solutions/chap06soln.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Examples and Exercises from Think Stats, 2nd Edition\n",
    "\n",
    "http://thinkstats2.com\n",
    "\n",
    "Copyright 2016 Allen B. Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "import brfss\n",
    "\n",
    "import thinkstats2\n",
    "import thinkplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'll start with the data from the BRFSS again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = brfss.ReadBrfss(nrows=None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the mean and standard deviation of female height in cm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(163.22347500412215, 7.269156286641344)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "female = df[df.sex==2]\n",
    "female_heights = female.htm3.dropna()\n",
    "mean, std = female_heights.mean(), female_heights.std()\n",
    "mean, std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`NormalPdf` returns a Pdf object that represents the normal distribution with the given parameters.\n",
    "\n",
    "`Density` returns a probability density, which doesn't mean much by itself."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03328731904744125"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pdf = thinkstats2.NormalPdf(mean, std)\n",
    "pdf.Density(mean + std)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`thinkplot` provides `Pdf`, which plots the probability density with a smooth curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Pdf(pdf, label='normal')\n",
    "thinkplot.Config(xlabel='x', ylabel='PDF', xlim=[140, 186])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Pdf` provides `MakePmf`, which returns a `Pmf` object that approximates the `Pdf`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZIAAAEKCAYAAAA4t9PUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAG55JREFUeJzt3X+QXWWZ4PHvQ+cXy0KMIbhuApMgWCUYidKApbJkYHWJNRBnBBN0B9iiNsLKjuOUbkltwQilteowpY66zgYIEKr4NTAOXSUMrpvRUURMs6IYhDFAKBpYDb8ZNQnNPPvHPQ03N/f27e7b5/78fqq6cu657zl57+nu+/T7Ps95b2QmkiTN1H6d7oAkqbcZSCRJLTGQSJJaYiCRJLXEQCJJaomBRJLUEgOJJKklpQaSiDg1Ih6KiO0R8ek6z8+PiJuK5++JiOXF/vdGxL0RcX/x78lVx3y3OOd9xdchZb4GSdLk5pR14ogYAr4OvBcYA7ZGxEhmPlDV7Dzgucw8IiLWA18A1gFPA6dl5pMR8VbgTmBp1XEfyczRsvouSZq60gIJcDywPTMfAYiIG4G1QHUgWQt8pti+BfhaRERm/qSqzTZgQUTMz8zdM+nIwQcfnMuXL5/JoZI0sO69996nM3NJs3ZlBpKlwONVj8eAExq1yczxiHgBWExlRDLhg8BPaoLI1RHxCnAr8Nlsss7L8uXLGR11ACNJ0xERj02lXZk5kqizr/YNf9I2EXE0lemuj1Y9/5HMXAmcWHz9cd3/PGJDRIxGxOjOnTun1XFJ0tSVGUjGgEOrHi8DnmzUJiLmAAuBZ4vHy4BvAmdn5sMTB2TmE8W/LwHXU5lC20dmbszM4cwcXrKk6chMkjRDZQaSrcCREbEiIuYB64GRmjYjwDnF9hnAlszMiHgd8C3gosy8a6JxRMyJiIOL7bnAHwA/L/E1SJKaKC1HUuQ8LqRScTUEbMrMbRFxGTCamSPAVcB1EbGdykhkfXH4hcARwMURcXGx733Ab4A7iyAyBHwHuKKs1yCpf7z88suMjY2xa9euTnel6yxYsIBly5Yxd+7cGR0fg/B5JMPDw2myXRpsjz76KAceeCCLFy8mol56djBlJs888wwvvfQSK1as2Ou5iLg3M4ebncM72yUNhF27dhlE6ogIFi9e3NJIzUAiaWAYROpr9bqUeR+JpEnctuWn3HTHKLv3vAzA/HlzWbdmmLUnH9PhnknTYyCR2qg2eFTbvedlNt92N5tvu9ugolKsXr2ayy+/nOHhpmmPaTGQSCWbLHg0Uh1UwNGKYHx8nDlzuvMtuzt7JfW4qQaPiQABTNre0Up/2LFjB2vWrOE973kPP/zhD1m6dCm33XYbDz30EOeffz6//e1vedOb3sSmTZtYtGgRq1ev5l3vehd33XUXp59+Ovfffz/7778/Dz74II899hhXX3011157LXfffTcnnHAC11xzDQAXXHABW7du5Xe/+x1nnHEGl156aamvy0AilWCyoNAoEEw8bhaEdu95mZvuGDWQtOCDH//r0s5961fOn/T5X/7yl9xwww1cccUVfOhDH+LWW2/li1/8Il/96lc56aSTuOSSS7j00kv58pe/DMDzzz/P9773PQDOPfdcnnvuObZs2cLIyAinnXYad911F1deeSXHHXcc9913H6tWreJzn/scr3/963nllVc45ZRT+NnPfsbb3va20l6zgUQqQW0QmM4oYu3Jx+zVrl5gmc40mbrLihUrWLVqFQDHHnssDz/8MM8//zwnnXQSAOeccw5nnnnmq+3XrVu31/GnnXYaEcHKlSt5wxvewMqVKwE4+uij2bFjB6tWreLmm29m48aNjI+P89RTT/HAAw8YSKRuN9kootlfqM1UB5bqv6Q/+PG/dpqrB82fP//V7aGhIZ5//vlJ2x9wwAF1j99vv/32Otd+++3H+Pg4jz76KJdffjlbt25l0aJFnHvuuaXfzW8gkWZBoyAyf97MlpxoZP68ufuMTJzmmr5Wg/tsWrhwIYsWLeL73/8+J554Itddd92ro5OZePHFFznggANYuHAhv/rVr7jjjjtYvXr17HW4DgOJNAsaBZGJRPpsWbdm2GmuPnTttde+mmw//PDDufrqq2d8rmOOOYa3v/3tHH300Rx++OG8+93vnsWe1udaW9IMNZrOatdfu7UJY6e5JveLX/yCt7zlLZ3uRteqd31ca0sqWb0gMttTWZOp/b8mprmkdjOQSDPUqDKrXdatGa4bTKR2M0cizYJOJG8bVXOpscx04cY6Wk1xGEikaZjJciftZllwfQsWLOCZZ55xKfkaE59HsmDBghmfw0AiTUOn8yKNWBbc3LJlyxgbG2Pnzp2d7krXmfiExJkykEjT0Om8SCOWBTc3d+7cfT4BULPDQCLNUDfd1Ga+RJ1kIJGa6IW8SCMTQcWcicpk+a/URLfmRRqp1zfvMVGZDCRSE92aF2mk3v0lYM5E5XFqS5qGbsqLNFK7DL05E5XNEYkkqSWOSKQ6ejnBPhlvVlQZHJFIdfRagn0yLu6oshlIpDp6LcE+GRd3VNmc2pKa6IUE+2S8WVFlc0QiSWqJIxKp0K8J9kZMvGu2OCKRCv2UYG/ExLvKYCCRCv2UYG/ExLvKUOrUVkScCnwFGAKuzMzP1zw/H9gMHAs8A6zLzB0R8V7g88A8YA/wqczcUhxzLHANsD9wO/DxbPXjvaQavZ5gb8TEu8pQ2ogkIoaArwNrgKOAsyLiqJpm5wHPZeYRwJeALxT7nwZOy8yVwDnAdVXHfAPYABxZfJ1a1muQJDVX5tTW8cD2zHwkM/cANwJra9qsBa4ttm8BTomIyMyfZOaTxf5twIKImB8RbwQOysy7i1HIZuADJb4GSVITZU5tLQUer3o8BpzQqE1mjkfEC8BiKiOSCR8EfpKZuyNiaXGe6nMune2OazAMWpXWZKzgUivKHJFEnX21uYxJ20TE0VSmuz46jXNOHLshIkYjYtTPaFY9jYJIv1VqNWIFl2ZLmYFkDDi06vEy4MlGbSJiDrAQeLZ4vAz4JnB2Zj5c1b76E+rrnROAzNyYmcOZObxkyZIWX4r6UaMg0m+VWo1YwaXZUubU1lbgyIhYATwBrAc+XNNmhEoy/W7gDGBLZmZEvA74FnBRZt410Tgzn4qIlyLincA9wNnAV0t8DRoQ/VqlNRkruDRbShuRZOY4cCFwJ/AL4ObM3BYRl0XE6UWzq4DFEbEd+DPg08X+C4EjgIsj4r7i65DiuQuAK4HtwMPAHWW9BklSc6XeR5KZt1O516N63yVV27uAM+sc91ngsw3OOQq8dXZ7KkmaKdfa0kCxUqs5K7g0XS6RooEyCOtpzYQVXGqFgUQDZRDW05oJK7jUCqe2NLAGsVKrESu41ApHJJKklhhIJEktcWpLfc9KrZmzgktT4YhEfc9KremxgkvTZSBR37NSa3qs4NJ0ObWlgWKlVnNWcGm6HJFIklpiIJEktcRAIklqiTkS9SVLfmffRL7EcmDVckSivmTJ7+yod80sB1YtA4n6kiW/s6NeKTBYDqy9ObWlvmfJ78xVlwKD5cCqzxGJJKklBhJJUksMJJKklpgjUd+w5Le9XBlYExyRqG9Y8ls+VwZWPQYS9Q1LfsvnysCqx6kt9SVLfsvhysCqxxGJJKklBhJJUksMJJKklpgjUU+z5Lc7WAo82ByRqKdZ8ts5lgJrgoFEPc2S386xFFgTnNpS37Dkt70sBdYERySSpJYYSCRJLSk1kETEqRHxUERsj4hP13l+fkTcVDx/T0QsL/Yvjoh/iIh/joiv1Rzz3eKc9xVfh5T5GiRJkystRxIRQ8DXgfcCY8DWiBjJzAeqmp0HPJeZR0TEeuALwDpgF3Ax8Nbiq9ZHMtPykAFkuW/3sxR48JQ5Ijke2J6Zj2TmHuBGYG1Nm7XAtcX2LcApERGZ+ZvM/AGVgCK9qlEQseS3sywFHmxlBpKlwONVj8eKfXXbZOY48AKweArnvrqY1ro4IqJeg4jYEBGjETG6c+fO6fdeXalRELHkt7MsBR5sZZb/1nuDzxm0qfWRzHwiIg4EbgX+GNi8z0kyNwIbAYaHh5udUz3Ict/uYSnwYCtzRDIGHFr1eBnwZKM2ETEHWAg8O9lJM/OJ4t+XgOupTKFJkjqkzECyFTgyIlZExDxgPTBS02YEOKfYPgPYkpkNRw8RMSciDi625wJ/APx81nsuSZqy0qa2MnM8Ii4E7gSGgE2ZuS0iLgNGM3MEuAq4LiK2UxmJrJ84PiJ2AAcB8yLiA8D7gMeAO4sgMgR8B7iirNcgSWqu1CVSMvN24PaafZdUbe8Czmxw7PIGpz12tvqn3mDJb++yFHgweGe7up4r/PYWS4EHj4FEXc8VfnuLpcCDx9V/1VMs+e1+lgIPHkckkqSWGEgkSS0xkEiSWmIgkSS1xGS7upL3jvQf7ynpX45I1JW8d6Q/eE/JYDCQqCt570h/8J6SweDUlrqe9470Lu8pGQyOSCRJLZk0kETEt6u2Lyq/O5KkXtNsRLKkarvuKr2SpMHWLEfiR9SqbSz5HRwT+RLLgftDs0ByeESMUPls9YntV2Xm6aX1TAPHkt/+Nn/e3H2+vxPlwAaS3tYskKyt2r68zI5Ilvz2t3Vrhuv+seAItPdNGkgy83sT2xGxpNi3s+xOSZb89p/qUmCwHLifNKvaioj484h4GngQ+KeI2BkRl0x2nCRpcDSr2vpT4D3AcZm5ODMXAScA746IT5TeO0lS12sWSM4GzsrMRyd2ZOYjwH8snpMkDbhmyfa5mfl07c7M3BkRltOoZZb8ClwZuNc1G5HsmeFz0pRY8ju4XBm4fzQLJMdExIsR8VLx9eLEY2BlOzqo/mbJ7+ByZeD+0az8d6hdHZEs+R0srgzcPyYNJBGxADgfOAL4GbApM8fb0TFJUm9oNrV1LTAM3A+8H/jL0nskSeopzaq2jsrMlQARcRXw4/K7JEnqJc0CyauZr8wcj4iSu6N+Z7mvmrEUuPdMtWprolLrbVVVXC+2o4PqL42CiCW/g81S4N42aSDJzKHMPKj4OjAz51RtH9SuTqp/NAoilvwONkuBe1uzqS2pNJb7aoKlwL2t2dRWSyLi1Ih4KCK2R8Sn6zw/PyJuKp6/JyKWF/sXR8Q/RMQ/R8TXao45NiLuL475qzBxI0kdVVogiYgh4OvAGuAo4KyIOKqm2XnAc5l5BPAl4AvF/l3AxcAn65z6G8AG4Mji69TZ770kaarKnNo6HtherBZMRNxI5RMXH6hqsxb4TLF9C/C1iIjM/A3wg4g4ovqEEfFG4KDMvLt4vBn4AHBHia9DLbJSSzNlBVdvKHNqaynweNXjsWJf3TbFHfMvAIubnHOsyTnVZVyYUdNhBVfvKTOQ1Mtd5AzazKh9RGyIiNGIGN25008H7iQXZtR0WMHVe8qc2hoDDq16vAx4skGbsYiYAywEnm1yzmVNzglAZm4ENgIMDw9PFpzURlZqqRkruHpPmSOSrcCREbEiIuYB64GRmjYjwDnF9hnAlsxs+KafmU8BL0XEO4tqrbOB22a/65KkqSptRFIsqXIhcCcwRGXl4G0RcRkwmpkjwFXAdRGxncpIZP3E8RGxAzgImBcRHwDel5kPABcA1wD7U0mym2iXpA4q9YbEzLwduL1m3yVV27uAMxscu7zB/lHgrbPXS0lSK7yzXaWw5FezzVLg7lXqne0aXJb8ajZYCtwbDCQqhSW/mg2WAvcGp7ZUOkt+NVOWAvcGRySSpJYYSCRJLXFqS7PGSi21ixVc3cURiWaNlVoqkxVc3ctAolljpZbKZAVX93JqS6WwUkuzzQqu7uWIRJLUEgOJJKklTm2pJVZqqdMmprms4uocRyRqiZVa6oR6P2NWcXWOgUQtsVJLnVCvggus4uoUp7Y0a6zUUrtUV3CBVVyd5ohEktQSRySaNhPs6mYun9J+jkg0bSbY1W1cPqWzDCSaNhPs6jYun9JZTm2pJSbY1Q1cPqWzHJFIklpiIJEktcSpLTVllZZ6lRVc7eGIRE01CiJWaqkbWcHVfgYSNdUoiFippW5kBVf7ObWlabFKS93OCq72c0QiSWqJIxLVZYJd/cbEe3kckagul0FRPzDx3h4GEtXlMijqBybe28OpLTVlgl29ysR7e5QaSCLiVOArwBBwZWZ+vub5+cBm4FjgGWBdZu4onrsIOA94BfiTzLyz2L8DeKnYP56Z/pk8S8yLaFCYL5ldpU1tRcQQ8HVgDXAUcFZEHFXT7Dzgucw8AvgS8IXi2KOA9cDRwKnA/yzON+H3M3OVQWR2mRdRPzNfUp4ycyTHA9sz85HM3APcCKytabMWuLbYvgU4JSKi2H9jZu7OzEeB7cX5VCLzIupn5kvKU+bU1lLg8arHY8AJjdpk5nhEvAAsLvb/qObYpcV2At+OiAT+V2ZuLKHvA8+8iPqN+ZLylBlIos6+nGKbyY59d2Y+GRGHAP87Ih7MzH/c5z+P2ABsADjssMOm3mtJ0rSUGUjGgEOrHi8DnmzQZiwi5gALgWcnOzYzJ/79dUR8k8qU1z6BpBipbAQYHh6uDWAqmGDXoJsYnZh8n7kycyRbgSMjYkVEzKOSPB+paTMCnFNsnwFsycws9q+PiPkRsQI4EvhxRBwQEQcCRMQBwPuAn5f4GvqeCXYNono/4ybfZ660QJKZ48CFwJ3AL4CbM3NbRFwWEacXza4CFkfEduDPgE8Xx24DbgYeAP4e+FhmvgK8AfhBRPwU+DHwrcz8+7JewyAwwa5BVC/xDibfZyoqA4D+Njw8nKOj/qVRT3XS0QS7BpW/B/VFxL1Tuc3CO9sHkHkRqTFvVpw+19oaQOZFpL15s2JrDCQDyLyItDdvVmyNU1sDzvlgyZsVW2UgGRDmRaTpM18yNU5tDQjzItLUmC+ZPgPJgDAvIk2N+ZLp8z6SPjXZVJZ5EWlqavMlgzbNNdX7SByR9KlGQcTpLGnqnOaaGgNJn2oURJzOkqbOaa6pcWqrjzSaznIqS2rdIE5zObU1gKzMksrjNFdjBpI+YmWWVB6nuRpzaqvHOZ0ltd+gTHM5tTUgnM6S2s9prr0ZSHqc01lS+znNtTentnqQ01lS96i3yGO/THU5tdXHnM6Suoef/+7qvz1jsiVPnM6SOmfdmuG6v5u797w8MKsHG0h6RKNRyPV/cV6HeiQJ9v4sE4APf+qqvX5XJ0YnBhJ1hKMQqffUG6H0++jEQNLFHIVIvad6hDIooxMDSRdp9imGjkKk3jIooxMDSReZbBrLUYjUewZldGIg6TBHIdJg6OfRiTckdsBUgocjEKl/1Y5OqnVTUPGGxC7mCEQabPWWWJnQizczOiJpk6mU8nbDXyCS2muq09udeH+Y6ojEQFIip7AkTcdkU17Q/qAy1UBisn0WNQsc1ZzCklSr0XIrE3bveZnNt93N5tvu7qqZDEckLZpJ8OiGb7yk7jfV95ey3luc2qoyG4FkOgGjmsFD0mzoxHtQVwSSiDgV+AowBFyZmZ+veX4+sBk4FngGWJeZO4rnLgLOA14B/iQz75zKOeuZTiCZ6TdrgoFDUtlafZ+Cqb1XdTyQRMQQ8E/Ae4ExYCtwVmY+UNXmvwBvy8zzI2I98IeZuS4ijgJuAI4H/i3wHeDNxWGTnrOeyQJJu74hklSGMt/DuiHZfjywPTMfKTp0I7AWqH7TXwt8pti+BfhaRESx/8bM3A08GhHbi/MxhXNOy3S+AQYMSd2mdhn7alMNMq0u11JmIFkKPF71eAw4oVGbzByPiBeAxcX+H9Ucu7TYbnbOafG+Dkn9qlGQqRdgWhnRlBlIos6+2nm0Rm0a7a93J37dubmI2ABsADjssMMa97KKn3kuaRBUB5h6nzk/XWUukTIGHFr1eBnwZKM2ETEHWAg8O8mxUzknAJm5MTOHM3N4yZIlLbwMSdJkyky2z6GSGD8FeIJKYvzDmbmtqs3HgJVVyfY/yswPRcTRwPW8lmz/P8CRVEYqk56znm5YIkWSek3Hk+1FzuNC4E4qpbqbMnNbRFwGjGbmCHAVcF2RTH8WWF8cuy0ibqaSRB8HPpaZrwDUO2dZr0GS1Jw3JEqS6nIZeUlSWxhIJEktMZBIklpiIJEktcRAIklqyUBUbUXES8BDne5HFzsYeLrTnehyXqPmvEbN9do1+r3MbHpH96B8QuJDUylhG1QRMer1mZzXqDmvUXP9eo2c2pIktcRAIklqyaAEko2d7kCX8/o05zVqzmvUXF9eo4FItkuSyjMoIxJJUkl6PpBExKaI+HVE/LzOc5+MiIyIg4vHERF/FRHbI+JnEfGO9ve4/epdo4j4TEQ8ERH3FV/vr3ruouIaPRQR/6EzvW6vRj9HEfFfi+uwLSK+WLXfa1TZd1PVz9COiLiv6jmvUWXfqoj4UXGNRiPi+GJ//7wfZWZPfwH/DngH8POa/YdSWW7+MeDgYt/7gTuofK7JO4F7Ot3/Tl0j4DPAJ+u0PQr4KTAfWAE8DAx1+jV06Br9PvAdYH7x+BCv0b6/a1XP/yVwiddon5+jbwNriu33A9+t2u6L96OeH5Fk5j9S+SyTWl8C/ht7fxTvWmBzVvwIeF1EvLEN3eyoSa5RPWuBGzNzd2Y+Cmyn8gFjfa3BNboA+Hxm7i7a/LrY7zWqEREBfAi4odjlNaraDRxUbC/ktU917Zv3o54PJPVExOnAE5n505qnlgKPVz0eK/YNqguLIfWmiFhU7PMavebNwIkRcU9EfC8ijiv2e432dSLwq8z8ZfHYa/SaPwX+IiIeBy4HLir298016rtAEhH/CvjvwCX1nq6zb1DL1r4BvAlYBTxFZVoCvEbV5gCLqEw7fAq4ufjL22u0r7N4bTQCXqNqFwCfyMxDgU9Q+WRY6KNr1HeBhMqb4wrgpxGxA1gG/N+I+DdUIv6hVW2X8dowc6Bk5q8y85XM/BfgCl6bdvAavWYM+Nti6uHHwL9QWSvJa1QlIuYAfwTcVLXba/Sac4C/Lbb/hj78Xeu7QJKZ92fmIZm5PDOXU/lmvSMz/x8wApxdVEu8E3ghM5/qZH87pWYu9g+BiSqTEWB9RMyPiBXAkcCP292/LvF3wMkAEfFmYB6VBfe8Rnv798CDmTlWtc9r9JongZOK7ZOBiem/vnk/6vlFGyPiBmA1cHBEjAF/nplXNWh+O5VKie3Ab4H/1JZOdli9awSsjohVVIbSO4CPAmTmtoi4GXgAGAc+lpmvdKLf7dTgGm0CNhWlnHuAc7JSbuM12vt3bT17T2v5c7T3z9F/Br5SjNx2ARuK5n3zfuSd7ZKklvTd1JYkqb0MJJKklhhIJEktMZBIklpiIJEktcRAIklqiYFEktQSA4nUZhFxXLFY5oKIOKD4rJO3drpf0kx5Q6LUARHxWWABsD8wlpn/o8NdkmbMQCJ1QETMA7ZSWTLjXYOwfIj6l1NbUme8HvjXwIFURiZSz3JEInVARIwAN1L5yIM3ZuaFHe6SNGM9v/qv1Gsi4mxgPDOvj4gh4IcRcXJmbul036SZcEQiSWqJORJJUksMJJKklhhIJEktMZBIklpiIJEktcRAIklqiYFEktQSA4kkqSX/H97wQtnAwrgsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf = pdf.MakePmf()\n",
