{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": [
     "remove_input"
    ]
   },
   "outputs": [],
   "source": [
    "path_data = '../../data/'\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\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": [
    "# Sampling from a Population\n",
    "\n",
    "The law of averages also holds when the random sample is drawn from individuals in a large population.\n",
    "\n",
    "As an example, we will study a population of flight delay times. The table `united` contains data for United Airlines domestic flights departing from San Francisco in the summer of 2015. The data are made publicly available by the [Bureau of Transportation Statistics](http://www.transtats.bts.gov/Fields.asp?Table_ID=293) in the United States Department of Transportation.\n",
    "\n",
    "There are 13,825 rows, each corresponding to a flight. The columns are the date of the flight, the flight number, the destination airport code, and the departure delay time in minutes. Some delay times are negative; those flights left early."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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>Date</th>\n",
       "      <th>Flight Number</th>\n",
       "      <th>Destination</th>\n",
       "      <th>Delay</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6/1/15</td>\n",
       "      <td>73</td>\n",
       "      <td>HNL</td>\n",
       "      <td>257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6/1/15</td>\n",
       "      <td>217</td>\n",
       "      <td>EWR</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>6/1/15</td>\n",
       "      <td>237</td>\n",
       "      <td>STL</td>\n",
       "      <td>-3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6/1/15</td>\n",
       "      <td>250</td>\n",
       "      <td>SAN</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6/1/15</td>\n",
       "      <td>267</td>\n",
       "      <td>PHL</td>\n",
       "      <td>64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13820</th>\n",
       "      <td>8/31/15</td>\n",
       "      <td>1978</td>\n",
       "      <td>LAS</td>\n",
       "      <td>-4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13821</th>\n",
       "      <td>8/31/15</td>\n",
       "      <td>1993</td>\n",
       "      <td>IAD</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13822</th>\n",
       "      <td>8/31/15</td>\n",
       "      <td>1994</td>\n",
