Statistics using matplotlib

statistics.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "553f4ef1-dfd9-4ff7-9610-d19ffd1c5534",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import statistics as stat\n",
    "import random as rnd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "dfa61f58-8d3c-4285-a9fa-3bc18300eeb3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[80, 40, 30, 80, 70, 70, 10, 40, 40, 60, 60, 40, 60, 70, 60, 90, 60, 70, 10, 10, 80, 80, 40, 90, 40, 80, 70, 40, 30]\n"
     ]
    }
   ],
   "source": [
    "x = []\n",
    "N = 29\n",
    "for i in range(N):\n",
    "    xi = rnd.randint(1, 9) * 10\n",
    "    x.append(xi)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b857502-f505-45b4-98d8-5dd311796bf7",
   "metadata": {},
   "source": [
    "Exercise 1\n",
    "1. Middle Value is the middle of the raw data,Median is the middle of a sorted data\n",
    "2. They are same,because the sum of data and the data length is not change if we sorting the data\n",
    "3. we must sort the data so the value of range is not negative and we can see the actually range of data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "970e4a0e-096c-4797-ac68-de709a29f73c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[47, 14, 45, 54, 59, 70, 40, 76, 26, 11, 79, 36, 19, 64, 11, 75, 62, 49, 52, 70, 39, 27, 57, 70, 29, 55, 12, 70, 18, 25, 20, 18, 43, 30, 32, 80, 55, 41, 24, 28, 67, 30, 23, 56, 24, 69, 67, 75, 47, 20, 19, 76, 47, 25, 23, 55, 79, 78, 80, 12, 21, 20, 28, 62, 62, 34, 51, 47, 60, 14, 28, 69, 15, 43, 20, 40, 53, 59, 26, 18, 47, 10, 14, 78, 74, 70, 65, 18, 60, 13, 34, 25, 46, 20, 28, 11, 19, 57, 15, 10]\n"
     ]
    }
   ],
   "source": [
    "x = [\n",
    "    rnd.randint(10, 80)\n",
    "    for i in range(0,100)\n",
    "]\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "d2e3a090-856e-40b5-90ab-c2529cc7386e",
   "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=20)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "148c040c-bc47-4b11-be13-6785074f5d9b",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ee06SlJWVJUmqra2NOANTW1ur/v37t3lMv98vv9/fansw5NPeZrt/kS2CIZ+CxnN4IYPkjRxeyCCRozPxQgbJGzmsZ2iOYvmK+ruQBg8erM2bN0ds27Jli3r37i3pxxf0ZmVlqby8PHx7IBBQZWWlCgsLoz0OAADwoKifgbnxxht15pln6s4779To0aO1bt06LV26VEuXLpUk+Xw+TZ06VXPnztXxxx+v/Px8zZgxQzk5ORoxYkS0xwEAAB4U9QJz+umna+XKlSorK9OcOXOUn5+vhQsXaty4ceF9br75ZjU0NGjSpEmqq6vTWWedpdWrV4dfAAwAALA/US8wknTRRRfpoosu2uftPp9Pc+bM0Zw5czri7gEAgMfxWUgAAMAcCgwAADCHAgMAAMyhwAAAAHMoMAAAwBwKDAAAMIcCAwAAzKHAAAAAcygwAADAHAoMAAAwhwIDAADMocAAAABzKDAAAMAcCgwAADCHAgMAAMyhwAAAAHMoMAAAwBwKDAAAMIcCAwAAzKHAAAAAcygwAADAHAoMAAAwhwIDAADMocAAAABzKDAAAMAcCgwAADCHAgMAAMyhwAAAAHMoMAAAwBwKDAAAMIcCAwAAzKHAAAAAcygwAADAHAoMAAAwhwIDAADMocAAAABzKDAAAMAcCgwAADCHAgMAAMyhwAAAAHMoMAAAwBwKDAAAMIcCAwAAzKHAAAAAcygwAADAHAoMAAAwhwIDAADMocAAAABzKDAAAMAcCgwAADCHAgMAAMzp8AJz1113yefzaerUqeFtu3fvVklJiXr06KGjjjpKo0aNUm1tbUePAgAAPKJDC8z69ev18MMP6+STT47YfuONN+rFF1/UihUrtHbtWlVXV2vkyJEdOQoAAPCQDisw33//vcaNG6dHHnlE3bt3D2+vr6/Xo48+qgULFuj888/XgAEDtGzZMr377rt67733OmocAADgIR1WYEpKSjRs2DAVFRVFbN+4caOampoitvfp00d5eXmqqKjoqHEAAICHJHTEQZ9++mm9//77Wr9+favbampq1KVLF3Xr1i1ie2Zmpmpqato8XjAYVDAYDF8PBAKSJH+cU3y8i97gR5g/zkX8aZEXMkjeyOGFDBI5OhMvZJC8kcMLGSQpIRS9+aNeYL766ivdcMMNWrNmjZKSkqJyzHnz5mn27Nmttk8/NaSUlOao3Ecs3T4wFOsRDpsXMkjeyOGFDBI5OhMvZJC8kcN6hsbGkMZG6VhRLzAbN27Ujh07dNppp4W3NTc366233tIDDzygV155RXv27FFdXV3EWZja2lplZWW1ecyysjKVlpaGrwcCAeXm5mrupjjtTYyPdoQjxh/ndPvAkGZsiFMw5Iv1OIfECxkkb+TwQgaJHJ2JFzJI3sjhhQySlNAUvVeuRL3ADBkyRB9//HHEtgkTJqhPnz665ZZblJubq8TERJWXl2vUqFGSpM2bN2v79u0qLCxs85h+v19+v7/V9mDIp73Ndv8iWwRDPgWN5/BCBskbObyQQSJHZ+KFDJI3cljP0BzF8hX1AtO1a1f17ds3Yltqaqp69OgR3j5x4kSVlpYqIyNDaWlpmjJligoLC3XGGWdEexwAAOBBHfIi3gO57777FBcXp1GjRikYDKq4uFgPPvhgLEYBAAAGHZEC8+abb0ZcT0pK0uLFi7V48eIjcfcAAMBj+CwkAABgDgUGAACYQ4EBAADmUGAAAIA5FBgAAGAOBQYAAJhDgQEAAOZQYAAAgDkUGAAAYA4FBgAAmEOBAQAA5lBgAACAORQYAABgDgUGAACYQ4EBAADmUGAAAIA5FBgAAGAOBQYAAJhDgQEAAOZQYAAAgDkUGAAAYA4FBgAAmEOBAQAA5lBgAACAORQYAABgDgUGAACYQ4EBAADmUGAAAIA5FBgAAGAOBQYAAJhDgQEAAOZQYAAAgDkUGAAAYA4FBgAAmEOBAQAA5lBgAACAORQYAABgDgUGAACYQ4EBAADmUGAAAIA5FBgAAGAOBQYAAJhDgQEAAOZQYAAAgDkUGAAAYA4FBgAAmEOBAQAA5lBgAACAORQYAABgDgUGAACYQ4EBAADmUGAAAIA5US8w8+bN0+mnn66uXbuqZ8+eGjFihDZv3hyxz+7du1VSUqIePXroqKOO0qhRo1RbWxvtUQAAgEdFvcCsXbtWJSUleu+997RmzRo1NTVp6NChamhoCO9z44036sUXX9SKFSu0du1aVVdXa+TIkdEeBQAAeFRCtA+4evXqiOuPP/64evbsqY0bN+rss89WfX29Hn30US1fvlznn3++JGnZsmU64YQT9N577+mMM86I9kgAAMBjol5gfq6+vl6SlJGRIUnauHGjmpqaVFRUFN6nT58+ysvLU0VFRZsFJhgMKhgMhq8HAgFJkj/OKT7edeT4Hcof5yL+tMgLGSRv5PBCBokcnYkXMkjeyOGFDJKUEIre/D7nXIf93wiFQvrjH/+ouro6vf3225Kk5cuXa8KECRGFRJIGDRqk8847T3fffXer48yaNUuzZ89utX358uVKSUnpmOEBAEBUNTY2auzYsaqvr1daWtphHatDz8CUlJTok08+CZeXQ1VWVqbS0tLw9UAgoNzcXM3dFKe9ifGHO2bM+OOcbh8Y0owNcQqGfLEe55B4IYPkjRxeyCCRozPxQgbJGzm8kEGSEpqi99LbDiswkydP1ksvvaS33npLvXr1Cm/PysrSnj17VFdXp27duoW319bWKisrq81j+f1++f3+VtuDIZ/2Ntv9i2wRDPkUNJ7DCxkkb+TwQgaJHJ2JFzJI3shhPUNzFMtX1N+F5JzT5MmTtXLlSr3++uvKz8+PuH3AgAFKTExUeXl5eNvmzZu1fft2FRYWRnscAADgQVE/A1NSUqLly5fr+eefV9euXVVTUyNJSk9PV3JystLT0zVx4kSVlpYqIyNDaWlpmjJligoLC3kHEgAAaJeoF5iHHnpIknTuuedGbF+2bJn+/Oc/S5Luu+8+xcXFadSoUQoGgyouLtaDDz4Y7VEAAIBHRb3AtOdNTUlJSVq8eLEWL14c7bsHAAC/AHwWEgAAMIcCAwAAzKHAAAAAcygwAADAHAoMAAAwhwIDAADMocAAAABzKDAAAMAcCgwAADCHAgMAAMyhwAAAAHMoMAAAwBwKDAAAMIcCAwAAzKHAAAAAcygwAADAHAoMAAAwhwIDAADMocAAAABzKDAAAMAcCgwAADCHAgMAAMyhwAAAAHMoMAAAwBwKDAAAMIcCAwAAzKHAAAAAcygwAADAHAoMAAAwhwIDAADMocAAAABzKDAAAMAcCgwAADCHAgMAAMyhwAAAAHMoMAAAwBwKDAAAMIcCAwAAzKHAAAAAcygwAADAHAoMAAAwhwIDAADMocAAAABzKDAAAMAcCgwAADCHAgMAAMyhwAAAAHMoMAAAwBwKDAAAMIcCAwAAzKHAAAAAcygwAADAnJgWmMWLF+vYY49VUlKSCgoKtG7duliOAwAAjIhZgXnmmWdUWlqq2267Te+//75OOeUUFRcXa8eOHbEaCQAAGBGzArNgwQJdddVVmjBhgk488UQtWbJEKSkpeuyxx2I1EgAAMCIhFne6Z88ebdy4UWVlZeFtcXFxKioqUkVFRav9g8GggsFg+Hp9fb0kKaGpoeOH7UAJIafGxpASmuLUHPLFepxD4oUMkjdyeCGDRI7OxAsZJG/k8EIG6X8/t51zh38wFwNff/21k+TefffdiO033XSTGzRoUKv9b7vtNieJCxcuXLhw4eKByxdffHHYXSImZ2AOVllZmUpLS8PX6+rq1Lt3b23fvl3p6ekxnOzwBAIB5ebm6quvvlJaWlqsxzkkXsggeSOHFzJI5OhMvJBB8kYOL2SQfnwGJS8vTxkZGYd9rJgUmKOPPlrx8fGqra2N2F5bW6usrKxW+/v9fvn9/lbb09PTTf9FtkhLSzOfwwsZJG/k8EIGiRydiRcySN7I4YUM0o8vGznsY0RhjoPWpUsXDRgwQOXl5eFtoVBI5eXlKiwsjMVIAADAkJg9hVRaWqrx48dr4MCBGjRokBYuXKiGhgZNmDAhViMBAAAjYlZgLrvsMn377beaOXOmampq1L9/f61evVqZmZkH/Fq/36/bbrutzaeVLPFCDi9kkLyRwwsZJHJ0Jl7IIHkjhxcySNHN4XMuGu9lAgAAOHL4LCQAAGAOBQYAAJhDgQEAAOZQYAAAgDmdtsDMmzdPp59+urp27aqePXtqxIgR2rx5c8Q+u3fvVklJiXr06KGjjjpKo0aNavXL8WKtPTlaOOd04YUXyufzadWqVUd20P1oT4aamhpdccUVysrKUmpqqk477TQ999xzMZq4bQ899JBOPvnk8C+CKiws1MsvvyxJ2rlzp6ZMmaLf/e53Sk5OVl5enq6//vrw5251JvvL0aKiokLnn3++UlNTlZaWprPPPls//PBDjCY+sLvuuks+n09Tp04Nb7Owvn+urRwtOuv6/rm2MlhY37NmzZLP54u49OnTR5Kt9b2/HC0srO+vv/5al19+uXr06KHk5GT169dPGzZsCN/unNPMmTOVnZ2t5ORkFRUVaevWrQd1H522wKxdu1YlJSV67733tGbNGjU1NWno0KFqaPjfBzjeeOONevHFF7VixQqtXbtW1dXVGjlyZAynbq09OVosXLhQPl/n+5Cu9mT405/+pM2bN+uFF17Qxx9/rJEjR2r06NHatGlTDCeP1KtXL911113auHGjNmzYoPPPP1/Dhw/Xp59+qurqalVXV+uee+7RJ598oscff1yrV6/WxIkTYz12K/vLIf34ze2CCy7Q0KFDtW7dOq1fv16TJ0+Oym++7Ajr16/Xww8/rJNPPjliu4X1/VP7ytGis67vn9pXBgvrW5JOOukkffPNN+HL22+/LUmm1re07xySjfW9a9cuDR48WImJiXr55Zf12Wef6d5771X37t3D+8yfP1+LFi3SkiVLVFlZqdTUVBUXF2v37t3tv6PD/jSlI2THjh1Oklu7dq1zzrm6ujqXmJjoVqxYEd7n888/d5JcRUVFrMY8oJ/naLFp0yZ3zDHHuG+++cZJcitXrozNgO3QVobU1FT3xBNPROyXkZHhHnnkkSM93kHp3r27+/vf/97mbc8++6zr0qWLa2pqOsJTHbyf5igoKHDTp0+P8UTt891337njjz/erVmzxp1zzjnuhhtucM7ZW9/7ytHCwvreXwYL6/u2225zp5xySrv376zr+0A5LKzvW265xZ111ln7vD0UCrmsrCz3t7/9Lbytrq7O+f1+99RTT7X7fjpPZTuAllN9LR8AtXHjRjU1NamoqCi8T58+fZSXl6eKioqYzNgeP88hSY2NjRo7dqwWL17c5mdBdTZtZTjzzDP1zDPPaOfOnQqFQnr66ae1e/dunXvuuTGacv+am5v19NNPq6GhYZ8fX1FfX6+0tDQlJHTezzz9eY4dO3aosrJSPXv21JlnnqnMzEydc845