{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "remove_input"
    ]
   },
   "outputs": [],
   "source": [
    "path_data = '../../../../data/'\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('fivethirtyeight')\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Variability of the Sample Mean ###\n",
    "By the Central Limit Theorem, the probability distribution of the mean of a large random sample is roughly normal. The bell curve is centered at the population mean. Some of the sample means are higher, and some lower, but the deviations from the population mean are roughly symmetric on either side, as we have seen repeatedly. Formally, probability theory shows that the sample mean is an *unbiased* estimate of the population mean.\n",
    "\n",
    "In our simulations, we also noticed that the means of larger samples tend to be more tightly clustered around the population mean than means of smaller samples. In this section, we will quantify the variability of the sample mean and develop a relation between the variability and the sample size."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start with our table of flight delays. The mean delay is about 16.7 minutes, and the distribution of delays is skewed to the right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Delay</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13820</th>\n",
       "      <td>-4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13821</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13822</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13823</th>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13824</th>\n",
       "      <td>-2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>13825 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Delay\n",
       "0        257\n",
       "1         28\n",
       "2         -3\n",
       "3          0\n",
       "4         64\n",
       "...      ...\n",
       "13820     -4\n",
       "13821      8\n",
       "13822      3\n",
       "13823     -1\n",
       "13824     -2\n",
       "\n",
       "[13825 rows x 1 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "united = pd.read_csv(path_data + 'united_summer2015.csv')\n",
    "delay = united[['Delay']]\n",
    "delay"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Delay    16.658156\n",
       "dtype: float64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pop_mean = np.mean(delay)\n",
    "pop_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "remove_input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "source = delay\n",
    "\n",
    "source_col = ''\n",
    "\n",
    "bins = np.arange(-20, 300, 10)\n",
    "\n",
    "if source_col =='':\n",
    "    source = source\n",
    "else:\n",
    "    source = source[source_col]\n",
    "\n",
    "unit = ''\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(7,5))\n",
    "\n",
    "ax.hist(source, bins=bins, density=True, color=('darkblue'), alpha=0.8, ec='white', zorder=5)\n",
    "\n",
    "ax.scatter(pop_mean, -0.0008, marker='^', color='darkblue', s=60, \n",
    "           zorder=15).set_clip_on(False)\n",
    "\n",
    "y_vals = ax.get_yticks()\n",
    "\n",
    "y_label = 'Percent per ' + (unit if unit else 'unit')\n",
    "\n",
    "x_label = 'Delay'\n",
    "\n",
    "ax.set_yticklabels(['{:g}'.format(x * 100) for x in y_vals])\n",
    "\n",
    "plt.ylim(-0.004, 0.04)\n",
    "\n",
    "plt.ylabel(y_label)\n",
    "\n",
    "plt.xlabel(x_label)\n",
    "\n",
    "plt.title('');\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's take random samples and look at the probability distribution of the sample mean. As usual, we will use simulation to get an empirical approximation to this distribution.\n",
    "\n",
    "We will define a function `simulate_sample_mean` to do this, because we are going to vary the sample size later. The arguments are the name of the table, the label of the column containing the variable, the sample size, and the number of simulations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"Empirical distribution of random sample means\"\"\"\n",
    "\n",
    "def simulate_sample_mean(table, label, sample_size, repetitions):\n",
    "    \n",
    "    means = make_array([])\n",
    "\n",
    "    for i in range(repetitions):\n",
    "        new_sample = table.sample(sample_size)\n",
    "        new_sample_mean = np.mean(new_sample.column(label))\n",
    "        means = np.append(means, new_sample_mean)\n",
    "\n",
    "    sample_means = Table().with_column('Sample Means', means)\n",
    "    \n",
    "    # Display empirical histogram and print all relevant quantities\n",
    "    sample_means.hist(bins=20)\n",
    "    plots.xlabel('Sample Means')\n",
    "    plots.title('Sample Size ' + str(sample_size))\n",
    "    print(\"Sample size: \", sample_size)\n",
    "    print(\"Population mean:\", np.mean(table.column(label)))\n",
    "    print(\"Average of sample means: \", np.mean(means))\n",
    "    print(\"Population SD:\", np.std(table.column(label)))\n",
    "    print(\"SD of sample means:\", np.std(means))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"Empirical distribution of random sample means\"\"\"\n",
    "\n",
    "def simulate_sample_mean(table, label, sample_size, repetitions, xlim=(), ylim=()):\n",
