{
 "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": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "import nsfg\n",
    "import first\n",
    "import thinkstats2\n",
    "import thinkplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Examples\n",
    "\n",
    "One more time, I'll load the data from the NSFG."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "live, firsts, others = first.MakeFrames()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And compute the distribution of birth weight for first babies and others."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Firsts 4413 4363\n",
      "Others 4735 4675\n"
     ]
    }
   ],
   "source": [
    "first_wgt = firsts.totalwgt_lb\n",
    "first_wgt_dropna = first_wgt.dropna()\n",
    "print('Firsts', len(first_wgt), len(first_wgt_dropna))\n",
    " \n",
    "other_wgt = others.totalwgt_lb\n",
    "other_wgt_dropna = other_wgt.dropna()\n",
    "print('Others', len(other_wgt), len(other_wgt_dropna))\n",
    "\n",
    "first_pmf = thinkstats2.Pmf(first_wgt_dropna, label='first')\n",
    "other_pmf = thinkstats2.Pmf(other_wgt_dropna, label='other')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the PMFs on the same scale, but it is hard to see if there is a difference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hya22IhuZ+g9FFmdmZo2v2jUSzw5sZmbdqjb770hJF0m6RtJcSVWvqZgNFv5wKrPaVOtx\nLANagCfJbtP9TuEVmZnZgFKthzE5Io4GkHQT8FjxJZkNDu7R2FBRrUfyWueTiOgouBYzMxuAqn6w\nlaTfpMdLwJ92Ppd0wCSKZtY77r3YQFbtrq2m/irEzMwGJt/ea9ag3EuxgcJBYmZmuThIzMwsFweJ\nWQ94uMnsQA4SMzPLxUFiVoMFi1fXuwSzhuUgMUs8bGXWOw4SMzPLxUFiVjAPi9lgV2iQSJoh6RlJ\nbZIWVtguSYvS9o2SppVsWyrpRUmbyvb5hqQdkjakx6lFnoNZI/HwmzWiwoJEUhNwLTATmAycKWly\nWbOZwKT0mAssLtl2MzCji8NfGRHN6bGiTws3M7MeKbJHMh1oi4htEbEPuB2YVdZmFnBLZNYAoySN\nAYiIB4FfFVifWU3DTn05NOUehQ1GRQbJWOC5kuX2tK6nbSq5IA2FLZV0aL4yzcwsj4F4sX0x8B6g\nGdhJF5/amD4aeJ2kdbt27erP+myQq9SrcE/DhrIig2QHML5keVxa19M2bxIRL0TE/oh4HbiBbAit\nUrvrI6IlIlpGjx7d4+LNoH8CwiFkA12RQbIWmCRpoqSDgDOA5WVtlgPnpLu3TgD2RsTO7g7aeQ0l\nOR3Y1FVbs6IUcUtvb47pELJGUO0z23stIjokLQDuA5qApRGxWdK8tH0JsAI4FWgDXgHO7dxf0m3A\nicDhktqB/x4RNwHfltQMBLAd+FJR52BmZtUVFiQA6dbcFWXrlpQ8D2B+F/ue2cX6s/uyRrP+5l6E\nDTYD8WK7mZk1EAeJGe4lmOXhIDEzs1wcJGYlPMGiWc85SMwGmPKw87Cc1ZuDxMzMcnGQmJlZLg4S\nswbXOZTlISxrVA4Ss17qjwvzXb1Gd6/twLH+5iAxa0AOAxtIHCRmZpaLg8SGLL9nxKxvOEjMzCwX\nB4nZIORrLNafHCRmZpaLg8TMzHJxkJiZWS4OEjMzy8VBYmZmuRQaJJJmSHpGUpukhRW2S9KitH2j\npGkl25ZKelHSprJ93iFppaRn09dDizwHa2x+L0j3/P2x/lBYkEhqAq4FZgKTgTMlTS5rNhOYlB5z\ngcUl224GZlQ49ELg/oiYBNyfls3MrE6K7JFMB9oiYltE7ANuB2aVtZkF3BKZNcAoSWMAIuJB4FcV\njjsLWJaeLwM+WUj1ZmZWkyKDZCzwXMlye1rX0zbljoiInen588ARlRpJmitpnaR1u3btqr1qswHK\nw1hWLwP6YntEBBBdbLs+IloiomX06NH9XJmZ2dBRZJDsAMaXLI9L63raptwLncNf6euLOes0M7Mc\nigyStcAkSRMlHQScASwva7McOCfdvXUCsLdk2Kory4HZ6fls4O6+LNrMzHqmsCCJiA5gAXAfsAW4\nIyI2S5onaV5qtgLYBrQBNwDnd+4v6TbgEeBISe2SvpA2XQacIulZ4C/Ssg1inoDQrLENL/LgEbGC\nLCxK1y0peR7A/C72PbOL9buBk/uwTDMzy2FAX2w3M7P6c5CYmVkuDhIzM8vFQWJmZrk4SMzMLBcH\niZmZ5eIgMTOzXBwkZmaWi4PEzMxycZCYmVkuDhIbkjx/l1nfcZDYoOWwMOsfDhIzM8vFQWI2CPhj\ndq2eHCQ2YPiXpVljcpCYmVkuDhIb9NyTMSuWg8SGhKEYJkPxnK0+Cg0SSTMkPSOpTdLCCtslaVHa\nvlHStGr7SvqGpB2SNqTHqUWeg9lQ4NCxPAoLEklNwLXATGAycKakyWXNZgKT0mMusLjGfa+MiOb0\nWIGZmdVNkT2S6UBbRGyLiH3A7cCssjazgFsiswYYJWlMjfuamVkDKDJIxgLPlSy3p3W1tKm27wVp\nKGyppEP7rmQzM+upgXixfTHwHqAZ2Al8p1IjSXMlrZO0bteuXf1Zn5nZkFJkkOwAxpcsj0vramnT\n5b4R8UJE7I+I14EbyIbBDhAR10dES0S0jB49OteJ2MDhi8bdK//+eD4y6wtFBslaYJKkiZIOAs4A\nlpe1WQ6ck+7eOgHYGxE7u9s3XUPpdDqwqcBzsAGouzAZqr84r3hg65A9dyve8KIOHBEdkhYA9wFN\nwNKI2CxpXtq+BFgBnAq0Aa8A53a3bzr0tyU1AwFsB75U1DmYmVl1hQUJQLo1d0XZuiUlzwOYX+u+\naf3ZfVymDUBXPLCVS056b73LGFQWLF7NNV/+YL3LsAFoIF5sN6vIQzd9w8Ng1lMOEjMzy8VBYmZm\nuThIbFDwUIxZ/ThIzMwsFweJ9bmi3xTo3odZY3GQmFlFniXAauUgMRvi3MOzvBwk1nD8l3Cx8nx/\n/W9jlThIbFDzX9tmxXOQmJlZLg4SG7A8zNJ/KvXs3NuzTg4SM6uJg8O64iCxwnX+AuqqB9G53r+o\n+k+tvTn3+qwWDhIbEL8sBkKNZkOVg8QK1V0vo5YeiHspA5ODf2hxkFhDcXCYDTwOEnuTnvwi9y99\nq/X/QFft/H9ocHCQDAJFDCP05Ji+WG42tBUaJJJmSHpGUpukhRW2S9KitH2jpGnV9pX0DkkrJT2b\nvh5a5Dn0h+7uaupuXU9/cecNnL4MrGp3ctnA0Zs/OmxwKSxIJDUB1wIzgcnAmZImlzWbCUxKj7nA\n4hr2XQjcHxGTgPvT8oDQn8MApT+wtexXLcQGcmhZ36r2x01RPdNa/k9099qN8H9qsPbai+yRTAfa\nImJbROwDbgdmlbWZBdwSmTXAKEljquw7C1iWni8DPlngOZiZWRVFBslY4LmS5fa0rpY23e17RETs\nTM+fB47oq4IrqfYmOsj+yqilXedy56Nz356+dndtS/8irKWX0dtbcLt6jcH6F5f1XPn/8c7lrtaX\nritvV61tpeW+kHcUod76qxemiCjmwNKngRkR8cW0fDZwfEQsKGlzD3BZRKxOy/cDXwMmdLWvpD0R\nMarkGL+OiAOuk0iaSzZcBnAk8EwPT+Fw4Jc93Kc/ub7ea+TawPXl0ci1wcCr748jYnS1nYYXVw87\ngPEly+PSulrajOhm3xckjYmInWkY7MVKLx4R1wPX97Z4SesioqW3+xfN9fVeI9cGri+PRq4NBm99\nRQ5trQUmSZoo6SDgDGB5WZvlwDnp7q0TgL1p2Kq7fZcDs9Pz2cDdBZ6DmZlVUViPJCI6JC0A7gOa\ngKURsVnSvLR9CbACOBVoA14Bzu1u33Toy4A7JH0B+Dnw2aLOwczMqityaIuIWEEWFqXrlpQ8D2B+\nrfum9buBk/u20op6PSzWT1xf7zVybeD68mjk2mCQ1lfYxXYzMxsaPEWKmZnl4iCpoNrULvUiabyk\nVZKekrRZ0oX1rqkSSU2Snki3dzcUSaMk3SnpaUlbJH2g3jV1knRx+nfdJOk2SSPrXM9SSS9K2lSy\nrmGmKOqivv+V/m03SrpL0qjujtHf9ZVs+6qkkHR4I9Um6YL0/dss6du1Hs9BUqbGqV3qpQP4akRM\nBk4A5jdQbaUuBLbUu4guXA3cGxFHAcfQIHVKGgt8BWiJiKlkN5mcUd+quBmYUbaukaYoupkD61sJ\nTI2IPwX+Ffib/i6qxM0cWB+SxgMfBX7R3wWVuJmy2iR9hGzmkGMiYgpwea0Hc5AcqJapXeoiInZG\nxOPp+UtkvwTLZwuoK0njgNOAG+tdSzlJ/xH4c+AmgIjYFxF76lvVmwwH3iJpOPBW4N/rWUxEPAj8\nqmx1w0xRVKm+iPjniOhIi2vI3oNWF118/wCuBP4aqNsF6i5q+zLZG8R/n9pUfI9eJQ6SA9UytUvd\nSZoAHAs8Wt9KDnAV2Q/J6/UupIKJwC7gu2no7UZJh9S7KICI2EH2F+AvgJ1k76n65/pWVVG/TlGU\n03nAP9W7iFKSZgE7IuJn9a6lgvcBH5L0qKT/J+k/1bqjg2QAkvQ24IfARRHxm3rX00nSXwIvRsT6\netfSheHANGBxRBwL/JYGmT06XWuYRRZ27wIOkfRX9a2qe+n2/Ya87VPS18mGgr9f71o6SXor8LfA\nf6t3LV0YDryDbNj8UrL366