For Medium06_2

For Medium06.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([102, 435, 348, 270, 106,  71, 188,  20, 102, 121, 466, 214, 330,\n",
       "       458,  87, 372,  99, 359, 151, 130, 149, 308, 257, 343, 491, 413,\n",
       "       293, 385, 191, 443, 276, 160, 459, 313,  21, 252, 235, 344,  48,\n",
       "       474,  58, 169, 475, 187, 463, 270, 189, 445, 174, 445,  50, 363,\n",
       "        54, 243, 319, 130, 484, 306, 134,  20, 328, 166, 273, 387,  88,\n",
       "       315,  13, 241, 264, 345,  52, 385, 339,  91, 366, 443, 454, 427,\n",
       "       263, 430,  34, 205,  80, 419,  49, 359, 387,   1, 389,  53, 105,\n",
       "       259, 309, 476, 190, 401, 217,  43, 161, 201])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# construct a population pickups for our lab\n",
    "np.random.seed(42)\n",
    "pickups = np.random.randint(0,500 , size=100)\n",
    "pickups"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "252.7"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# population mean\n",
    "pickups.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "144.25342283634035"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# population standard deviation\n",
    "pickups.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([166, 201, 458, 190, 445,  87, 385, 427, 387, 166, 474,  49, 430,\n",
       "       205,  54, 343, 413, 389,  20,  58, 191,  87, 463,  88, 389,  52,\n",
       "       102,   1, 102,  20])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# draw a sample from population\n",
    "sample = np.random.choice(pickups, size=30)\n",
    "sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "228.06666666666666"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# our first sample mean\n",
    "sample_mean = sample.mean()\n",
    "sample_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "166.96890756052164"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# standard deiveation for this sample\n",
    "sample_std = np.std(sample, ddof=1)\n",
    "sample_std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30.48421235763086"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# estimated standard error for sapmle mann\n",
    "sample_std/(30 ** 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26.336951228264823"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# theorical standard error for sapmle mann\n",
    "pickups.std()/(30 ** 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# construct the simulated sampling distribution\n",
    "sample_props = []\n",
    "for _ in range(100000):\n",
    "    sample = np.random.choice(pickups, size=30)\n",
    "    sample_props.append(sample.mean())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the simulated mean of the sampling distribution\n",
    "simulated_mean = np.mean(sample_props)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# the simulated standard deviation of the sampling distribution\n",
    "simulated_std = np.std(sample_props)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1.7000e+01, 2.9400e+02, 3.0210e+03, 1.2917e+04, 2.8275e+04,\n",
       "        3.1747e+04, 1.7958e+04, 5.0680e+03, 6.6100e+02, 4.2000e+01]),\n",
       " array([136.76666667, 159.24666667, 181.72666667, 204.20666667,\n",
       "        226.68666667, 249.16666667, 271.64666667, 294.12666667,\n",
       "        316.60666667, 339.08666667, 361.56666667]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa5f0910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the simulated sampling distribution,\n",
    "# under the Central Limit Theorem,\n",
    "# it is expected normal\n",
    "plt.hist(sample_props)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(252.7, 252.74267033333336)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the theorical mean and simulated mean\n",
    "(pickups.mean(), simulated_mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(26.336951228264823, 26.327169537452452)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the theorical standard error and simulated standard error\n",
    "(pickups.std()/(30 ** 0.5), simulated_std)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
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