    "thinkplot.Pmf(pmf, label='normal')\n",
    "thinkplot.Config(xlabel='x', ylabel='PDF', xlim=[140, 186])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you have a `Pmf`, you can also plot it using `Pdf`, if you have reason to think it should be represented as a smooth curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Pdf(pmf, label='normal')\n",
    "thinkplot.Config(xlabel='x', ylabel='PDF', xlim=[140, 186])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using a sample from the actual distribution, we can estimate the PDF using Kernel Density Estimation (KDE).\n",
    "\n",
    "If you run this a few times, you'll see how much variation there is in the estimate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Pdf(pdf, label='normal')\n",
    "\n",
    "sample = np.random.normal(mean, std, 500)\n",
    "sample_pdf = thinkstats2.EstimatedPdf(sample, label='sample')\n",
    "thinkplot.Pdf(sample_pdf, label='sample KDE')\n",
    "thinkplot.Config(xlabel='x', ylabel='PDF', xlim=[140, 186])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Moments\n",
    "\n",
    "Raw moments are just sums of powers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def RawMoment(xs, k):\n",
    "    return sum(x**k for x in xs) / len(xs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first raw moment is the mean.  The other raw moments don't mean much."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(163.22347500412215, 26694.74321809659, 4374411.46250422)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RawMoment(female_heights, 1), RawMoment(female_heights, 2), RawMoment(female_heights, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "163.22347500412215"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def Mean(xs):\n",
    "    return RawMoment(xs, 1)\n",
    "\n",
    "Mean(female_heights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The central moments are powers of distances from the mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def CentralMoment(xs, k):\n",
    "    mean = RawMoment(xs, 1)\n",
    "    return sum((x - mean)**k for x in xs) / len(xs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first central moment is approximately 0.  The second central moment is the variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-9.903557940122168e-14, 52.84042567529328, -46.88569506887073)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CentralMoment(female_heights, 1), CentralMoment(female_heights, 2), CentralMoment(female_heights, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "52.84042567529328"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def Var(xs):\n",
    "    return CentralMoment(xs, 2)\n",
    "\n",
    "Var(female_heights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The standardized moments are ratios of central moments, with powers chosen to make the dimensions cancel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def StandardizedMoment(xs, k):\n",
    "    var = CentralMoment(xs, 2)\n",
    "    std = np.sqrt(var)\n",
    "    return CentralMoment(xs, k) / std**k"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The third standardized moment is skewness."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.3624108479155668e-14, 1.0, -0.1220649274510512)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "StandardizedMoment(female_heights, 1), StandardizedMoment(female_heights, 2), StandardizedMoment(female_heights, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.1220649274510512"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def Skewness(xs):\n",
    "    return StandardizedMoment(xs, 3)\n",
    "\n",
    "Skewness(female_heights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normally a negative skewness indicates that the distribution has a longer tail on the left.  In that case, the mean is usually less than the median."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Median(xs):\n",
    "    cdf = thinkstats2.Cdf(xs)\n",
    "    return cdf.Value(0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But in this case the mean is greater than the median, which indicates skew to the right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(163.22347500412215, 163.0)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Mean(female_heights), Median(female_heights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because the skewness is based on the third moment, it is not robust; that is, it depends strongly on a few outliers.  Pearson's median skewness is more robust."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def PearsonMedianSkewness(xs):\n",
    "    median = Median(xs)\n",
    "    mean = RawMoment(xs, 1)\n",
    "    var = CentralMoment(xs, 2)\n",
    "    std = np.sqrt(var)\n",
    "    gp = 3 * (mean - median) / std\n",
    "    return gp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pearson's skewness is positive, indicating that the distribution of female heights is slightly skewed to the right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0922289055190516"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PearsonMedianSkewness(female_heights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Birth weights\n",
    "\n",
    "Let's look at the distribution of birth weights again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "import first\n",
    "\n",
    "live, firsts, others = first.MakeFrames()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on KDE, it looks like the distribution is skewed to the left."