mWHR0kB6plape6kTSCLES+HxE/qnc9ZVqBT0jaTjYkeJKk79W3pDdp\nB9ojorMXdydZsDSCvwD+LSJ2RcRrwI+AP6tzTZW8kKYmorspiupJ0hzgL4GzorHe3/Besj8UfpZ+\nRsYBj0t6Z12r+oN24EdpNvbHyEYVaroZwEFyoFqmdqmL9NfBTcCWiLii3vWUi4i/iYhxETGB7Pv2\nQEQ0zF/VEfE88JykI9Oqk4Gn6lhSqV8AJ0h6a/p3PpkGuRGgTENPUSRpBtnQ6ici4pV611MqIp6M\niD+KiAnpZ6QdmJb+XzaCHwMfAZD0PuAgapxg0kFSJl2o65yeZQtwR8n0LPXWCpxN9pf+hvQ4td5F\nDTAXAN+XtBFoBv6+zvUAkHpJdwKPA0+S/WzW9V3Qkm4DHgGOlNSepiW6DDhF0rNkvajLGqy+a4C3\nAyvTz8eSbg/S//U1hC5qWwq8J90SfDswu9Yend/ZbmZmubhHYmZmuThIzMwsFweJmZnl4iAxM7Nc\nHCRmZpaLg8QGLUlXSrqoZPk+STeWLH9H0iVVjvFwDa+zvdIsrpJOlNTlmwolfVJS3d7lLOnlKtv/\npZ6z+9rA4SCxwewh0rvDJQ0je5fulJLtfwZ0GxQRkefd5SfS/bvT/xq4Lsfxi/YPwPn1LsIan4PE\nBrOHgc7PG5kCbAJeknSopIOB95O9ARBJl0pamz7H4pudB+j8q13SMEnXpc9qWClphaRPl7zWBZIe\nl/SkpKPSpJrzgIvTG+M+VFpYeufw7yPil2n5ZklLJK2T9K9p3jIkjZT03XTcJ9JU30iaI+makuPd\nI+nEzpol/Q9JP5O0RtIRaf1ESY+kY/1dyb5jJD2Y6txUUuty4Mxef/dtyHCQ2KAVEf8OdEh6N1nP\n4BGy2ZI/ALQAT0bEPkkfBSaRfYRAM3CcpD8vO9yngAlkn1FzNn8IqE6/jIhpwGLgv0bEdmAJcGVE\nNEfET8vat5JCrMSEVMNpwBJlH2w1PzuVOJrsl/oyVf/Aq0OANRFxDPAg8F/S+qvJJqw8mmyG4U6f\nB+6LiGayz2jZQPaivwYOlnRYldezIc5BYoPdw2Qh0hkkj5QsP5TafDQ9niD75X4UWbCU+iDwfyLi\n9TQ30qqy7Z0TaK4nC4RqxpBNaV/qjnT8Z4FtqY4PAt8DiIingZ+TTffdnX1A56dTltbTCtyWnv9D\nSfu1wLmSvgEcnT7rptOLZLMRm3XJQWKDXed1kqPJhrbWkPUmSq+PCPifqefQHBF/EhE39fB1fp++\n7iebjrua3wHlPYvy+Yq6m7+ogzf//JYe67WSOZLK6zngmOlDjv6cbJbrmyWdU3bc33VTh5mDxAa9\nh8mmFP9VROyPiF8Bo8jCpDNI7gPOS5/zgqSxkv6o7DgPAf85XSs5guxCejUvkU0gWMkW4E/K1n0m\nHf+9wHuAZ4CfAmelut4HvDut3w40p/bjyYbEqnmIP3x871mdKyX9MfBCRNxA9smW09J6Ae9Mr2XW\nJQeJDXZPkt2ttaZs3d7OC93pkwhvBR6R9CTZLLzlAfBDsmm/nyIbanoc2Fvltf8ROL3SxXayaxfH\npl/WnX4BPEb2qX7zIuJVsru6hqW6fgDMSR+F+hDwb6meRRx4vaWSC4H56Viln/p5ItlnZDwBfI7s\nWgrAcWTXWjow64Zn/zWrkaS3RcTL6eLzY0Brns+SkHQ18I8R8S+SbgbuiYg7+6jc3FJ9yyPi/nrX\nYo2tlrFcM8vcI2kU2Qf+fKsPPpDo74Hj85dVmE0OEauFeyRmZpaLr5GYmVkuDhIzM8vFQWJmZrk4\nSMzMLBcHiZmZ5eIgMTOzXP4/ELUE9s0PPjIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb65eb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 0.4 / 16\n",
    "\n",
    "# plot PMFs of birth weights for first babies and others\n",
    "thinkplot.PrePlot(2)\n",
    "thinkplot.Hist(first_pmf, align='right', width=width)\n",
    "thinkplot.Hist(other_pmf, align='left', width=width)\n",
    "thinkplot.Config(xlabel='Weight (pounds)', ylabel='PMF')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`PercentileRank` computes the fraction of `scores` less than or equal to `your_score`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def PercentileRank(scores, your_score):\n",
    "    count = 0\n",
    "    for score in scores:\n",
    "        if score <= your_score:\n",
    "            count += 1\n",
    "\n",
    "    percentile_rank = 100.0 * count / len(scores)\n",