       "      <td>ORD</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13823</th>\n",
       "      <td>8/31/15</td>\n",
       "      <td>2000</td>\n",
       "      <td>PHX</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13824</th>\n",
       "      <td>8/31/15</td>\n",
       "      <td>2013</td>\n",
       "      <td>EWR</td>\n",
       "      <td>-2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>13825 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          Date  Flight Number Destination  Delay\n",
       "0       6/1/15             73         HNL    257\n",
       "1       6/1/15            217         EWR     28\n",
       "2       6/1/15            237         STL     -3\n",
       "3       6/1/15            250         SAN      0\n",
       "4       6/1/15            267         PHL     64\n",
       "...        ...            ...         ...    ...\n",
       "13820  8/31/15           1978         LAS     -4\n",
       "13821  8/31/15           1993         IAD      8\n",
       "13822  8/31/15           1994         ORD      3\n",
       "13823  8/31/15           2000         PHX     -1\n",
       "13824  8/31/15           2013         EWR     -2\n",
       "\n",
       "[13825 rows x 4 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "united = pd.read_csv(path_data + 'united_summer2015.csv')\n",
    "united"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One flight departed 16 minutes early, and one was 580 minutes late. The other delay times were almost all between -10 minutes and 200 minutes, as the histogram below shows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-16"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "united['Delay'].min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "580"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "united['Delay'].max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "delay_bins = np.append(np.arange(-20, 301, 10), 600)\n",
    "\n",
    "unit = 'minute'\n",
    "\n",
    "fig, ax1 = plt.subplots()\n",
    "\n",
    "ax1.hist(united['Delay'], bins=delay_bins, density=True, alpha=0.8, ec='white')\n",
    "\n",
    "y_vals = ax1.get_yticks()\n",
    "\n",
    "y_label = 'Percent per ' + (unit if unit else 'unit')\n",
    "\n",
    "x_label = 'Delay' + (unit if unit else '(unit)')\n",
    "\n",