Ef+C60xKSko0bNiwiHUs2Vvf+8oh2Vnf+8tgZX1v3bpVOTk5+vWvf61x48Zp+/bt+9y3M6/vfeWwsr5feOEFDRw4UJdeeql69uypU089VY888kj49qqqKtXU1EQ81tLT01VQUHBw6/uwatYR0tzc7IYNG+YGDx4c3vbkk0+6Ll26tNr39NNPdzfffPORHK/d2srhnHOTJk1yEydODF9XJ/0XmnP7zrBr1y43dOhQJ8klJCS4tLQ098orr8Royn376KOPXGpqqouPj3fp6enuX//6V5v7ffvtty4vL8/deuutR3jC9tlXjoqKCifJZWRkuMcee8y9//77burUqa5Lly5uy5YtMZ460lNPPeX69u3rfvjhB+eci/hXv6X1vb8cztlY3wfKYGF9//vf/3bPPvus+/DDD93q1atdYWGhy8vLc4FAoNW+nXl97y+HlfXt9/ud3+93ZWVl7v3333cPP/ywS0pKco8//rhzzrl33nnHSXLV1dURX3fppZe60aNHt/t+TBSYa665xvXu3dt99dVX4W2WvsG1aCvH888/74477jj33Xffhbd1xm9wLdrK4JxzkydPdoMGDXKvvfaa++CDD9ysWbNcenq6++ijj2I0aduCwaDbunWr27Bhg5s2bZo7+uij3aeffhqxT319vRs0aJC74IIL3J49e2I06f7tK0fLN4aysrKI/fv16+emTZsWo2lb2759u+vZs6f78MMPw9ssFpgD5bCwvg+UwTk76/undu3a5dLS0lo9RWxhff/UT3NYWd+JiYmusLAwYtuUKVPcGWec4Zz7BRWYkpIS16tXL/fll19GbC8vL3eS3K5duyK25+XluQULFhzBCdtnXzluuOEG5/P5XHx8fPgiycXFxblzzjknNsPuw74ybNu2zUlyn3zyScT2IUOGuKuvvvpIjnjQhgwZ4iZNmhS+HggEXGFhoRsyZEj4X6MWtOT48ssvnST3j3/8I+L20aNHu7Fjx8ZoutZWrlzpJLV63Leshddee83E+j5QjsmTJ3f69X2gDJbX98CBAyN+sFtd3y05rKzvvLy8iLOOzjn34IMPupycHOecc1988YWT5DZt2hSxz9lnn+2uv/76dt9P53vy7/9zzmnKlClauXKl3nzzTeXn50fcPmDAACUmJqq8vFyjRo2SJG3evFnbt2/f52saYuFAOaZNm6a//OUvEdv69eun++67TxdffPGRHHWfDpShsbFRklq9Cj4+Pl6hUOiIzXkoQqGQgsGgJCkQCKi4uFh+v18vvPCCkpKSYjxd+7XkOPbYY5WTk9Pqbe5btmzRhRdeGKPpWhsyZIg+/vjjiG0TJkxQnz59dMsttyg3N9fE+j5QjqOPPlpXX311xO2dbX0fKIPV9f3999/riy++0BVXXCHJ7vr+aQ4r63vw4MFtzti7d29JUn5+vrKyslReXq7+/ftL+vHvp7KyUtdee2377+jwelbHufbaa116erp788033TfffBO+NDY2hve55pprXF5ennv99dfdhg0bXGFhYavTVrHWnhw/p052ivlAGfbs2eOOO+4493//93+usrLSbdu2zd1zzz3O5/Pt8zUmsTBt2jS3du1aV1VV5T766CM3bdo05/P53Kuvvurq6+tdQUGB69evn9u2bVtEzr1798Z69Aj7y+Gcc/fdd59LS0tzK1ascFu3bnXTp093SUlJbtu2bTGefP9+/rSFhfXdlrbehfRTnW19t+WnGays77/+9a/uzTffdFVVVe6dd95xRUVF7uijj3Y7duwwtb73l8M5G+t73bp1LiEhwd1xxx1u69at7sknn3QpKSnun//8Z3ifu+66y3Xr1s09//zz7qOPPnLDhw93+fn5B3VmrNMWGEltXpYtWxbe54cffnDXXXed6969u0tJSXGXXHKJ++abb2I3dBvak6Otr+lM3+Dak2HLli1u5MiRrmfPni4lJcWdfPLJrd52GWtXXnml6927t+vSpYv71a9+5YYMGRL+of/GG2/sM2dVVVVsB/+Z/eVoMW/ePNerVy+XkpLiCgsL3X/+858YTdt+P//Bb2F9t8VrBcY5G+v7sssuc9nZ2a5Lly7umGOOcZdddln4h7ql9b2/HC0srO8XX3zR9e3b1/n9ftenTx+3dOnSiNtDoZCbMWOGy8zMdH6/3w0ZMsRt3rz5oO7D55xz7T9fAwAAEHtmfg8MAABACwoMAAAwhwIDAADMocAAAABzKDAAAMAcCgwAADCHAgMAAMyhwAAAAHMoMAAAwBwKDAAAMIcCAwAAzKHAAAAAc/4feICFMM+npz0AAAAASUVORK5CYII=",
      "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",
    "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": "markdown",
   "id": "c300e42c-d638-4c81-b398-1f256a6e84dd",
   "metadata": {},
