{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# HIDDEN\n",
    "from datascience import *\n",
    "%matplotlib inline\n",
    "path_data = '../../../data/'\n",
    "import matplotlib.pyplot as plots\n",
    "plots.style.use('fivethirtyeight')\n",
    "import math\n",
    "import numpy as np\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# HIDDEN\n",
    "\n",
    "colors = Table.read_table(path_data + 'roulette_wheel.csv').column('Color')\n",
    "pockets = make_array('0','00')\n",
    "for i in np.arange(1, 37):\n",
    "    pockets = np.append(pockets, str(i)) \n",
    "\n",
    "wheel = Table().with_columns(\n",
    "    'Pocket', pockets,\n",
    "    'Color', colors\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Central Limit Theorem ###\n",
    "Very few of the data histograms that we have seen in this course have been bell shaped. When we have come across a bell shaped distribution, it has almost invariably been an empirical histogram of a statistic based on a random sample.\n",
    "\n",
    "The examples below show two very different situations in which an approximate bell shape appears in such histograms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Net Gain in Roulette ###\n",
    "In an earlier section, the bell appeared as the rough shape of the total amount of money we would make if we placed the same bet repeatedly on different spins of a roulette wheel. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Pocket</th> <th>Color</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>0     </td> <td>green</td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>00    </td> <td>green</td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1     </td> <td>red  </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>2     </td> <td>black</td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>3     </td> <td>red  </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>4     </td> <td>black</td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>5     </td> <td>red  </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>6     </td> <td>black</td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>7     </td> <td>red  </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>8     </td> <td>black</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (28 rows omitted)</p>"
      ],
      "text/plain": [
       "Pocket | Color\n",
       "0      | green\n",
       "00     | green\n",
       "1      | red\n",
       "2      | black\n",
       "3      | red\n",
       "4      | black\n",
       "5      | red\n",
       "6      | black\n",
       "7      | red\n",
       "8      | black\n",
       "... (28 rows omitted)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wheel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall that the bet on red pays even money, 1 to 1. We defined the function `red_winnings` that returns the net winnings on one \\$1 bet on red. Specifically, the function takes a color as its argument and returns 1 if the color is red. For all other colors it returns -1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def red_winnings(color):\n",
    "    if color == 'red':\n",
    "        return 1\n",
    "    else:\n",
    "        return -1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The table `red` shows each pocket's winnings on red."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Pocket</th> <th>Color</th> <th>Winnings: Red</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>0     </td> <td>green</td> <td>-1           </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>00    </td> <td>green</td> <td>-1           </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1     </td> <td>red  </td> <td>1            </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>2     </td> <td>black</td> <td>-1           </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>3     </td> <td>red  </td> <td>1            </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>4     </td> <td>black</td> <td>-1           </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>5     </td> <td>red  </td> <td>1            </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>6     </td> <td>black</td> <td>-1           </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>7     </td> <td>red  </td> <td>1            </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>8     </td> <td>black</td> <td>-1           </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (28 rows omitted)</p>"
      ],
      "text/plain": [
       "Pocket | Color | Winnings: Red\n",
       "0      | green | -1\n",
       "00     | green | -1\n",
       "1      | red   | 1\n",
       "2      | black | -1\n",
       "3      | red   | 1\n",
       "4      | black | -1\n",
       "5      | red   | 1\n",
       "6      | black | -1\n",
       "7      | red   | 1\n",
       "8      | black | -1\n",
       "... (28 rows omitted)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "red = wheel.with_column(\n",
    "    'Winnings: Red', wheel.apply(red_winnings, 'Color')\n",
    "    )\n",
    "red"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Your net gain on one bet is one random draw from the `Winnings: Red` column. There is an 18/38 chance making \\$1, and a 20/38 chance of making -$1. This probability distribution is shown in the histogram below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/choldgraf/anaconda/envs/textbook/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "red.select('Winnings: Red').hist(bins=np.arange(-1.5, 1.6, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now suppose you bet many times on red. Your net winnings will be the sum of many draws made at random with replacement from the distribution above.\n",