    "ax1.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.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the purposes of this section, it is enough to zoom in on the bulk of the data and ignore the 0.8% of flights that had delays of more than 200 minutes. This restriction is just for visual convenience; the table still retains all the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.008390596745027125"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "united_delay_more_than_200 = united[united['Delay']>200]\n",
    "\n",
    "len(united_delay_more_than_200)/len(united)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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aZWUlpk+fjqtXr8LY2Bg1NTVYunQpAKB79+5Yu3YtAgIC8PHHH6us2JaEhobC3d0dw4cPl7mMWCzuwIqkVelbo66uVsHRpu0YC1Q9qYK4rFTh8ZpMnb9zTcWeKYZ9U0x7+ubs7CxznuBQi4iIwO3bt3Hw4EEMHjwYTk5OTfN0dXXh6+uL48ePd2iorVmzBllZWTh69Ch0dXVlLtdaA1StslwCA4M6hccbGBgqPNakuwmce5gqPF5TicVitf7ONRF7phj2TTGq7Jvg3Y//+te/8P7772PcuHEtnuXo6OiIwsJCpRbXmrCwMKSkpCAtLQ19+vTpsPUSEVHnJXhLraKiAn379pU5XyKRoL6+XilFtWX16tVITU3FkSNH8Nprr3XIOomIqPMTHGoODg64deuWzPmZmZlSuyRVJSQkBAcOHEBCQgLMzMxQUlICADAyMoKxsbHK109ERJ2X4N2PM2fOxN69e5GZmdk07eVuyF27duHIkSMICgpSfoV/EB8fjydPnmDq1Kno379/089nn32m8nUTEVHnJnhLbcWKFbh8+TKmTJkCJycniEQihIaGory8HCUlJZg8eTIWLVqkyloBvNgNSkRE1BLBoaanp4ekpCQcPHgQ3333HUQiEZ4/f45BgwZh+vTp8PPz65DbZBEREcki9x1FZs6ciZkzZ6qiFiIionZR6DZZ//73v5tO37e3t4ebmxu30oiISO3kCrWUlBSsX78ev/76KyQSCYAXJ4vY2tpi/fr13IIjIiK1EhxqiYmJ+OCDD+Ds7IyIiAg4OTlBIpHg7t272Lt3LxYtWoT6+nrMmjVLlfUSERHJJDjUtm/fDi8vLxw5cgSGhtK3blq4cCEmTZqE7du3M9SIiEhtBF+ndv/+fcycObNZoAGAoaEh/P398euvvyq1OCIiInkIDjUXFxc8ePBA5vxff/0V/fv3V0pRREREihAcap988gn27NmDQ4cONZuXkpKCvXv3YsOGDUotjoiISB6Cj6l99tlnsLCwwPz58xEaGoq+fftCJBIhNzcXDx8+hKOjI3bs2IEdO3Y0jRGJREhKSlJJ4URERH8kONRu374NkUgEOzs7AGg6fmZgYAA7OzvU1dXhzp07UmN47RoREXUkwaGWk5OjyjqIiIjaTfAxNSIios6OoUZERFqDoUZERFqDoUZERFqDoUZERFqDoUZERFpDcKgNGjQIGRkZMucfPXoUgwYNUkpRREREihAcavfu3UNNTY3M+TU1NU0PDhUqMzMTAQEBGDBgAMzMzJCYmNjq8gUFBTAzM2v2c+LECbnWS0RE2kmuh4S2doeQX375Bd27d5dr5TU1NXB1dUVgYCAWL14seFxKSgoGDhzY9Nrc3Fyu9RIRkXZqNdT27duH/fv3N73eunUr9uzZ02y5iooK3Lp1CxMmTJBr5T4+PvDx8QEALF26VPC4Hj16wMbGRq51ERGR9ms11GpqalBSUtL0urKyEo2NjVLLiEQidOvWDXPnzkVoaKhqqvyDOXPmoLa2Fo6Ojli6dCmmTp3aIeslIqLOrdVQW7hwIRYuXAgA8PDwQFRUFCZNmtQhhbXE2NgYGzZswIgRI9ClSxdkZGQgODgYcXFx8Pf3V1tdRETUOQg+pnbjxg1V1iGIhYUFli9f3vR68ODBKC8vR0xMTKuhJhaLO6K8FlXpW6OurlbB0abtGAtUPamCuKxU4fGaTJ2/c03FnimGfVNMe/rm7Owsc55cJ4oAwJMnT1BUVITHjx9DIpE0m+/t7S3vW7aLl5dXm2dNttYAVassl8DAoE7h8QYGhgqPNeluAucepgqP11RisVitv3NNxJ4phn1TjCr7JjjUHj9+jNWrV+PQoUNoaGhoNl8ikUAkEqG8vFypBbYlJyeHJ40QEREAOUJtxYoVOHLkCBYuXAhvb2+YmZm1e+XV1dXIzc0FADQ2NqKoqAg3btyAubk57O3tERERgStXriAtLQ3Ai7Mx9fT04OHhAR0dHRw9ehTx8fEIDw9vdy1ERKT5BIfaiRMnsGjRImzatElpK7927Rp8fX2bXkdGRiIyMhKBgYGIi4tDcXEx8vLypMZs3boVhYWF0NXVhaOjI3bu3MmTRIiICIAcoaavrw9HR0elrnzUqFGoqKiQOT8uLk7qdVBQEIKCgpRaAxERaQ/Bt8maOnUqjh8/rspaiIiI2kVwqC1fvhzFxcVYvHgxLl26hOLiYjx8+LDZDxERkboI3v3o5eUFkUiE7OxsJCUlyVyuo89+JCIieklwqH300Uet3tCYiIhI3QSHWlhYmCrrICIiajeFnnzd0NCA8vJyPH/+XNn1EBERKUyuULt69SqmTZsGW1tbODk5ITMzEwBQVlYGPz8//PjjjyopkoiISAjBofbTTz9h0qRJyMvLQ0BAgNR9Hy0sLFBdXY1vvvlGJUUSEREJITjUNmzYAEdHR1y8eBEff/xxs/mjRo3C5cuXlVocERGRPASH2tWrVzF79mwYGhq2eBZkr169pB4oSkRE1NEEh5qOjg50dGQvXlJSgq5duyqlKCIiIkUIDjVPT08cPXq0xXn19fU4ePAghg8frrTCiIiI5CU41P72t7/hzJkz+OCDD5CTkwMAKC4uxokTJzBlyhTk5eVh5cqVKiuUiIioLYIvvv7zn/+MXbt2YdWqVdi3bx8AYMmSJZBIJDA1NUV8fDyGDRumskKJiIjaIjjUAGDGjBmYNGkSTp06hbt376KxsRF9+/bF2LFjYWxsrKoaiYiIBJEr1ACgW7dumDx5sipqISIiahfBx9QyMjKwatUqmfNXrVol80QSIiKijiA41D777DP89ttvMufX1tYiJiZGKUUREREpQnCo3bp1C56enjLnDxo0CLdv31ZGTURERAoRHGrPnz/H06dPZc5/+vQp6urqlFIUERGRIgSHmqurK9LS0tDY2NhsXmNjI9LS0uDi4qLU4lqSmZmJgIAADBgwAGZmZkhMTFT5OomISDMIPvtx8eLFWLBgAQIDAxEWFoYBAwYAAH7++WdERUXhypUriIuLU1mhL9XU1MDV1RWBgYFYvHixytenyUQ6Orhc3vw/IUL0MtJBTwNJ2wsSEXUigkPtvffeQ15eHiIjI3H8+HEAgEgkgkQigUgkwurVq+Hv76+yQl/y8fGBj48PAGDp0qUqX58me/S0AZGXHik0dusbVuhp0PzG1UREnZlc16mFhIRgxowZSE9PR35+PiQSCfr27QtfX1/06dNHRSUSEREJIyjUnj59Cj8/P/j7+2P27NlYvny5qutSKrFYrLZ1V+lbo66uVsHRpu0YCzx7/kzh8VVPqiAuK1V43eqmzt+5pmLPFMO+KaY9fXN2dpY5T1Code3aFdevX8eMGTMULkKdWmuAqlWWS2BgoPhZoQYGhgqP1euip/B4k+4mcO5hqvC61UksFqv1d66J2DPFsG+KUWXfBJ/9+MYbb+D8+fMqKYKIiEgZBIdadHQ0rl69inXr1iE/P7/FU/uJiIjUSfCJIsOGDYNEIkFsbCxiY2Oho6MDPT09qWVEIhF+/fVXpRf5e9XV1cjNzQXw4vq4oqIi3LhxA+bm5rC3t1fpuomIqHMTHGrvvvsuRCL1n+J97do1+Pr6Nr2OjIxEZGQkAgMDO+Q6OSIi6rwEh1pnCYxRo0ahoqJC3WUQEVEnJPiYGhERUWcnV6jdu3cPH374ITw9PWFvb49z584BAMrKyrBy5UpkZ2erokYiIiJBBO9+vHPnDt5++200NjZi6NChuHfvHhoaGgAAFhYWuHTpEurq6rBz506VFUtERNQawaG2fv16dO/eHSdOnICuri6cnJyk5vv4+OC7775Tdn1ERESCCd79eP78eSxYsADW1tYtngVpb2+PBw8eKLU4IiIiecj1kFAjIyOZ8x8/fgxdXV2lFEVERKQIuR4Sevbs2RbnSSQSpKenw9PTU1l1ERERyU1wqC1ZsgSHDx/G5s2bUV5eDuDFHT3+85//YN68ebh27ZrG3b2fiIi0i1wPCS0sLMSmTZsQFRXVNA0AdHV1sXHjRowfP141VRIREQkg10NC//rXv2LGjBlIS0tDbm4uGhsb0bdvX0yZMgW9e/dWVY1ERESCtBlqdXV1yMjIQH5+Pnr06IEJEyZg6dKlHVEbERGRXFoNtZKSEkyaNAl5eXmQSCQAACMjIxw4cADe3t4dUiAREZFQrZ4osnHjRuTn52Pp0qU4cOAAIiMjYWBggI8++qij6iMiIhKs1S21kydPIjAwEBs3bmyaZm1tjQULFuD+/fvo1auXygskIiISqtUttZKSErz++utS00aMGAGJRIKioiKVFkZERCSvVkOtoaEBhoaGUtNevq6trVVdVURERApo8+zH/Px8XLlypel1VVUVAEAsFsPY2LjZ8l5eXkosj4iISLg2Qy0yMhKRkZHNpv/xZBGJRAKRSNR0txEiIqKO1mqoxcbGdlQdRERE7dZqqAUFBam8gPj4eOzYsQMlJSVwcXFBZGQkRo4c2eKyBQUFGDRoULPpycnJGDdunKpLJSKiTk6u22QpW2