    "    \n",
    "    means = np.array([])\n",
    "\n",
    "    for i in range(repetitions):\n",
    "        new_sample = table.sample(sample_size, replace=True)\n",
    "        new_sample_mean = np.mean(new_sample[label])\n",
    "        means = np.append(means, new_sample_mean)\n",
    "\n",
    "    sample_means = pd.DataFrame({'Sample Means':means})\n",
    "    \n",
    "    # Display empirical histogram and print all relevant quantities\n",
    "\n",
    "    unit = ''\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(8,5))\n",
    "\n",
    "    ax.hist(sample_means, bins=(20), density=True, color='blue', alpha=0.8, ec='white', zorder=5)\n",
    "\n",
    "    y_label = 'Percent per ' + (unit if unit else 'unit')\n",
    "\n",
    "    x_label = 'Sample Means'\n",
    "    \n",
    "    plt.xlim(xlim)\n",
    "    \n",
    "    plt.ylim(ylim)\n",
    "    \n",
    "    y_vals = ax.get_yticks()\n",
    "\n",
    "    ax.set_yticklabels(['{:g}'.format(x * 100) for x in y_vals])\n",
    "\n",
    "    plt.ylabel(y_label)\n",
    "\n",
    "    plt.xlabel(x_label)\n",
    "\n",
    "    plt.title('Sample Size ' + str(sample_size))\n",
    "\n",
    "    print(\"Sample size: \", sample_size)\n",
    "    print(\"Population mean:\", np.mean(table[label]))\n",
    "    print(\"Average of sample means: \", np.mean(means))\n",
    "    print(\"Population SD:\", np.std(table[label]))\n",
    "    print(\"SD of sample means:\", np.std(means))\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us simulate the mean of a random sample of 100 delays, then of 400 delays, and finally of 625 delays. We will perform 10,000 repetitions of each of these process. The `xlim` and `ylim` lines set the axes consistently in all the plots for ease of comparison. If we knew that the limits would not change we could set the limits as default values in teh function `simulate_sample_mean`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample size:  100\n",
      "Population mean: 16.658155515370705\n",
      "Average of sample means:  16.634773000000003\n",
      "Population SD: 39.48019985160957\n",
      "SD of sample means: 3.9215571662887947\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "simulate_sample_mean(delay, 'Delay', 100, 10000, (5,35), (0, 0.25))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample size:  400\n",
      "Population mean: 16.658155515370705\n",
      "Average of sample means:  16.63435025\n",
      "Population SD: 39.48019985160957\n",
      "SD of sample means: 1.9477845083452987\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "simulate_sample_mean(delay, 'Delay', 400, 10000, (5,35), (0, 0.25))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample size:  625\n",
      "Population mean: 16.658155515370705\n",
      "Average of sample means:  16.62309216\n",
      "Population SD: 39.48019985160957\n",
      "SD of sample means: 1.5602303871372762\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "simulate_sample_mean(delay, 'Delay', 625, 10000, (5,35), (0, 0.25))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see the Central Limit Theorem in action – the histograms of the sample means are roughly normal, even though the histogram of the delays themselves is far from normal.\n",
    "\n",
    "You can also see that each of the three histograms of the sample means is centered very close to the population mean. In each case, the \"average of sample means\" is very close to 16.66 minutes, the population mean. Both values are provided in the printout above each histogram. As expected, the sample mean is an unbiased estimate of the population mean."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The SD of All the Sample Means ###\n",
    "\n",
    "You can also see that the histograms get narrower, and hence taller, as the sample size increases. We have seen that before, but now we will pay closer attention to the measure of spread.\n",
    "\n",
    "The SD of the population of all delays is about 40 minutes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "39.48019985160957"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pop_sd = np.std(delay['Delay'])\n",
    "pop_sd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Take a look at the SDs in the sample mean histograms above. In all three of them, the SD of the population of delays is about 40 minutes, because all the samples were taken from the same population.\n",
    "\n",
    "Now look at the SD of all 10,000 sample means, when the sample size is 100. That SD is about one-tenth of the population SD. When the sample size is 400, the SD of all the sample means is about one-twentieth of the population SD. When the sample size is 625, the SD of the sample means is about one-twentyfifth of the population SD.\n",
    "\n",
    "It seems like a good idea to compare the SD of the empirical distribution of the sample means to the quantity \"population SD divided by the square root of the sample size.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the numerical values. For each sample size in the first column, 10,000 random samples of that size were drawn, and the 10,000 sample means were calculated. The second column contains the SD of those 10,000 sample means. The third column contains the result of the calculation \"population SD divided by the square root of the sample size.\"\n",