    "\n",
    "It will take a bit of math to list all the possible values of your net winnings along with all of their chances. We won't do that; instead, we will approximate the probability distribution by simulation, as we have done all along in this course. \n",
    "\n",
    "The code below simulates your net gain if you bet \\$1 on red on 400 different spins of the roulette wheel. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "num_bets = 400\n",
    "repetitions = 10000\n",
    "\n",
    "net_gain_red = make_array()\n",
    "\n",
    "for i in np.arange(repetitions):\n",
    "    spins = red.sample(num_bets)\n",
    "    new_net_gain_red = spins.column('Winnings: Red').sum()\n",
    "    net_gain_red = np.append(net_gain_red, new_net_gain_red)\n",
    "\n",
    "\n",
    "results = Table().with_column(\n",
    "    'Net Gain on Red', net_gain_red\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/choldgraf/anaconda/envs/textbook/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.hist(bins=np.arange(-80, 50, 6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's a roughly bell shaped histogram, even though the distribution we are drawing from is nowhere near bell shaped.\n",
    "\n",
    "**Center.** The distribution is centered near -\\$20, roughly. To see why, note that your winnings will be \\$1 on about 18/38 of the bets, and -\\$1 on the remaining 20/38. So your average winnings per dollar bet will be roughly -5.26 cents:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.05263157894736842"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_per_bet = 1*(18/38) + (-1)*(20/38)\n",
    "average_per_bet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So in 400 bets you expect that your net gain will be about -\\$21:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-21.052631578947366"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "400 * average_per_bet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For confirmation, we can compute the mean of the 10,000 simulated net gains:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-20.859"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(results.column(0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Spread.** Run your eye along the curve starting at the center and notice that the point of inflection is near 0. On a bell shaped curve, the SD is the distance from the center to a point of inflection. The center is roughly -\\$20, which means that the SD of the distribution is around \\$20.\n",
    "\n",
    "In the next section we will see where the \\$20 comes from. For now, let's confirm our observation by simply calculating the SD of the 10,000 simulated net gains:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20.257603979740548"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(results.column(0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Summary.** The net gain in 400 bets is the sum of the 400 amounts won on each individual bet. The probability distribution of that sum is approximately normal, with an average and an SD that we can approximate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Average Flight Delay ###\n",
    "The table `united` contains data on departure delays of 13,825 United Airlines domestic flights out of San Francisco airport in the summer of 2015. As we have seen before, the distribution of delays has a long right-hand tail."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "united = Table.read_table(path_data + 'united_summer2015.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/choldgraf/anaconda/envs/textbook/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "united.select('Delay').hist(bins=np.arange(-20, 300, 10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean delay was about 16.6 minutes and the SD was about 39.5 minutes. Notice how large the SD is, compared to the mean. Those large deviations on the right have an effect, even though they are a very small proportion of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(16.658155515370705, 39.480199851609314)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_delay = np.mean(united.column('Delay'))\n",
    "sd_delay = np.std(united.column('Delay'))\n",
    "\n",
    "mean_delay, sd_delay"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now suppose we sampled 400 delays at random with replacement. You could sample without replacement if you like, but the results would be very similar to with-replacement sampling. If you sample a few hundred out of 13,825 without replacement, you hardly change the population each time you pull out a value.\n",
    "\n",
    "In the sample, what could the average delay be? We expect it to be around 16 or 17, because that's the population average; but it is likely to be somewhat off. Let's see what we get by sampling. We'll work with the table `delay` that only contains the column of delays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "delay = united.select('Delay')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15.77"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(delay.sample(400).column('Delay'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The sample average varies according to how the sample comes out, so we will simulate the sampling process repeatedly and draw the empirical histogram of the sample average. That will be an approximation to the probability histogram of the sample average."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sample_size = 400\n",
    "repetitions = 10000\n",
    "\n",
    "means = make_array()\n",
    "\n",
    "for i in np.arange(repetitions):\n",
    "    sample = delay.sample(sample_size)\n",