pqKkJDQ7Ft2zaMGDEC8fHxmDlzJrKysmBvby9zXEpKCgYOHNj02tzcvCPKfaWIdHRwubxR4fG9jHTQ00CixIqIiNqm1lCLjY1FUFAQ5s6dCwDYsmULfvjhB3z11VdYv369zHE9evSAjY1NR5X5Snr0tAGRlx4pPH7rG1boadD8YbJERKok+NEzylZfX4/s7GyMGTNGavqYMWNw8eLFVsfOmTMHTk5OmDBhAg4fPqzKMomISIOobUutrKwMDQ0NsLKykppuZWWF0tLSFscYGxtjw4YNGDFiBLp06YKMjAwEBwcjLi4O/v7+HVE2ERF1Ymrd/QgAIpH0LqqXlwa0xMLCQupBpIMHD0Z5eTliYmJaDTWxWKycYhVQpW+NujpFL1Q3bcdY4NnzZwqPb89YAKh6UgVxWcv/OekI6vydayr2TDHsm2La0zdnZ2eZ89QWahYWFtDV1W22Vfbo0aNmW2+t8fLyQmJiYqvLtNYAVassl8DAoE7h8QYGhm0vJINeFz2Fx7dnLACYdDeBcw9Thce3h1gsVuvvXBOxZ4ph3xSjyr6p7Ziavr4+PD09cerUKanpp06dana/ydbk5OTwpBEiIgKg5t2Py5Ytw6JFi+Dl5YXXX38dX331FYqLixEcHAwAiIiIwJUrV5CWlgYA2LdvH/T09ODh4QEdHR0cPXoU8fHxCA8PV+OnICKizkKtoTZ9+nSUl5djy5YtKCkpwYABA5CUlAQHBwcAQHFxMfLy8qTGbN26FYWFhdDV1YWjoyN27tzJk0Q6ofZc58Zr3IhIUWo/UWTBggVYsGBBi/Pi4uKkXgcFBXXIXU6o/dpznRuvcSMiRantmBoREZGyMdSIiEhrMNSIiEhrMNSIiEhrMNSIiEhrMNSIiEhrMNSIiEhrMNSIiEhrqP3ia6I/au9Ttw2NLZVYDRFpEoYadTrtfer2x4MMlFgNEWkS7n4kIiKtwS010jqGhl1xuVyxGyLzZspEmo2hRlqnvF6CrRcfKjSWN1Mm0mzc/UhERFqDoUZERFqDux+Jfqe9lxPwmByRejHUiH6nvZcTbBttg/s1PEmFSF0YakRKxCd+E6kXQ42ok2jvrk9TQ11U1jYoNJZ3YSFtwVAj6iTau+szbJilwuN5FxbSFhoZavHx8dixYwdKSkrg4uKCyMhIjBw5Ut1lEWms9lywDvB4IHUeGhdqqampCA0NxbZt2zBixAjEx8dj5syZyMrKgr29vbrLI9JI7blgHWjfCTLt2W0KMFBJmsaFWmxsLIKCgjB37lwAwJYtW/DDDz/gq6++wvr165W+vgd1ItyvUfw4x1PFhxJpjPbsOm3PblOgfYEKMBS1jaiiokJjfpv19fXo2bMnvvzyS0ybNq1pekhICG7duoWMjAz1FUdERGqnUXcUKSsrQ0NDA6ysrKSmW1lZobS0VE1VERFRZ6FRofaSSCR9LY9EImk2jYiIXj0aFWoWFhbQ1dVttlX26NGjZltvRET06tGoUNPX14enpydOnTolNf3UqVN4/fXX1VQVERF1Fhp39uOyZcuwaNEieHl54fXXX8dXX32F4uJiBAcHq7s0IiJSM43aUgOA6dOnIzIyElu2bMGoUaOQlZWFpKQkODg4qLs0pYqPj4eHhwdsbGzw5ptv4vz58+ouqdOIjIyEmZmZ1M9rr73WNF8ikSAyMhIuLi74r//6L0yePBk///yzGitWj8zMTAQEBGDAgAEwMzNDYmKi1Hwhfaqrq8OqVavQr18/2NraIiAgAPfv3+/Ij9Gh2urZkiVLmn33xo0bJ7XMq9az7du3489//jPs7e3h6OgIf39/3Lp1S2qZjvyuaVyoAcCCBQuQk5OD0tJS/Pjjj/D29lZ3SUr18gLzlStX4syZMxg+fDhmzpyJwsJCdZfWaTg7O+POnTtNP78P/ZiYGMTGxiI6OhonT56ElZUV3n33XTx58kSNFXe8mpoauLq6IioqCl27dm02X0ifwsLCkJ6eji+//BIZGRl48uQJ/P390dCg+MXSnVlbPQOAt956S+q7d/DgQan5r1rPzp07h/nz5+PYsWNIS0tDly5dMG3aNDx+/LhpmY78rmnUdWqvirFjx8LNzQ07duxomjZkyBBMnTpVJReYa5rIyEikpaXhwoULzeZJJBK4uLhg4cKFCAkJAQA8ffoUzs7O2LBhwyu7m7pXr17YvHkzZs2aBUBYnyorK+Hk5ITY2Fj4+fkBAIqKiuDu7o7k5GSMHTtWbZ+nI/yxZ8CLLbXy8nIcOHCgxTGves8AoLq6Gg4ODkhMTMTEiRM7/LumkVtq2qy+vh7Z2dkYM2aM1PQxY8bg4sWLaqqq88nPz8eAAQPg4eGBefPmIT8/HwBQUFCAkpISqf517doVI0eOZP9+R0ifsrOz8ezZM6ll7Ozs0L9//1e6lxcuXICTkxO8vLzw4Ycf4uHD/7u9GHv2ItQaGxthZmYGoOO/axp3ooi24wXmbRs6dCg+//xzODs749GjR9iyZQt8fHyQlZWFkpISAGixfw8ePFBHuZ2SkD6VlpZCV1cXFhYWzZZ5Vb+L48aNg6+vL3r37o179+5h48aNmDJlCk6fPg0DAwP2DEBoaCjc3d0xfPhwAB3/XWOodVK8wFy28ePHS70eOnQoPD09sW/fPgwbNgwA+yeUIn16lXv53nvvNf3Zzc0Nnp6ecHd3x7FjxzBlyhSZ416Vnq1ZswZZWVk4evQodHV1peZ11HeNux87GV5gLj9jY2O4uLggNzcXNjY2AMD+tUFIn6ytrdHQ0ICysjKZy7zqevbsCVtbW+Tm5gJ4tXsWFhaGlJQUpKWloU+fPk3TO/q7xlDrZHiBufxqa2shFothY2OD3r17w8bGRqp/tbW1uHDhAvv3O0L65OnpCT09Pall7t+/jzt37rCX/19ZWRkePHjQ9A/3q9qz1atXIzk5GWlpaVKX1wAd/13j7sdOiBeYt+7vf/873n77bdjZ2TUdU/vtt98QGBgIkUiEJUuWYNu2bXB2doaTkxO2bt0KIyMjzJgxQ92ld6jq6uqmLYjGxkYUFRXhxo0bMDc3h729fZt9MjU1xZw5c/Dxxx/DysoK5ubmWLt2Ldzc3PDWW2+p8ZOpTms9Mzc3R1RUFKZMmQIbGxvcu3cPn3zyCaysrPDOO+8AeDV7FhISggMHDiAhIQFmZmZNx9CMjIxgbGws6O+kMvvGU/o7qfj4eMTExKCkpAQDBgzAp59+qnXX4ylq3rx5OH/+PMrKymBpaYmhQ4di7dq1cHFxAfBiP3xUVBS+/vprVFRUwMvLC1u3boWrq6uaK+9YZ8+eha+vb7PpgYGBiIuLE9Sn2tparFu3DsnJyaitrcXo0aOxbds22NnZdeRH6TCt9Wz79u2YNWsWbty4gcrKStjY2GDUqFFYu3atVD9etZ69PMvxj1avXo2wsDAAwv5OKqtvDDUiItIaPKZGRERag6FGRERag6FGRERag6FGRERag6FGRERag6FGRERag6FGpGQFBQUtPmCys5k8eTImT56s7jKIlIqhRq+sxMREqScY29jYwMXFBdOnT8f//M//vHIPFVWVL774otMHPGkP3iaLXnmhoaHo27cvnj17htLSUpw7dw5hYWGIjY3F/v37MXDgQHWXqBKHDh3qkPXs3r0b1tbWUg/bJFIVhhq98saOHdv0yBoA+Nvf/oYff/wRAQEBCAwMxE8//YSuXbuqsULV0NfXV3cJRErH3Y9ELXjzzTexatUqFBYWIikpqWn63bt3MW/ePDg6OsLa2hojR45EQkJCm+937949rFy5EsOGDUPPnj3h4OAAf39//Pzzz03LVFVVoWfPnli9enWz8RUVFbC2tsbf//53AC/uUWhmZobk5GRs27YNbm5u6NWrF4KCglBeXo7nz58jIiIC/fv3h62tLebNm4fq6mqp9/zjMbWXxwL/8Y9/YP/+/Rg2bFjTZzx9+rTU2CVLlsDd3b1ZnS936RYUFAAA3N3dIRaLkZmZ2bSb9/fj6uvrsXnzZgwdOhTW1tZ47bXXsGLFClRUVLTZU6KWcEuNSAZ/f3988sknOHnyJObOnYs7d+5gwoQJsLCwwLJly2Bqaorvv/8eH3zwAaqqqrB06VKZ73Xt2jVkZmbC19cXDg4OePDgAf73f/8XkyZNQlZWFmxsbGBiYoJ33nkHqamp2LRpE7p0+b+/nocOHUJ9fT38/f2l3jcmJgb6+vpYvnw5CgsLERcXh6VLl8LW1ha//PILQkJCcPPmTXz99dewtrZGVFRUm5/78OHDKCsrQ3BwMAwNDREXF4fZs2cjJycH5ubmcvUwMjISISEhMDExwcqVKwG8uHs78OImt7Nnz8aZM2cwZ84cuLm5IS8vD7t370Z2dja+//576OnpybU+IoYakQy9evWCiYkJ8vLyALw49vbyuVDdunUDAMyfPx/BwcGIjIzE3Llzm/7B/qPx48dj6tSpUtP8/f3xpz/9Cd988w1CQkIAvLgb/MGDB3Hy5En4+Pg0LZuUlARXV9dmW0d1dXX44YcfmnYlVlRUIDExEd7e3khPT4eOzoudMffv30diYiIiIyPbfJJwXl4erly5AktLSwDAG2+8gdGjRyM5ORkLFy4U1LuX3nnnHURERMDKyqpZICcnJ+P48eM4fPgwRo8e3TTd29sbfn5+SElJQUBAgFzrI+LuR6JWGBsbo7q6GhUVFTh9+jSmTZuGp0+foqysrOln3LhxePLkCa5duybzfV6GIAD89ttvKC8vh6mpKRwdHZGdnd0076233oKtrS0OHDjQNK2goABZWVkt/gMfEBAgdWxs6NChAICgoKCmQAMALy8vPHnyBI8ePWrzM0+bNq0p0ADAw8MDJiYmyM/Pb3OsPA4dOgQnJye4ublJ9dPLywvGxsY4c+aMUtdHrwZuqRG1orq6GpaWlrh79y4kEgmio6MRHR3d4rKtBUZtbS0+/fRTJCUlobi4WGqehYVF0591dHTg5+eHXbt24cmTJ+jevTuSkpIgEolafMjpH581ZWJi0ur0iooKWFlZtfKJAXt7+2bTTE1N8fjx41bHyevu3bsQi8VwdHRscb6QACb6I4YakQz3799HVVUV+vXrh8bGRgDA0qVLpXYL/l5rDyENDQ3F3r178f7772PEiBEwMTGBjo4OwsLCmt77pcDAQPzzn/9Eeno6goKCcPDgQYwePRq2trbN3ldXV7fF9f1+K+33JJK2H58o6z1/P1bWLsyGhoY23/+lxsZGuLi4yDzO16NHD8HvRfQSQ41Ihpe7AMeMGYM+ffoAALp06SL34+UBIDU1FQEBAc3+Aa+oqGj2j3f//v0xZMgQHDhwAC4uLvjPf/6DFStWKPQZVMXMzAyVlZXNpt+7d6/ZNFkB2LdvX2RnZ2P06NEyQ5hIXvwmEbXgxx9/xJYtW9C7d2/4+fnBysoKo0ePxtdff42ioqJmy7e1q0xXV7fZVlJycjIePHjQ4vKBgYE4e/YsYmJiYGRkBF9fX8U/jAr069cPVVVVuH79etO06upqfPvtt82W7datW4un6E+fPh2lpaX44osvms17/vw5T+snhXBLjV55P/zwA3Jzc/H8+XM8fPgQZ86cwalTp2Bvb4/9+/fD0NAQALB9+3ZMmDAB3t7emDt3LhwdHVFWVobr16/j5MmTKCwslLmOiRMn4ttvv0X37t3h6uqKnJwcpKamNm0B/tGMGTOwdu1aHD58GH5+fjA2NlbFR1fYjBkzEBERgdmzZ2Px4sV4/vw5EhISYGlp2Sz0Bw8ejK+//hpRUVFwcnKCkZERJk6cCD8/P6SnpyM0NBSZmZnw9vaGSCRCbm4u0tLSsHHjRrz33ntq+oSkqRhq9Mp7uUtQX18f5ubmcHV1RWRkJGbNmoXu3bs3Lefk5ITTp09j8+bNOHjwIB49egQLCwv0798fGzZsaHMdenp6OHToEBISEuDp6YmUlBSsW7euxeXNzc0xYcIEpKend8rT2s3MzJCQkIC1a9ciPDwcPXv2xJIlS2BiYoJly5ZJLRsaGooHDx7g888/R1VVFezt7TFx4kTo6Ohg79692LVrF/bt24fjx49DX18f9vb28PPzw5/+9Cc1fTrSZKKKioq2jxwTUYebP38+MjMzcfPmTZknbxCRNB5TI+qEysrK8K9//Qt+fn4MNCI5cPcjUSeSn5+PixcvYt++fZBIJFiwYIG6SyLSKAw1ok4kMzMTy5Ytg52dHWJjY+Hg4KDukog0Co+pERGR1uAxNSIi0hoMNSIi0hoMNSIi0hoMNSIi0hoMNSIi0hoMNSIi0hr/D5wH8lbVtsswAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "delay_bins = np.arange(-20, 201, 10)\n",
    "\n",
    "unit = 'minute'\n",
    "\n",
    "fig, ax1 = plt.subplots()\n",
    "\n",
    "ax1.hist(united['Delay'], bins=delay_bins, density=True, alpha=0.8, ec='white')\n",
    "\n",
    "y_vals = ax1.get_yticks()\n",
    "\n",
    "y_label = 'Percent per ' + (unit if unit else 'unit')\n",
    "\n",
    "x_label = 'Delay' + (unit if unit else '(unit)')\n",
    "\n",
    "ax1.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.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The height of the [0, 10) bar is just under 3% per minute, which means that just under 30% of the flights had delays between 0 and 10 minutes. That is confirmed by counting rows: \n",
    "\n",
    "**Notice** the height of the bar depends upon bin size, for bin size the upper limit of 10 in not included hence we are using records where the delay is equal to or greater than 0 and less than 10 i.e. [0,100)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2935985533453888"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "united_delay_between_0_and_10 = united[(united['Delay']>=0) & (united['Delay']<10)]\n",
    "\n",