   ]
  },
  {
   "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": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "birth_weights = live.totalwgt_lb.dropna()\n",
    "pdf = thinkstats2.EstimatedPdf(birth_weights)\n",
    "thinkplot.Pdf(pdf, label='birth weight')\n",
    "thinkplot.Config(xlabel='Birth weight (pounds)', ylabel='PDF')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean is less than the median, which is consistent with left skew."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7.265628457623368, 7.375)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Mean(birth_weights), Median(birth_weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And both ways of computing skew are negative, which is consistent with left skew."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5895062687577989, -0.23300028954731833)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Skewness(birth_weights), PearsonMedianSkewness(birth_weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adult weights\n",
    "\n",
    "Now let's look at adult weights from the BRFSS.  The distribution looks skewed to the right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "adult_weights = df.wtkg2.dropna()\n",
    "pdf = thinkstats2.EstimatedPdf(adult_weights)\n",
    "thinkplot.Pdf(pdf, label='Adult weight')\n",
    "thinkplot.Config(xlabel='Adult weight (kg)', ylabel='PDF')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean is greater than the median, which is consistent with skew to the right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(78.99245299687198, 77.27)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Mean(adult_weights), Median(adult_weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And both ways of computing skewness are positive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.054840012109306, 0.2643673381618039)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Skewness(adult_weights), PearsonMedianSkewness(adult_weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distribution of income is famously skewed to the right. In this exercise, we’ll measure how strong that skew is.\n",
    "The Current Population Survey (CPS) is a joint effort of the Bureau of Labor Statistics and the Census Bureau to study income and related variables. Data collected in 2013 is available from http://www.census.gov/hhes/www/cpstables/032013/hhinc/toc.htm. I downloaded `hinc06.xls`, which is an Excel spreadsheet with information about household income, and converted it to `hinc06.csv`, a CSV file you will find in the repository for this book. You will also find `hinc2.py`, which reads this file and transforms the data.\n",
    "\n",
    "The dataset is in the form of a series of income ranges and the number of respondents who fell in each range. The lowest range includes respondents who reported annual household income “Under \\$5000.” The highest range includes respondents who made “\\$250,000 or more.”\n",
    "\n",
    "To estimate mean and other statistics from these data, we have to make some assumptions about the lower and upper bounds, and how the values are distributed in each range. `hinc2.py` provides `InterpolateSample`, which shows one way to model this data. It takes a `DataFrame` with a column, `income`, that contains the upper bound of each range, and `freq`, which contains the number of respondents in each frame.\n",
    "\n",
    "It also takes `log_upper`, which is an assumed upper bound on the highest range, expressed in `log10` dollars. The default value, `log_upper=6.0` represents the assumption that the largest income among the respondents is $10^6$, or one million dollars.\n",
    "\n",
    "`InterpolateSample` generates a pseudo-sample; that is, a sample of household incomes that yields the same number of respondents in each range as the actual data. It assumes that incomes in each range are equally spaced on a `log10` scale."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def InterpolateSample(df, log_upper=6.0):\n",
    "    \"\"\"Makes a sample of log10 household income.\n",
    "\n",
    "    Assumes that log10 income is uniform in each range.\n",
    "\n",
    "    df: DataFrame with columns income and freq\n",
    "    log_upper: log10 of the assumed upper bound for the highest range\n",
    "\n",
    "    returns: NumPy array of log10 household income\n",
    "    \"\"\"\n",
    "    # compute the log10 of the upper bound for each range\n",
    "    df['log_upper'] = np.log10(df.income)\n",
    "\n",
    "    # get the lower bounds by shifting the upper bound and filling in\n",
    "    # the first element\n",