    "    new_mean = np.mean(sample.column('Delay'))\n",
    "    means = np.append(means, new_mean)\n",
    "\n",
    "results = Table().with_column(\n",
    "    'Sample Mean', means\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/choldgraf/anaconda/envs/textbook/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.hist(bins=np.arange(10, 25, 0.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once again, we see a rough bell shape, even though we are drawing from a very skewed distribution. The bell is centered somewhere between 16 ad 17, as we expect."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Central Limit Theorem ###\n",
    "\n",
    "The reason why the bell shape appears in such settings is a remarkable result of probability theory called the **Central Limit Theorem**. \n",
    "\n",
    "**The Central Limit Theorem says that the probability distribution of the sum or average of a large random sample drawn with replacement will be roughly normal, *regardless of the distribution of the population from which the sample is drawn*.**\n",
    "\n",
    "As we noted when we were studying Chebychev's bounds, results that can be applied to random samples *regardless of the distribution of the population* are very powerful, because in data science we rarely know the distribution of the population.\n",
    "\n",
    "The Central Limit Theorem makes it possible to make inferences with very little knowledge about the population, provided we have a large random sample. That is why it is central to the field of statistical inference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Proportion of Purple Flowers ###\n",
    "Recall Mendel's probability model for the colors of the flowers of a species of pea plant. The model says that the flower colors of the plants are like draws made at random with replacement from {Purple, Purple, Purple, White}.\n",
    "\n",
    "In a large sample of plants, about what proportion will have purple flowers? We would expect the answer to be about 0.75, the proportion purple in the model. And, because proportions are means, the Central Limit Theorem says that the distribution of the sample proportion of purple plants is roughly normal.\n",
    "\n",
    "We can confirm this by simulation. Let's simulate the proportion of purple-flowered plants in a sample of 200 plants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Color</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>Purple</td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>Purple</td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>Purple</td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>White </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "Color\n",
       "Purple\n",
       "Purple\n",
       "Purple\n",
       "White"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "colors = make_array('Purple', 'Purple', 'Purple', 'White')\n",
    "\n",
    "model = Table().with_column('Color', colors)\n",
    "\n",
    "model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "props = make_array()\n",
    "\n",
    "num_plants = 200\n",
    "repetitions = 10000\n",
    "\n",
    "for i in np.arange(repetitions):\n",
    "    sample = model.sample(num_plants)\n",
    "    new_prop = np.count_nonzero(sample.column('Color') == 'Purple')/num_plants\n",
    "    props = np.append(props, new_prop)\n",
    "    \n",
    "results = Table().with_column('Sample Proportion: 200', props)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/choldgraf/anaconda/envs/textbook/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.hist(bins=np.arange(0.65, 0.85, 0.01))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There's that normal curve again, as predicted by the Central Limit Theorem, centered at around 0.75 just as you would expect.\n",
    "\n",
    "How would this distribution change if we increased the sample size? Let's run the code again with a sample size of 800, and collect the results of simulations in the same table in which we collected simulations based on a sample size of 200. We will keep the number of `repetitions` the same as before so that the two columns have the same length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "props2 = make_array()\n",
    "\n",
    "num_plants = 800\n",
    "\n",
    "for i in np.arange(repetitions):\n",
    "    sample = model.sample(num_plants)\n",
    "    new_prop = np.count_nonzero(sample.column('Color') == 'Purple')/num_plants\n",
    "    props2 = np.append(props2, new_prop)\n",
    "    \n",
    "results = results.with_column('Sample Proportion: 800', props2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/choldgraf/anaconda/envs/textbook/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.hist(bins=np.arange(0.65, 0.85, 0.01))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both distributions are approximately normal but one is narrower than the other. The proportions based on a sample size of 800 are more tightly clustered around 0.75 than those from a sample size of 200. Increasing the sample size has decreased the variability in the sample proportion.\n",
    "\n",
    "This should not be surprising.  We have leaned many times on the intuition that a larger sample size generally reduces the variability of a statistic.  However, in the case of a sample average, we can *quantify* the relationship between sample size and variability.\n",
    "\n",
    "Exactly how does the sample size affect the variability of a sample average or proportion? That is the question we will examine in the next section."
   ]
  }
 ],
 "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": "3.4.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}