    "len(united_delay_between_0_and_10)/len(united)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Empirical Distribution of the Sample\n",
    "\n",
    "Let us now think of the 13,825 flights as a population, and draw random samples from it with replacement. It is helpful to package our code into a function. The function `empirical_hist_delay` takes the sample size as its argument and draws an empiricial histogram of the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def empirical_hist_delay(n):\n",
    "    \n",
    "    unit = 'minute'\n",
    "\n",
    "    fig, ax1 = plt.subplots()\n",
    "\n",
    "    ax1.hist(united['Delay'].sample(n), bins=delay_bins, density=True, alpha=0.8, ec='white')\n",
    "\n",
    "    y_vals = ax1.get_yticks()\n",
    "\n",
    "    y_label = 'Percent per ' + (unit if unit else 'unit')\n",
    "\n",
    "    x_label = 'Delay' + (unit if unit else '(unit)')\n",
    "\n",
    "    ax1.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.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we saw with the dice, as the sample size increases, the empirical histogram of the sample more closely resembles the histogram of the population. Compare these histograms to the population histogram above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "empirical_hist_delay(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "empirical_hist_delay(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most consistently visible discrepancies are among the values that are rare in the population. In our example, those values are in the the right hand tail of the distribution. But as the sample size increases, even those values begin to appear in the sample in roughly the correct proportions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "empirical_hist_delay(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convergence of the Empirical Histogram of the Sample\n",
    "What we have observed in this section can be summarized as follows:\n",
    "\n",
    "For a large random sample, the empirical histogram of the sample resembles the histogram of the population, with high probability.\n",
    "\n",
    "This justifies the use of large random samples in statistical inference. The idea is that since a large random sample is likely to resemble the population from which it is drawn, quantities computed from the values in the sample are likely to be close to the corresponding quantities in the population."
   ]
  }
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