    "    return percentile_rank"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If this is the list of scores."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "t = [55, 66, 77, 88, 99]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And you got the 88, your percentile rank is 80."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "80.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PercentileRank(t, 88)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Percentile` takes a percentile rank and computes the corresponding percentile. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Percentile(scores, percentile_rank):\n",
    "    scores.sort()\n",
    "    for score in scores:\n",
    "        if PercentileRank(scores, score) >= percentile_rank:\n",
    "            return score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The median is the 50th percentile, which is 77."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "77"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Percentile(t, 50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a more efficient way to compute percentiles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Percentile2(scores, percentile_rank):\n",
    "    scores.sort()\n",
    "    index = percentile_rank * (len(scores)-1) // 100\n",
    "    return scores[index]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's hope we get the same answer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "77"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Percentile2(t, 50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Cumulative Distribution Function (CDF) is almost the same as `PercentileRank`.  The only difference is that the result is 0-1 instead of 0-100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def EvalCdf(sample, x):\n",
    "    count = 0.0\n",
    "    for value in sample:\n",
    "        if value <= x:\n",
    "            count += 1\n",
    "\n",
    "    prob = count / len(sample)\n",
    "    return prob"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "t = [1, 2, 2, 3, 5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can evaluate the CDF for various values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 0.2, 0.6, 0.8, 0.8, 1.0)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "EvalCdf(t, 0), EvalCdf(t, 1), EvalCdf(t, 2), EvalCdf(t, 3), EvalCdf(t, 4), EvalCdf(t, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's an example using real data, the distribution of pregnancy length for live births."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LiF051mNmZiXkuaewGhgnaaykgcD5wNLCFSQdBTwA/ElE/GuOtZiZWRfktqcQEa2SrgYe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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe5c45c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cdf = thinkstats2.Cdf(live.prglngth, label='prglngth')\n",