   "source": [
    "n = b - a + 1\n",
    "  = 60 - 20 + 1\n",
    "  = 41  \n",
    "Average Value = N * 1/n * the width of the bins\n",
    "              = 1000 * 1/41 * 4\n",
    "              = 97,5609"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "eaa6548e-d018-4c7b-bb74-50cb3d8389cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 6000; a=1; b=6; dice = []\n",
    "for i in range(N):\n",
    "    xi = rnd.randint(a, b)\n",
    "    dice.append(xi)\n",
    "plt.hist(dice, bins=6)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ccf3e0ef-9b8a-43e7-9275-efdc1f3a7796",
   "metadata": {},
   "source": [
    "The value is 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "0674de5d-9a59-453c-b600-3140776c019a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu = 100\n",
    "si = 5\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,1)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"mu = 100 si = 5\")\n",
    "\n",
    "mu = 200\n",
    "si = 5\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,2)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"mu = 200 si = 5\")\n",
    "\n",
    "mu = 300\n",
    "si = 5\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,3)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"mu = 300 si = 5\")\n",
    "\n",
    "mu = 100\n",
    "si = 10\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,4)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"mu = 100 si = 10\")\n",
    "\n",
    "mu = 200\n",
    "si = 10\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,5)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"mu = 200 si = 10\")\n",
    "\n",
    "mu = 300\n",
    "si = 10\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,6)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"mu = 300 si = 10\")\n",
    "\n",
    "mu = 100\n",
    "si = 20\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,7)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"mu = 100 si = 20\")\n",
    "\n",
    "mu = 200\n",
    "si = 20\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,8)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"mu = 200 si = 20\")\n",
    "\n",
    "mu = 300\n",
    "si = 20\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,9)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"mu = 300 si = 20\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b02225db-e324-444e-96d8-1e4da7b74d18",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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