ef5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import statistics as stat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "89a99aa3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40.0\n"
     ]
    }
   ],
   "source": [
    "print(stat.median(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0d20670d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10, 10, 20, 20, 20, 20, 20, 30, 30, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 50, 50, 60, 60, 60, 70, 70, 70, 70]\n"
     ]
    }
   ],
   "source": [
    "y = sorted(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b17d81e5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "median = 40.0\n"
     ]
    }
   ],
   "source": [
    "med = (y[13]+y[14])/2\n",
    "print('median =', med)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "79ab9033",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40.0\n"
     ]
    }
   ],
   "source": [
    "print(stat.median(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e38dba6d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean = 40.714285714285715\n"
     ]
    }
   ],
   "source": [
    "sx = sum(x)\n",
    "N = len(x)\n",
    "mean = sx/N\n",
    "print('mean =', mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "d2d1a9e7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40.714285714285715\n"
     ]
    }
   ],
   "source": [
    "print(stat.mean(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "eb76672d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean = 40.714285714285715\n"
     ]
    }
   ],
   "source": [
    "sy = sum(y)\n",
    "N = len(y)\n",
    "mean = sy/N\n",
    "print('mean =', mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "5e31f9b4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40.714285714285715\n"
     ]
    }
   ],
   "source": [
    "print(stat.mean(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d26ec9d8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10, 10, 20, 20, 20, 20, 20, 30, 30, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 50, 50, 60, 60, 60, 70, 70, 70, 70]\n"
     ]
    }
   ],
   "source": [
    "y = sorted(x)\n",
    "print(y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c46f4562",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mode = 40\n"
     ]
    }
   ],
   "source": [
    "print('mode =', stat.mode(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "da09d4e1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40\n"
     ]
    }
   ],
   "source": [
    "print(stat.mode(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4bc6cd38",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "cf6b69a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x, bins=7, range=[10, 80])\n",
    "plt.yticks(range(0,11,1))\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "5ef08f2c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(y, bins=7, range=[10, 80])\n",
    "plt.yticks(range(0,11,1))\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "59b63e93",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = [10,11,12,13,14,30,50,59,70,72,73]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "e80b3617",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x, bins=7, range=[10, 80])\n",
    "plt.yticks(range(0,7,1))\n",
    "plt.xticks(range(10,90,10))\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "6c9b1c6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x, bins=4, range=[10, 80])\n",
    "plt.yticks(range(0,7,1))\n",
    "plt.xticks([10,27,45,62])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "c1bb8669",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x, bins=2, range=[10, 80])\n",
    "plt.yticks(range(0,7,1))\n",
    "plt.xticks([10,45])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "fcb02e68",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x, bins=19, range=[10, 80])\n",
    "plt.yticks(range(0,7,1))\n",
    "plt.xticks(range(10,80,4))\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "b36c9f88",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N = 1000\n",
      "xmin = 20\n",
      "xmax = 60\n",
      "mean = 39.642\n"
     ]
    }
   ],
   "source": [
    "import statistics as stat\n",
    "import random as rnd\n",
    "\n",
    "N = 1000; a = 20; b = 60; x = []\n",
    "for i in range(N):\n",
    "    xi = rnd.randint(a, b)\n",
    "    x.append(xi)\n",
    "    \n",
    "print('N =', len(x))\n",
    "print('xmin =', min(x))\n",
    "print('xmax =', max(x))\n",
    "print('mean =', stat.mean(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "efc17d4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "plt.hist(x, bins=10)\n",
    "plt.xticks(np.arange(20,64,4))\n",
    "plt.xlim([20,60])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "12c7a99a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 1000; a = 20; b = 60; x = []\n",
    "for i in range(N):\n",
    "    xi = rnd.randint(a, b)\n",
    "    x.append(xi)\n",
    "    \n",
    "plt.hist(x, bins=10)\n",
    "plt.xticks(np.arange(20,64,4))\n",
    "plt.xlim([20,60])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "aae40ec9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 1000; a = 20; b = 60; x = []\n",
    "for i in range(N):\n",
    "    xi = rnd.randint(a, b)\n",
    "    x.append(xi)\n",
    "    \n",
    "plt.hist(x, bins=10)\n",
    "plt.xticks(np.arange(20,64,4))\n",
    "plt.xlim([20,60])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "929aed9b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 1000; a = 20; b = 60; x = []\n",
    "for i in range(N):\n",
    "    xi = rnd.randint(a, b)\n",
    "    x.append(xi)\n",
    "    \n",
    "plt.hist(x, bins=10)\n",
    "plt.xticks(np.arange(20,64,4))\n",
    "plt.xlim([20,60])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "68145ad6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 1000; a = 20; b = 60; x = []\n",
    "for i in range(N):\n",
    "    xi = rnd.randint(a, b)\n",
    "    x.append(xi)\n",
    "    \n",
    "plt.hist(x, bins=10)\n",
    "plt.xticks(np.arange(20,64,4))\n",
    "plt.xlim([20,60])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "5d640099",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10; a = 1; b = 10; x = []\n",
    "for i in range(N):\n",
    "    xi = rnd.randint(a, b)\n",
    "    x.append(xi)   \n",
    "plt.hist(x, bins=10)\n",
    "plt.xticks(np.arange(1,11,1))\n",
    "plt.xlim([1,10])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "374cae5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 100; a = 1; b = 10; x = []\n",
    "for i in range(N):\n",
    "    xi = rnd.randint(a, b)\n",
    "    x.append(xi)   \n",
    "plt.hist(x, bins=10)\n",
    "plt.xticks(np.arange(1,11,1))\n",
    "plt.xlim([1,10])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "0905c860",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 1000; a = 1; b = 10; x = []\n",
    "for i in range(N):\n",
    "    xi = rnd.randint(a, b)\n",
    "    x.append(xi)   \n",
    "plt.hist(x, bins=10)\n",
    "plt.xticks(np.arange(1,11,1))\n",
    "plt.xlim([1,10])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "fe8f4c12",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10000; a = 1; b = 10; x = []\n",
    "for i in range(N):\n",
    "    xi = rnd.randint(a, b)\n",
    "    x.append(xi)   \n",
    "plt.hist(x, bins=10)\n",
    "plt.xticks(np.arange(1,11,1))\n",
    "plt.xlim([1,10])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "25cd4fd9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 100000; a = 1; b = 10; x = []\n",
    "for i in range(N):\n",
    "    xi = rnd.randint(a, b)\n",
    "    x.append(xi)   \n",
    "plt.hist(x, bins=10)\n",
    "plt.xticks(np.arange(1,11,1))\n",
    "plt.xlim([1,10])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "701f0f8b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}