    "\n",
    "The cell takes a while to run, as it's a large simulation. But you'll soon see that it's worth the wait."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "repetitions = 10000\n",
    "sample_sizes = np.arange(25, 626, 25)\n",
    "\n",
    "sd_means = np.array([])\n",
    "\n",
    "for n in sample_sizes:\n",
    "    means = np.array([])\n",
    "    for i in np.arange(repetitions):\n",
    "        means = np.append(means, np.mean(delay['Delay'].sample(n, replace=True)))\n",
    "    sd_means = np.append(sd_means, np.std(means))\n",
    "\n",
    "sd_comparison = pd.DataFrame(\n",
    "    {'Sample Size n':sample_sizes,\n",
    "    'SD of 10,000 Sample Means':sd_means,\n",
    "    'pop_sd/sqrt(n)':pop_sd/np.sqrt(sample_sizes)}\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Sample Size n</th>\n",
       "      <th>SD of 10,000 Sample Means</th>\n",
       "      <th>pop_sd/sqrt(n)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>25</td>\n",
       "      <td>7.890499</td>\n",
       "      <td>7.896040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>50</td>\n",
       "      <td>5.544631</td>\n",
       "      <td>5.583343</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>75</td>\n",
       "      <td>4.521931</td>\n",
       "      <td>4.558781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>100</td>\n",
       "      <td>3.959873</td>\n",
       "      <td>3.948020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>125</td>\n",
       "      <td>3.520749</td>\n",
       "      <td>3.531216</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>150</td>\n",
       "      <td>3.238875</td>\n",
       "      <td>3.223545</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>175</td>\n",
       "      <td>2.966418</td>\n",
       "      <td>2.984423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>200</td>\n",
       "      <td>2.779681</td>\n",
       "      <td>2.791672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>225</td>\n",
       "      <td>2.613087</td>\n",
       "      <td>2.632013</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>250</td>\n",
       "      <td>2.491289</td>\n",
       "      <td>2.496947</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>275</td>\n",
       "      <td>2.358647</td>\n",
       "      <td>2.380746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>300</td>\n",
       "      <td>2.285085</td>\n",
       "      <td>2.279390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>325</td>\n",
       "      <td>2.165918</td>\n",
       "      <td>2.189967</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>350</td>\n",
       "      <td>2.076965</td>\n",
       "      <td>2.110305</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>375</td>\n",
       "      <td>2.031482</td>\n",
       "      <td>2.038749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>400</td>\n",
       "      <td>1.970609</td>\n",
       "      <td>1.974010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>425</td>\n",
       "      <td>1.926096</td>\n",
       "      <td>1.915071</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>450</td>\n",
       "      <td>1.878757</td>\n",
       "      <td>1.861114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>475</td>\n",
       "      <td>1.802092</td>\n",
       "      <td>1.811476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>500</td>\n",
       "      <td>1.765423</td>\n",
       "      <td>1.765608</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>525</td>\n",
       "      <td>1.713650</td>\n",
       "      <td>1.723057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>550</td>\n",
       "      <td>1.675659</td>\n",
       "      <td>1.683441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>575</td>\n",
       "      <td>1.648763</td>\n",
       "      <td>1.646438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>600</td>\n",
       "      <td>1.619837</td>\n",
       "      <td>1.611772</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>625</td>\n",
       "      <td>1.575032</td>\n",
       "      <td>1.579208</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Sample Size n  SD of 10,000 Sample Means  pop_sd/sqrt(n)\n",
       "0              25                   7.890499        7.896040\n",
       "1              50                   5.544631        5.583343\n",
       "2              75                   4.521931        4.558781\n",
       "3             100                   3.959873        3.948020\n",
       "4             125                   3.520749        3.531216\n",
       "5             150                   3.238875        3.223545\n",
       "6             175                   2.966418        2.984423\n",
       "7             200                   2.779681        2.791672\n",
       "8             225                   2.613087        2.632013\n",
       "9             250                   2.491289        2.496947\n",
       "10            275                   2.358647        2.380746\n",
       "11            300                   2.285085        2.279390\n",
       "12            325                   2.165918        2.189967\n",
