{
 "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:  16.635344\n",
      "Population SD: 39.48019985160957\n",
      "SD of sample means: 3.9598180364334925\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:  16.65006075\n",
      "Population SD: 39.48019985160957\n",
      "SD of sample means: 1.964001145158637\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:  16.657137439999996\n",
      "Population SD: 39.48019985160957\n",
      "SD of sample means: 1.5758014080937504\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",
    "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>7.903416</td>\n",
       "      <td>7.896040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>50</td>\n",
       "      <td>5.563648</td>\n",
       "      <td>5.583343</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>75</td>\n",
       "      <td>4.594680</td>\n",
       "      <td>4.558781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>100</td>\n",
       "      <td>4.007013</td>\n",
       "      <td>3.948020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>125</td>\n",
       "      <td>3.580775</td>\n",
       "      <td>3.531216</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>150</td>\n",
       "      <td>3.238786</td>\n",
       "      <td>3.223545</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>175</td>\n",
       "      <td>2.981999</td>\n",
       "      <td>2.984423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>200</td>\n",
       "      <td>2.809697</td>\n",
       "      <td>2.791672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>225</td>\n",
       "      <td>2.624104</td>\n",
       "      <td>2.632013</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>250</td>\n",
       "      <td>2.496046</td>\n",
       "      <td>2.496947</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>275</td>\n",
       "      <td>2.332986</td>\n",
       "      <td>2.380746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>300</td>\n",
       "      <td>2.312306</td>\n",
       "      <td>2.279390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>325</td>\n",
       "      <td>2.220895</td>\n",
       "      <td>2.189967</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>350</td>\n",
       "      <td>2.124817</td>\n",
       "      <td>2.110305</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>375</td>\n",
       "      <td>2.050591</td>\n",
       "      <td>2.038749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>400</td>\n",
       "      <td>1.959227</td>\n",
       "      <td>1.974010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>425</td>\n",
       "      <td>1.910624</td>\n",
       "      <td>1.915071</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>450</td>\n",
       "      <td>1.853313</td>\n",
       "      <td>1.861114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>475</td>\n",
       "      <td>1.811124</td>\n",
       "      <td>1.811476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>500</td>\n",
       "      <td>1.761155</td>\n",
       "      <td>1.765608</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>525</td>\n",
       "      <td>1.729508</td>\n",
       "      <td>1.723057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>550</td>\n",
       "      <td>1.676110</td>\n",
       "      <td>1.683441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>575</td>\n",
       "      <td>1.642273</td>\n",
       "      <td>1.646438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>600</td>\n",
       "      <td>1.619059</td>\n",
       "      <td>1.611772</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>625</td>\n",
       "      <td>1.600824</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                   7.903416        7.896040\n",
       "1              50                   5.563648        5.583343\n",
       "2              75                   4.594680        4.558781\n",
       "3             100                   4.007013        3.948020\n",
       "4             125                   3.580775        3.531216\n",
       "5             150                   3.238786        3.223545\n",
       "6             175                   2.981999        2.984423\n",
       "7             200                   2.809697        2.791672\n",
       "8             225                   2.624104        2.632013\n",
       "9             250                   2.496046        2.496947\n",
       "10            275                   2.332986        2.380746\n",
       "11            300                   2.312306        2.279390\n",
       "12            325                   2.220895        2.189967\n",
       "13            350                   2.124817        2.110305\n",
       "14            375                   2.050591        2.038749\n",
       "15            400                   1.959227        1.974010\n",
       "16            425                   1.910624        1.915071\n",
       "17            450                   1.853313        1.861114\n",
       "18            475                   1.811124        1.811476\n",
       "19            500                   1.761155        1.765608\n",
       "20            525                   1.729508        1.723057\n",
       "21            550                   1.676110        1.683441\n",
       "22            575                   1.642273        1.646438\n",
       "23            600                   1.619059        1.611772\n",
       "24            625                   1.600824        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."
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    "### 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."
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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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