    "    df['log_lower'] = df.log_upper.shift(1)\n",
    "    df.loc[0, 'log_lower'] = 3.0\n",
    "\n",
    "    # plug in a value for the unknown upper bound of the highest range\n",
    "    df.loc[41, 'log_upper'] = log_upper\n",
    "    \n",
    "    # use the freq column to generate the right number of values in\n",
    "    # each range\n",
    "    arrays = []\n",
    "    for _, row in df.iterrows():\n",
    "        vals = np.linspace(row.log_lower, row.log_upper, row.freq)\n",
    "        arrays.append(vals)\n",
    "\n",
    "    # collect the arrays into a single sample\n",
    "    log_sample = np.concatenate(arrays)\n",
    "    return log_sample\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "import hinc\n",
    "income_df = hinc.ReadData()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/downey/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:26: DeprecationWarning: object of type <class 'numpy.float64'> cannot be safely interpreted as an integer.\n"
     ]
    }
   ],
   "source": [
    "log_sample = InterpolateSample(income_df, log_upper=6.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fFvHi8vej9oxpGhpb4tfo2Sozu87MVphZafhTYGbXtkRxIu3Z7CcLopN6Jx8/iGOPOjzReqR9aHBPIVz5f5tgaOsVBOcWTgF+YWa4+z3xlyjS/qzfuI1XXv8gas+YOjbBaqQ9aWxP4WvA59x9kbvvdPcd7r4QuDR8T0Ri8MC8uuEsxo4YwtDB/RKsRtqTxkIh393XpU8Mp+XHUZBIe/fuh5+y9K11UfvKqTqXIC2nsVDYfZDvichBcHfufrRuaOyJpwzlqIF9EqxI2pvGLkk93szerGe6AUfHUI9Iu7bkjbW8t24TAFlZHbj6Qg2NLS2rsVAYBRwGbEibPhjYGEtFIu1UVVU19z3+atSeOmkEh/XWUVppWY0dPvo1UOzu61N/gLLwPRFpJs+88g6fbNkJQJfcjlz22VMSrkjao8ZCYYi773P4yN0LgCGxVCTSDpXt3sODTy2P2peefwp5XXMTrEjaq8ZCoaHfys7NWYhIe/bowtcp3hVcu9GnZzemnTEi4YqkvWosFJaZ2ZfSJ5rZjcDyevqLyAHavrOURxe+EbWvumAcHXMaO90nEo/GfvO+DfzDzK6mLgTGAB2Bz8VZmEh7cd/jS6msqgZgyBF9OGPMsIQrkvassQHxNgGnmdlZQO3+7BPhXc0icojeX7+J55bWPUDn2ukTNDS2JKpJ+6juvghYFHMtIu2Ku/Onh1+K2mNHDGHUsQMTrEikCaOkikg8Fhe8z/vrNwPBjWrXXXJqwhWJKBREElFeUcm9c5dE7Ysnj6R/3+4JViQSUCiIJODhp1dQVFwGQM/8Llx6vm5Uk9Yh1lAwsylmttrM1pjZ9xvod5mZuZlpOEjJeJ9s2cmji+ouQb3movF0zu2YYEUidWILBTPLAm4FpgInADPN7IR6+uUB3wReTX9PJBPd8+grVFfXADBscD/OHDs84YpE6sS5pzAOWOPuH7r7HuABYHo9/X4K/A9QHmMtIq3CG6sL93pWwg2fn6hLUKVViTMUjmDv0VULw2kRMzsZGOTuj8dYh0irUFlZzZ0PvRC1zxw7nOFDDkuwIpF9xRkK9W3+ePSmWQeCkVa/2+gHmc0yswIzK9iyZUszlijSch5+dgUbw1FQczvlcM1F4xOuSGRfcYZCITAopT2QvZ/BkEdwl/RzZrYOmADMre9ks7vf4e5j3H1M3759YyxZJB4fb97B3595LWpfc9F4enXvmmBFIvWLMxSWAcPM7Cgz6wjMAObWvunuO929j7sPcfchwBLg4nBYbpGM4e7cPntxdHJ56JH9+OzEfa65EGkVYgsFd68CbgLmA+8AD7r7SjO72cwujut7RVqb55a+x8o1wU5yBzO+cuUZdOigW4SkdYp1fF53nwfMS5v24/30nRxnLSJJKN61m7seeTlqXzh5JEcN7JNgRSIN0+aKSIzufnQJu8oqgODhOVdO1f2Z0ropFERi8vb7H+81LPaXLj+d3E45CVYk0jiFgkgMKiuruX324qg9YdTRjDlxcIIViTSNQkEkBnOeqbsnoXNuR268dGLCFYk0jUJBpJmtLdy61z0JV184TvckSJuhUBBpRlVV1fz2vkXU1AT3JBx39OFMmXRiwlWJNJ1CQaQZPfzMa6zfuA2AnOwsvj5zsga8kzZFoSDSTNZv3Macp1dE7asuHMeAfj0SrEjkwCkURJpB+mGj4UMO48IzP5NwVSIHTqEg0gweWfgGawu3ApCdncXXr5qsoSykTdJvrcghWr9xOw8+VTeO48xpYxl4WM8EKxI5eAoFkUNQXV3Drfcv2msE1Ismj0y4KpGDp1AQOQSPLnyDDzYED37KyurATVefRVaW/ltJ26XfXpGDtH7jNmanHDa6cuoYBh2uw0bStikURA5CeUUlv7rrWaqqqgE4ZlBfLjn7pISrEjl0CgWRg/Cnh1+icFMRENyk9o1rztZhI8kI+i0WOUAvFLzPwlffjdpfunySDhtJxlAoiByAjZt3cFvKkNiTRg/l7PHHJViRSPNSKIg0UWVlNb+6+1kq9lQCcHiffL5yxRka20gyikJBpInumftKdNdyVlYHvnv9eXTO7ZhwVSLNS6Eg0gRL31rHvMVvR+3rpp/K0YP6JliRSDwUCiKN2LK9hN/dtyhqjx0xhGlnjEiwIpH4KBREGlBdXcOv71lA6e4KAHr36MrXr9IzEiRzKRREGjD7yQJWr/0UgA5mfOe688jrmptwVSLxUSiI7Meyt9fx92fqHppz5bSxHHf04QlWJBI/hYJIPdYWbuXXdy/Aw/bI4QO59LyTE61JpCUoFETSbNuxi5/dPi+6H6Ffrzy+fe05Oo8g7YJCQSRFeUUl/3XHUxQVlwHQJbcjP/zyNLrndU64MpGWoVAQCdXU1PDru59l3cfBDWodOnTgezecr3GNpF1RKIiE7nrkFQpWro/aX77idEYeOzDBikRankJBBHjqhZU88fxbUfuSc07i3FOPT7AikWTEGgpmNsXMVpvZGjP7fj3vf8fMVpnZm2a2wMwGx1mPSH1WrPqIO+e8ELUnjDyKay4an2BFIsmJLRTMLAu4FZgKnADMNLMT0rq9Boxx95HAHOB/4qpHpD7rN27jl395Jrr09JhBffnmF87WlUbSbsW5pzAOWOPuH7r7HuABYHpqB3df5O5lYXMJoAO40mK27yzd69LTPj278YNZU+nUMSfhykSSE2coHAFsSGkXhtP250bgyfreMLNZZlZgZgVbtmxpxhKlvarYU8l///Eptu0oBSC3Uw4/nDWVnvldEq5MJFlxhkJ9+99ezzTM7BpgDPCL+t539zvcfYy7j+nbV8MVy6Gpqqrm/+5ZwAcbgg2MDmb8yxfPZ/CA3glXJpK87Bg/uxAYlNIeCGxM72Rm5wL/DzjT3StirEeE8opKfvmXp3ntnbqd2BsvncTJxw9q4G+JtB9xhsIyYJiZHQV8DMwArkrtYGYnA7cDU9x9c4y1iFBSWs7Pbp/H++vrftUuPmsUU04/McGqRFqX2ELB3avM7CZgPpAF/NndV5rZzUCBu88lOFzUDXgovNrjI3e/OK6apP3aWrSLn972BIWbiqJpl51/CjOmjU2wKpHWJ849Bdx9HjAvbdqPU16fG+f3iwBs+LSIn972eHRS2YAbLp3ItDM+k2xhIq1QrKEgkrT31m3iZ7fPY1dZcLoqK6sD37z6bCaNHppwZSKtk0JBMtaKVR/xiz8/zZ7KKgA6dczh3/7ps4zSeEYi+6VQkIy0uOA9fnvfc9TU1ACQ1zWXH315GkMH90u4MpHWTaEgGeexRW9y1yMvR+2+PfP4969dwBH9eiRYlUjboFCQjOHu3PfYq/xjwevRtEH9e/HvX5lG7x7dEqxMpO1QKEhGqK6u4Q+zF7Pw1XejaccedTg/nDWVbl06JViZSNuiUJA2b09lFb+661mWvb0umjb6hMH8yw3n0TFHv+IiB0L/Y6RNe/fDT/nD7OfZ8GndTWlnjT+Wr155JllZeoaUyIFSKEibVLq7gvseW8rTL63ca5TFS845iWsuGq/nIYgcJIWCtCnuzpI31vKnh1+kqLgsmt6pYw7XTZ/AZydpHCORQ6FQkDZjy/YS7pzzIgUr1+81ffQJg/nS5ZPo2ysvocpEModCQVq9mpoa5i1+m/ufWBY9JQ2gR14Xbrh0IqeddLQOF4k0E4WCtGprC7dy2wPPRw/EqXXeacfzhYsn0LWzLjcVaU4KBWmVyisqmf1kAY8/9yY1XncqeeBhPfnqjDM57ujDE6xOJHMpFKTVWbHqI+548AW2FJVE07Kzs7j0vJP5/Lknk52dlWB1IplNoSCtxo6SMv7895d5acWavaafOHQAX77yDI1dJNICFAqSOHdn4avvcvcjSyjdXfeY7m5dOnHd9FM5a/yxOpEs0kIUCpKowk1F3D57Mas++GSv6aePHsYXP3ca3fM6J1SZSPukUJAWVVlZzXvrN7FyzUZWrtnIOx9+SnV1TfT+Yb3zmXXF6Zx03KAEqxRpvxQKEqv0EFi9dhOVVdX79OtgxvSzR3H5lNF06piTQKUiAgoFaWZNDYFUxx51OLMun8SQI/q0UJUisj8KBTkkBxMCh/fJ58ShAxgxbAAnDh2gB+CItCIKBTkgCgGRzKZQkAalh8C7azdRpRAQyVgKBdnLnsoq3l+/WSEg0k4pFNqpyspqikrK2FFcRlFxGes3buPt9zfy3rrGDwf179s9CIGhAzhhaH+FgEgGUShkEHendPceioprV/alFBXvjlb8RcWl7CjeTVFx2V53DjdGISDSfigU2oCqqmp2lIQr95IyinaWsaOkLGXlX8aO4t1sLy7d60awg6UQEGm/FAoJcXfKyvewo2Q3RTvrtuB3lJSxvbYdHt4pKS1v9u/vYEb3vM707N6VHnmd6dszj+OPPlwhINLOKRSaWXV1DTt3BVv124vL2FlSxvadwco92NIPQqCouKzRY/cHo1PHHHrmd6Znfld65HehZ35neuR3oVd+V7rndaZX9y70yO9CftdcOnTo0OzfLyJtW6yhYGZTgN8AWcCd7v7fae93Au4BRgPbgCvdfV2cNR2s8orKYAu+ZHfdYZudpRSVpB6zL6Nk12688Y87IAbk53WmR16XaKXeMy/4M1jx1/3kdtIQESJy8GILBTPLAm4FzgMKgWVmNtfdV6V0uxEocvehZjYD+DlwZVw1paupqaG4tJyinSnH56MrcnaHJ2aD16nPBm4uOdlZ9OoebtHnBVv0Pbt3Dbbu84KVfI/8LnTv1pmsLG3Vi0j84txTGAescfcPAczsAWA6kBoK04GfhK/nAL8zM3P3Zt3Y/njzDhYXvM/2HaXhMfvgsM6O4rJm36oHyO/WmR7hln3P7nVb8bXt2i39zrk5ek6AiLQqcYbCEcCGlHYhMH5/fdy9ysx2Ar2Brc1ZyNaiXcyZv/yQPiM7O4uetSv1vNpj9p2jrfnocE5eZz0uUkTarDhDob5N4PQN86b0wcxmAbMAjjzyyAMupE/P/V9N061Lp/BYfXAitnYl3yt/72P2XTt31Fa9iGS8OEOhEEh9UspAYON++hSaWTbQHdie/kHufgdwB8CYMWMO+IhPnx5dufS8U+jdo2t0CWbt4ZycHG3Vi4jUijMUlgHDzOwo4GNgBnBVWp+5wHXAK8BlwMLmPp8AwWWaV104rrk/VkQk48QWCuE5gpuA+QSXpP7Z3Vea2c1AgbvPBf4E3Gtmawj2EGbEVY+IiDQu1vsU3H0eMC9t2o9TXpcDl8dZg4iINJ0ufhcRkYhCQUREIgoFERGJKBRERCSiUBARkYjFcFtArMxsC7D+IP96H5p5CI0EaV5an0yZD9C8tFaHMi+D3b1vY53aXCgcCjMrcPcxSdfRHDQvrU+mzAdoXlqrlpgXHT4SEZGIQkFERCLtLRTuSLqAZqR5aX0yZT5A89JaxT4v7eqcgoiINKy97SmIiEgDMi4UzCzXzJaa2RtmttLM/rOePp3MbLaZrTGzV81sSMtX2rgmzsv1ZrbFzF4Pf/4piVqbwsyyzOw1M3u8nvfaxDKp1ci8tKVlss7M3grrLKjnfTOzW8Ll8qaZnZJEnU3RhHmZbGY7U5bLj+v7nKSZWQ8zm2Nm75rZO2Z2atr7sS6TWEdJTUgFcLa77zKzHOBFM3vS3Zek9LkRKHL3oWY2A/g5cGUSxTaiKfMCMNvdb0qgvgP1LeAdIL+e99rKMqnV0LxA21kmAGe5+/6ufZ8KDAt/xgO3se9jdVuThuYF4AV3v7DFqjk4vwGecvfLzKwj0CXt/ViXScbtKXhgV9jMCX/ST5xMB+4OX88BzrFW+KzNJs5Lm2BmA4ELgDv306VNLBNo0rxkkunAPeHv4hKgh5n1T7qoTGVm+cAZBM+awd33uPuOtG6xLpOMCwWIdu1fBzYDz7j7q2ldjgA2QPAwIGAn0Ltlq2yaJswLwKXhbuQcMxtUz/utwf8B/wrU7Of9NrNMaHxeoG0sEwg2Mp42s+Xhs9DTRcslVBhOa40amxeAU8PDsU+a2YktWVwTHQ1sAf4SHp6808y6pvWJdZlkZCi4e7W7n0TwXOhxZjYirUt9W6Ctcgu8CfPyGDDE3UcCz1K3td1qmNmFwGZ3X95Qt3qmtbpl0sR5afUrLvUZAAAG5UlEQVTLJMVEdz+F4JDE183sjLT328RyCTU2LysIhnoYBfwWeKSlC2yCbOAU4DZ3PxkoBb6f1ifWZZKRoVAr3O16DpiS9lYhMAjAzLKB7gSPA2219jcv7r7N3SvC5h+B0S1cWlNMBC42s3XAA8DZZvbXtD5tZZk0Oi9tZJkA4O4bwz83A/8A0h9mHi2X0EBgY8tUd2Aamxd3L649HBs+FTLHzPq0eKENKwQKU44IzCEIifQ+sS2TjAsFM+trZj3C152Bc4F307rNBa4LX18GLPRWeMNGU+Yl7VjixQQnP1sVd/+Buw909yEEz+Fe6O7XpHVrE8ukKfPSFpYJgJl1NbO82tfA+cDbad3mAteGV7xMAHa6+yctXGqjmjIvZnZ47XkqMxtHsP7b1tK1NsTdPwU2mNmx4aRzgFVp3WJdJpl49VF/4G4zyyJY6A+6++NmdjNQ4O5zCU7i3Gtmawi2RmckV26DmjIv3zSzi4Eqgnm5PrFqD1AbXSb1aqPL5DDgH+F6Mhu4392fMrOvALj7HwiesT4NWAOUAV9MqNbGNGVeLgO+amZVwG5gRmvc8AC+AdwXXnn0IfDFllwmuqNZREQiGXf4SEREDp5CQUREIgoFERGJKBRERCSiUBARkYhCQZqVme1Ka19vZr9roe9edyA3IzVUW/p8pEx/+WDrawlmdknt6J9m9hMz+5dm/OzJZjY5bdovzezs5voOSV4m3qcgEht3Py3pGhrxrwQ3zDWr8D6MLwBuZu8DF4RjVP2W4K7thc39nZIM7SlIizGzwWa2IBwoboGZHRlOv8vMLkvptyv8s7+ZLbZg7Pu3zez0cPr5ZvaKma0ws4fMrFvK13wjnP6WmR0X9u9lZo+E37vEzEbWU9tR4WcuM7OfNjAPtbVNNrPnrG7c+/tS7pYda2YvhwOvLTWzPAuejfGXsK7XzOyssO/1YW2PmdlaM7vJzL4T9lliZr3CfseY2VMWDPb2Qu28pdU2HKiob+hoMzsp/Lw3zewfZtYzpdY3w3n/hZml39GMmR1PcOPXt4AbgO8QDgbo7uuB3mZ2+P7+zaRtUShIc+tsdQ8xeR24OeW93xEM+TsSuA+4pZHPugqYHw4IOAp4PTw89CPg3HDwswKClVStreH024DaQyf/CbwWfu8PgXvq+a7fEAxCNhb4tInzejLwbeAEgtEtJ4Z3oc4GvhUOvHYuwd2zXwdw988AMwnuVM8NP2dEOK/jgJ8BZeFgaK8A14Z97gC+4e6jw/n6fT31TCQY9K0+9wD/Fv4bvAX8Rzj9L8BX3P1UoHo/f7cKyCMc19/dV7p76gixK8Lvlgygw0fS3HaHK3Eg2BIGxoTNU4HPh6/vBf6nkc9aBvzZggcMPeLur5vZmQQr4ZfCDfOOBCvPWn8P/1ye8l2TgEsB3H2hmfU2s+5p3zWxtk9Y288bqQ1gqbsXhvP5OjCEYMjvT9x9Wfh9xeH7kwgOteDu75rZemB4+DmL3L0EKDGznQSjrEKw8h4Z7gmdBjxkdY+Y6FRPPf0Jhl3eSzivPdz9+XDS3eFn9QDy3L32PMn9wD4PoHH3983sJ8CPgWwzuxf4WUowbAYG7PdfSdoUhYIkqXaMlSrCvdbwEExHAHdfbMHwxxcQjIv0C6CI4LkSM/fzmbWjk1ZT9/vd1KGGD3TMl4qU17XfZ/v5nIYeGJT6OTUp7ZrwMzsAO1LDdj92E4wu21RNfoiRu//JzD4A+gCzgKsJwhMgN/xuyQA6fCQt6WXqBrq7GngxfL2OuuGlpxM8YQ4zG0zw7II/EgyYdwqwhOAwzdCwT5fwWHpDFoffR3j1zNbaLfgUL6XVdrDeBQaY2djw+/IsGAo8tYbhwJHA6qZ8YFjrWjO7PPz7Zmaj6un6DjC0nr+/EyiqPSdDcML4eXcvItg7mRBOr3cQQjPrZ3VXdW0lGKQtL6XLcPYdXVXaKO0pSEv6JsHhoO8RHOaoHd3xj8CjZrYUWEDwYBGAycD3zKwS2AVc6+5bwkNSfzOz2kMoPwLea+B7f0LwJKs3CUaVvK6ePt8C7jezbwEPH9zsBY9PNLMrgd9aMNz5boLzCr8H/mBmbxHsGV3v7hXW9CeOXg3cZmY/IgjNB4A30vosBv7XzKye0T+vC7+/C+HIm+H0G4E/mlkpwfM6dtbz3fkE5zT6EuwVrCY8XxMe2htKcG5HMoBGSRXJIGb2G+Axd3+2if271T54xsy+D/R392/tp+9kAHd/LmXa54BT3P3fD7F0aSW0pyCSWf4LGH8A/S8wsx8QrAvW0/CzH9bVMy0b+N8D+D5p5bSnICIiEZ1oFhGRiEJBREQiCgUREYkoFEREJKJQEBGRiEJBREQi/x+Ba2vnkRqlugAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "log_cdf = thinkstats2.Cdf(log_sample)\n",
