Central Limit Theorem - Part III.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Central Limit Theorem - Part III\n",
    "\n",
    "You saw how the **Central Limit Theorem** worked for the sample mean in the earlier concept.  However, let's consider another example to see a case where the **Central Limit Theorem** doesn't work...\n",
    "\n",
    "Work through the questions and use the created variables to answer the questions that follow below the notebook.\n",
    "\n",
    "Run the below cell to get started."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f400852a048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "np.random.seed(42)\n",
    "\n",
    "pop_data = np.random.gamma(1,100,3000)\n",
    "plt.hist(pop_data);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`1.` In order to create the sampling distribution for the variance of 100 draws of this distribution, follow these steps:\n",
    "\n",
    "`a.` Use numpy's **random.choice** to simulate 100 draws from the `pop_data` array.   <br><br>\n",
    "`b.` Compute the variance of these 100 draws. <br><br>\n",
    "`c.` Write a loop to simulate this process 10,000 times, and store each variance into an array called **var_size_100**.<br><br>\n",
    "`d.` Plot a histogram of your sample variances.<br><br>\n",
    "`e.` Use **var_size_100** and **pop_data** to answer the quiz questions below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10716.243119563425"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use numpy's random.choice to simulate 100 draws from the pop_data array\n",
    "sample = np.random.choice(pop_data, 100)\n",
    "# Compute the variance of these 100 draws\n",
    "np.var(sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write a loop to simulate this process 10,000 times\n",
    "# store each variance into an array called var_size_100\n",
    "var_size_100 = []\n",
    "for _ in range(10000):\n",
    "    sample_100 = np.random.choice(pop_data, 100)\n",
    "    var_size_100.append(np.var(sample_100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4003a58c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot a histogram of the sample \n",
    "plt.hist(sample)\n",
    "plt.title('Histogram of Sample Variance')\n",
    "plt.xlabel('Means')\n",
    "plt.ylabel('Frequency');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dwKmSRqZO8VNTmZmZtcHwRipJeg1wAXAGRef02yLiAUmHAj8HvlNlthOAc4GHJC1JZZcC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\nfl8zDblhswAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f400385ba20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot a histogram of the sample var_size_100\n",
    "plt.hist(var_size_100)\n",
    "plt.title('Histogram of Sample Variances')\n",
    "plt.xlabel('Means')\n",
    "plt.ylabel('Frequency');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hgw0Tx73A6DQ9Grg3Tf8AOKpWvQbGdjXZtcJaKaZhwG1kVxF4FGir/izJjsR7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\nxGFmZoU4cZiZWSFOHGZmVsj/B0cr6o7Af2kGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40037e4438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot a histogram of the pop_data\n",
    "plt.hist(pop_data)\n",
    "plt.title('Histogram of Variance of pop_data')\n",
    "plt.xlabel('Means')\n",
    "plt.ylabel('Frequency');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9955.7693930654896, 99.778601879689063, 100.35978700795846)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute statistics of \"pop_data\"\n",
    "np.var(pop_data), np.std(pop_data), pop_data.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10716.243119563425, 103.51928863532353)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute statistics of \"sample\"\n",
    "np.var(sample), np.std(sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6417706.24569772, 2533.3192151202975)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute statistics of var_size_100\n",
    "np.var(var_size_100), np.std(var_size_100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "101.51376314358205"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample.mean() #mean of 100 sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6417706.24569772"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# mean of the sampling distribution for the sample variance.\n",
    "np.var(var_size_100).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}