       "13            350                   2.076965        2.110305\n",
       "14            375                   2.031482        2.038749\n",
       "15            400                   1.970609        1.974010\n",
       "16            425                   1.926096        1.915071\n",
       "17            450                   1.878757        1.861114\n",
       "18            475                   1.802092        1.811476\n",
       "19            500                   1.765423        1.765608\n",
       "20            525                   1.713650        1.723057\n",
       "21            550                   1.675659        1.683441\n",
       "22            575                   1.648763        1.646438\n",
       "23            600                   1.619837        1.611772\n",
       "24            625                   1.575032        1.579208"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sd_comparison"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The values in the second and third columns are very close. If we plot each of those columns with the sample size on the horizontal axis, the two graphs are essentially indistinguishable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "unit = ''\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8,5))\n",
    "\n",
    "ax.plot(sd_comparison['Sample Size n'], sd_comparison[['SD of 10,000 Sample Means']],\n",
    "       label=['SD of 10,000 Sample Means'], lw=5\n",
    "        , color='gold', zorder=10)\n",
    "\n",
    "ax.plot(sd_comparison['Sample Size n'], sd_comparison[['pop_sd/sqrt(n)']],\n",
    "       label=['pop_sd/sqrt(n)'], alpha=0.2, color='red', zorder=10)\n",
    "\n",
    "x_label = 'Sample Size n'\n",
    "\n",
    "y_vals = ax.get_yticks()\n",
    "\n",
    "ax.set_yticklabels(['{:g}'.format(x * 100) for x in y_vals])\n",
    "\n",
    "plt.ylabel(y_label)\n",
    "\n",
    "plt.xlabel(x_label)\n",
    "\n",
    "ax.legend(bbox_to_anchor=(1.04,1), loc=\"upper left\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There really are two curves there. But they are so close to each other that it looks as though there is just one.\n",
    "\n",
    "What we are seeing is an instance of a general result. Remember that the graph above is based on 10,000 replications for each sample size. But there are many more than 10,000 samples of each size. The probability distribution of the sample mean is based on the means of *all possible samples* of a fixed size.\n",
    "\n",
    "**Fix a sample size.** If the samples are drawn at random with replacement from the population, then\n",
    "\n",
    "$$\n",
    "{\\mbox{SD of all possible sample means}} ~=~\n",
    "\\frac{\\mbox{Population SD}}{\\sqrt{\\mbox{sample size}}}\n",
    "$$\n",
    "\n",
    "This is the standard deviation of the averages of all the possible samples that could be drawn. **It measures roughly how far off the sample means are from the population mean.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Central Limit Theorem for the Sample Mean ###\n",
    "If you draw a large random sample with replacement from a population, then, regardless of the distribution of the population, the probability distribution of the sample mean is roughly normal, centered at the population mean, with an SD equal to the population SD divided by the square root of the sample size."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Accuracy of the Sample Mean ###\n",
    "The SD of all possible sample means measures how variable the sample mean can be. As such, it is taken as a measure of the accuracy of the sample mean as an estimate of the population mean. The smaller the SD, the more accurate the estimate.\n",
    "\n",
    "The formula shows that:\n",
    "- The population size doesn't affect the accuracy of the sample mean. The population size doesn't appear anywhere in the formula.\n",
    "- The population SD is a constant; it's the same for every sample drawn from the population. The sample size can be varied. Because the sample size appears in the denominator, the variability of the sample mean *decreases* as the sample size increases, and hence the accuracy increases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
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    "### The Square Root Law ###\n",
    "From the table of SD comparisons, you can see that the SD of the means of random samples of 25 flight delays is about 8 minutes. If you multiply the sample size by 4, you'll get samples of size 100. The SD of the means of all of those samples is about 4 minutes. That's smaller than 8 minutes, but it's not 4 times as small; it's only 2 times as small. That's because the sample size in the denominator has a square root over it. The sample size increased by a factor of 4, but the SD went down by a factor of $2 = \\sqrt{4}$. In other words, the accuracy went up by a factor of $2 = \\sqrt{4}$.\n",
    "\n",
    "In general, when you multiply the sample size by a factor, the accuracy of the sample mean goes up by the square root of that factor.\n",
    "\n",
    "So to increase accuracy by a factor of 10, you have to multiply sample size by a factor of 100. Accuracy doesn't come cheap!"
   ]
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