    "thinkplot.Cdf(log_cdf)\n",
    "thinkplot.Config(xlabel='Household income (log $)',\n",
    "               ylabel='CDF')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample = np.power(10, log_sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NwJfMrF+HRu5+j7s3u3tzQ0PDqAc6Ei+/coydHYcAyGYzLFs0J9V4RESSkmSCaAXiw6s1Au1l6nzf3bvcfSuwmShhjFvPb++5CrascQ61ucRu44iIpCrJBLEGWG5mS82sFrgJWNWnzveAqwHMbA7RJactCcZ0yl7Y1nP/4SyNHiciFSyxBOHu3cDtwAPAJuA+d99gZp8wsxtCtQeAfWa2EXgQ+DN335dUTKPh+W09ZxBnLVGCEJHKlej1EXdfDazuU3ZXbNqBj4bPuOfutLzUkyDOXDIhnsoVETkpepN6BNo7DpU66Js6pY55s+tTjkhEJDlKECPwfOz9h+VL5uoFORGpaEoQI/Bc/P2HZep/SUQqmxLECMRfkDtbTzCJSIVTghimo8c6ad11AICMGct1g1pEKpwSxDC98NKe0mvgixfMZlJdLtV4RESSpgQxTM/3ekFOZw8iUvkGTRBm9tXY9C2JRzOOtWzXC3IiUl2GOoNYGZv+cJKBjHdbWveWps9YnG6HgSIiY2GoBNG399WqdOjwMfYfOgJAribLwrn9OpwVEak4Q3W10Whmnybqurs4XeLuH0ossnFka1vP2cOSBbPJZnXrRkQq31AJ4s9i02uTDGQ829bW03/g0sbZKUYiIjJ2Bk0Q7v61sQpkPIufQTQt0ABBIlIdhrxWYma3mNmTZnYkfNaa2bvHIrjxYnvsDKJpoc4gRKQ6DHoGERLBR4i6436S6F7ExcAnzQx3/3ryIaarqytP255DpfklC2alGI2IyNgZ6gziA8DvuPuD7n7I3Q+6+8+Bt4ZlFa9tzwEKhQIAc2fVM3lSbcoRiYiMjaESxDR339a3MJRNSyKg8SZ+g3rJAl1eEpHqMVSCOHaSyyrG1tbY/Qc9wSQiVWSox1zPNbNnypQbsCyBeMadbe3xJ5iUIESkegyVIFYC84AdfcqXAO2JRDSOuHuvS0xNC/WIq4hUj6EuMf0z8LK7b49/gKNhWUU78PJRXjl6AoBJdTmNQS0iVWWoBNHk7v0uMbn7WqApkYjGke3t+0vTSxbM1hjUIlJVhkoQkwZZNnk0AxmPXtrZkyAWz5+ZYiQiImNvqASxxsze37fQzG4FnkgmpPFje3vP/YfF8/WCnIhUl6FuUn8E+E8zeyc9CaEZqAV+J8nAxoPeZxBKECJSXYbqrG838Fozuxo4PxT/V3ibuqLl8wVadx0ozeslORGpNkOdQQDg7g8CDyYcy7iyc+8hurrzAMycNoX60wa7HSMiUnk08s0A4peXdPYgItVICWIAuv8gItVOCWIAO9qVIESkuiWaIMzsWjPbbGYtZnbHIPXeZmZuZs1JxjMSO2I3qBedrncgRKT6JJYgzCwL3A1cB6wAbjazFWXq1QMfAh5LKpaR6u7Os7OjZ5CgRiUIEalCSZ5BXAq0uPsWd+8E7gVuLFPvr4F/AI4nGMuItHccouAOQMPMeibV5VKOSERk7CWZIBbSuxfY1lBWYmYXAYvc/f4E4xix+OWlxtNnpBiJiEh6kkwQ5Xq289JCswxRj7B/MuSKzG4zs7Vmtrajo2MUQyxvx66eG9SLTtcNahGpTkkmiFZgUWy+kd5jSNQTvZ39kJltAy4DVpW7Ue3u97h7s7s3NzQ0JBhyRE8wiYgkmyDWAMvNbKmZ1QI3AauKC939kLvPcfcmd28CHgVuCF2Jp6p198HStJ5gEpFqlViCcPdu4HbgAWATcJ+7bzCzT5jZDUlt91R1d+dp1xNMIiLD64vpZLn7amB1n7K7Bqh7VZKxDNfOvS9TKBQAmDNzqp5gEpGqpTep+4j34No4T2cPIlK9lCD6aNvTc/9h4Tw94ioi1UsJoo+23TqDEBEBJYh+2mJPMC2YOz3FSERE0qUEEePuvS4xLZirS0wiUr2UIGIOvHyU4ye6AJgyqZaZ06akHJGISHqUIGLil5cWzpuBWbneQkREqoMSREzv+w+6vCQi1U0JIiY+BoQShIhUOyWImPYOPcEkIlKkBBHTHn9JTmcQIlLllCCC7u48e/YdLs2fPmdaitGIiKRPCSLoOPBKaZjRmdOmUFerTvpEpLopQQTxG9TzG3T/QURECSKIJ4jT5yhBiIgoQQS9H3FVghARUYII2tUHk4hIL0oQgV6SExHpTQmC6BHXjv3RI64GzJtdn25AIiLjgBIEsHv/YTxMz545ldpcokN1i4hMCEoQ9H2CSS/IiYiAEgQAu/e+XJrWI64iIhElCGD3vp4EMW+2ziBEREAJAuh9BjFPl5hERAAlCCC6SV00b5aeYBIRASUI3J1dsZvUOoMQEYlUfYLYd/AIXd15AKZOqaP+tEkpRyQiMj5UfYLYtVed9ImIlKMEEX/EtUGXl0REipQg1M23iEhZShDxYUb1DoSISEmiCcLMrjWzzWbWYmZ3lFn+UTPbaGbPmNnPzGxJkvGUs2ef3oEQESknsQRhZlngbuA6YAVws5mt6FPtKaDZ3V8FfBf4h6TiGcie2DsQc/UOhIhISZJnEJcCLe6+xd07gXuBG+MV3P1Bdz8aZh8FGhOMp5/jJ7o4fOQ4ANlshtkzThvLzYuIjGtJJoiFwI7YfGsoG8itwA/LLTCz28xsrZmt7ejoGLUA42cPDTOnYmajtm4RkYkuyQRRrrX1MmWY2e8BzcAnyy1393vcvdndmxsaGkYtwF4JQpeXRER6SXJknFZgUWy+EWjvW8nM3gR8DLjS3U8kGE8/Hb3OIJQgRETikjyDWAMsN7OlZlYL3ASsilcws4uALwA3uPueBGMpa1eHnmASERlIYgnC3buB24EHgE3Afe6+wcw+YWY3hGqfBKYC3zGzdWa2aoDVJaK942BpesFcvSQnIhKX6ODL7r4aWN2n7K7Y9JuS3P5Q4m9RL2hQghARiavaN6kLhUKvcSDUzYaISG9VmyD2HjxCPl8AYHr9ZCbV5VKOSERkfKnaBNFrmFH1wSQi0k/VJog9+3sSxNzZesRVRKSv6k0Q++LjUOsMQkSkr+pNEPFO+nQGISLST9UmiL0HXilNq5sNEZH+qjZBdOzvSRBzZk5NMRIRkfGpKhNEd3eevQd69+QqIiK9VWWCaO84VOpWtmFmPbW5RF8oFxGZkKoyQbTt7umDaeG8GSlGIiIyflVlgtgZ74NJnfSJiJRV9QlCfTCJiJRXlQli976et6jnqxdXEZGyqj5BaKAgEZHyqi5BdHfn2Rd7SW6uhhoVESmr6hLE3oNHSo+4zpw2hVwum2o8IiLjVfUliPgLcupiQ0RkQFWYINTFhojIcFRdgmjddaA0PU9nECIiA6q6BLG+pb00fcbiuSlGIiIyvlVVgujs6ubFHXtL8+edOT/FaERExreqShBbduylUCgAsKBhOtOmTk45IhGR8au6EkRrR2n6zCW6vCQiMpiqShDb2/eXppsWzkkxEhGR8a+qEsSO2BNMi+fPSjESEZHxr2oShLvTvkfjQIiIDFfVJIhtbfs4fOQ4AFMm1WqYURGRIVRNgnh6c2tp+qIVizGzFKMRERn/qiZBvLBtd2n6guULUoxERGRiSDRBmNm1ZrbZzFrM7I4yy+vM7Nth+WNm1pRULC/t7HmCaVljQ1KbERGpGIklCDPLAncD1wErgJvNbEWfarcCB9z9TOCfgb9PIhZ3Z/f+nl5cdYNaRGRoSZ5BXAq0uPsWd+8E7gVu7FPnRuBrYfq7wBstgZsDBw8fI5+P3qCeOqWOSXW50d6EiEjFSTJBLAR2xOZbQ1nZOu7eDRwCZo92IC+/cqw0PaN+ymivXkSkIiWZIMqdCfhJ1MHMbjOztWa2tqOjo8xXBnfwcE+CmF6v/pdERIajJsF1twKLYvONQPsAdVrNrAaYDuzvUwd3vwe4B6C5ublfAhnKotNn8uF3vYFDh48zQwlCRGRYkkwQa4DlZrYUaANuAn63T51VwC3Ab4C3AT939xEngKHMmn4ar28+a7RXKyJS0RJLEO7ebWa3Aw8AWeDL7r7BzD4BrHX3VcC/Ad8wsxaiM4ebkopHRERGJskzCNx9NbC6T9ldsenjwNuTjEFERE5O1bxJLSIiI6MEISIiZSlBiIhIWUoQIiJSlhKEiIiUZQm8dpAoM+sAtp/k1+cAe0cxnIlA+1wdtM/V4VT2eYm7j6gr6wmXIE6Fma119+a04xhL2ufqoH2uDmO9z7rEJCIiZSlBiIhIWdWWIO5JO4AUaJ+rg/a5OozpPlfVPQgRERm+ajuDEBGRYaqKBGFm15rZZjNrMbM70o5nOMxskZk9aGabzGyDmX04lM8ys5+Y2Qvh58xQbmb26bCPz5jZxbF13RLqv2Bmt8TKX21mz4bvfLo43OtA2xjDfc+a2VNmdn+YX2pmj4V4vm1mtaG8Lsy3hOVNsXXcGco3m9lbYuVlfxcG2sYY7e8MM/uumT0XjvfllX6czeyPw+/1ejP7lplNqrTjbGZfNrM9ZrY+VpbacR1sGwNy94r+EHU1/iKwDKgFngZWpB3XMOKeD1wcpuuB54EVwD8Ad4TyO4C/D9PXAz8kGqXvMuCxUD4L2BJ+zgzTM8Oyx4HLw3d+CFwXystuYwz3/aPAvwP3h/n7gJvC9OeBPwzTHwA+H6ZvAr4dpleE41wHLA3HPzvY78JA2xij/f0a8L4wXQvMqOTjTDTU8FZgcuzf/j2VdpyB1wMXA+tjZakd14G2Meg+jNV/grQ+4R/wgdj8ncCdacd1EvvxfeDNwGZgfiibD2wO018Abo7V3xyW3wx8IVb+hVA2H3guVl6qN9A2xmg/G4GfAW8A7g+/zHuBmr7Hk2iskcvDdE2oZ32PcbHeQL8Lg21jDPZ3GlFjaX3KK/Y40zMW/axw3O4H3lKJxxlooneCSO24DrSNweKvhktMxV/GotZQNmGEU+qLgMeAee6+EyD8nBuqDbSfg5W3lilnkG2MhX8B/hwohPnZwEF37y4TZ2nfwvJDof5I/y0G20bSlgEdwFcsuqz2JTM7jQo+zu7eBvwj8BKwk+i4PUFlH+eiNI/riNvCakgQVqZswjy6ZWZTgf8HfMTdXx6sapkyP4ny1JjZ/wD2uPsT8eIyVX2IZRPp36KG6DLE59z9IuAI0WWBgUykfSsrXBO/keiy0ALgNOC6MlUr6TgPZSz2ZcTfqYYE0Qosis03Au0pxTIiZpYjSg7fdPf/CMW7zWx+WD4f2BPKB9rPwcoby5QPto2kXQHcYGbbgHuJLjP9CzDDzIqjH8bjLO1bWD6daOjakf5b7B1kG0lrBVrd/bEw/12ihFHJx/lNwFZ373D3LuA/gNdS2ce5KM3jOuK2sBoSxBpgeXh6oZboJteqlGMaUngi4d+ATe7+T7FFq4Dikwy3EN2bKJa/OzypcBlwKJxePgBcY2Yzw19u1xBdd90JHDazy8K23t1nXeW2kSh3v9PdG929ieg4/dzd3wk8CLytTDzxON8W6nsovyk8/bIUWE50Q6/s70L4zkDbSJS77wJ2mNnZoeiNwEYq+DgTXVq6zMymhJiK+1yxxzkmzeM60DYGNhY3pdL+EN29f57oyYaPpR3PMGN+HdHp3zPAuvC5nug66s+AF8LPWaG+AXeHfXwWaI6t638BLeHz3lh5M7A+fOcz9Lw4WXYbY7z/V9HzFNMyov/4LcB3gLpQPinMt4Tly2Lf/1jYr82EpzsG+10YaBtjtK8XAmvDsf4e0dMqFX2cgb8CngtxfYPoSaSKOs7At4jusXQR/fV+a5rHdbBtDPTRm9QiIlJWNVxiEhGRk6AEISIiZSlBiIhIWUoQIiJSlhKEiIiUpQQhIiJlKUFIKszslT7z7zGzz4zRtreZ2ZwR1B8wtr77ESv/9cnGNxbM7LfN7K4+ZR/vM19rZg/H3jyWKqMEIZIAd39t2jEM4c+BzwKY2QIz+yHwATNbZ2Z/DODunUQvWr0jvTAlTUoQMu6Y2RIz+1kY1ORnZrY4lH/VzN4Wq/dK+Dk//KW7zqIBaP5bKL/GzH5jZk+a2XdCx4dFHwzlz5rZOaH+LDP7Xtjuo2b2qjKxLQ3rXGNmfz3IPhRju8rMHrKeAYG+GbpGwMwuMbNfm9nTZva4mdVbNHDOV0JcT5nZ1aHue0JsPzCzrWZ2u5l9NNR51MxmhXpnmNmPzOwJM/tlcd+Yb5NwAAADWElEQVT6xHYWcMLd94aijxD1pvpZ4BLgR7Hq3wPeOegBk4qlBCFpmRwa9HVmtg74RGzZZ4Cvu/urgG8Cnx5iXb9L1D/NhcBKYF24hPSXwJvc/WKiriw+GvvO3lD+OeBPQ9lfAU+F7f4F8PUy2/oUUc+rlwC7hrmvFxE1wiuIunq4IvQR9G3gw+6+kqgDu2PAHwG4+wVEffx/zcwmhfWcH/b1UuBvgKMe9QD7G6K+eCAa1P6D7v7qsF+fLRPPFcCTsflOou4Zcu7e5e6bYsvWEyUNqUJKEJKWY+5+YfEDxK+HX040ohxE/fS8boh1rQHeG66hX+Duh4lGzFoBPBIS0C3Akth3ir3jPkE0qAthO98AcPefA7PNbHqfbV1B1MdOMbbheNzdW929QNSnVhNwNrDT3deE7b3s0TgF8RieA7YDZ4X1POjuh929g2hMhB+E8meBpnCG9FrgO2Gfv0A0YExf84nGoCj6JFFb8PvhjO2q4gJ3zwOdZlY/zH2VCqKbTzIRFDsM6yb8URMu09QCuPvDZvZ64L8D3zCzTwIHgJ+4+80DrPNE+Jmn5//BcPvLH2kHZidi08Xt2QDrKRdDufUUYvOFsM4M0YA4Fw4RzzGiLrMBcPdDRMmh2Hvo981ssbsfD1XqgOP9VyOVTmcQMh79mqiLZoiuf/8qTG8DXh2mbwRyEN2zIBpo6ItEXaRfDDxKdCnnzFBnSrj2PpiHw/YIf0Xv9f6DND3SJ7aT9RywwMwuCdurD08LxWM4C1hM1FPpkEKsW83s7eH7ZmYry1TdBJxZnDGzc82s2BY8S5Rwiv+2s4HiuA1SZZQgZDz6ENElo2eAdwEfDuVfBK40s8eB1xCNvgZR1+DrzOwp4K3Ap8JlmPcA3wrreRTod8O2j48DzaH+39HTp37ch4E/MrM1xP4KH6nwhNA7gH81s6eBnxB1a/1ZIGtmzxLdo3iPu58YeE39vBO4NaxzA1Ei7eth4KLizXKiy2a/Bt5LNKzt34TLdABXA6tHtHNSMdTdt0gVMrNPAT9w95/Gyj7u7h/vU+8/gDvdfVhnMVJZdAYhUp3+FpjSp+yh+Ex40up7Sg7VS2cQIiJSls4gRESkLCUIEREpSwlCRETKUoIQEZGylCBERKSs/w/pK9U0n9b93gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cdf = thinkstats2.Cdf(sample)\n",
    "thinkplot.Cdf(cdf)\n",
    "thinkplot.Config(xlabel='Household income ($)',\n",
    "               ylabel='CDF')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the median, mean, skewness and Pearson’s skewness of the resulting sample. What fraction of households report a taxable income below the mean? How do the results depend on the assumed upper bound?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(74278.70753118739, 51226.45447894046)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "Mean(sample), Median(sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4.949920244429579, 0.7361258019141795)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "Skewness(sample), PearsonMedianSkewness(sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.660005879566872"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# About 66% of the population makes less than the mean\n",
    "\n",
    "cdf.Prob(Mean(sample))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All of this is based on an assumption that the highest income is one million dollars, but that's certainly not correct.  What happens to the skew if the upper bound is 10 million?\n",
    "\n",
    "Without better information about the top of this distribution, we can't say much about the skewness of the distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}