    "thinkplot.Cdf(cdf)\n",
    "thinkplot.Config(xlabel='Pregnancy length (weeks)', ylabel='CDF', loc='upper left')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Cdf` provides `Prob`, which evaluates the CDF; that is, it computes the fraction of values less than or equal to the given value.  For example, 94% of pregnancy lengths are less than or equal to 41."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.94064276344556186"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cdf.Prob(41)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "`Value` evaluates the inverse CDF; given a fraction, it computes the corresponding value.  For example, the median is the value that corresponds to 0.5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "39"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cdf.Value(0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In general, CDFs are a good way to visualize distributions.  They are not as noisy as PMFs, and if you plot several CDFs on the same axes, any differences between them are apparent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KjqdaRPxtRHRHxEKSf7vvRUTdfNqNiKeAJyQdkx56A/BwgSFlPQ68WtL09P/5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\nswonBTMzq/j/6bL/SsDUZnYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb658358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "first_cdf = thinkstats2.Cdf(firsts.totalwgt_lb, label='first')\n",
    "other_cdf = thinkstats2.Cdf(others.totalwgt_lb, label='other')\n",
    "\n",
    "thinkplot.PrePlot(2)\n",
    "thinkplot.Cdfs([first_cdf, other_cdf])\n",
    "thinkplot.Config(xlabel='Weight (pounds)', ylabel='CDF')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we can see that first babies are slightly, but consistently, lighter than others.\n",
    "\n",
    "We can use the CDF of birth weight to compute percentile-based statistics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "weights = live.totalwgt_lb\n",
    "live_cdf = thinkstats2.Cdf(weights, label='live')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, the median is the 50th percentile."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.375"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "median = live_cdf.Percentile(50)\n",
    "median"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The interquartile range is the interval from the 25th to 75th percentile."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6.5, 8.125)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iqr = (live_cdf.Percentile(25), live_cdf.Percentile(75))\n",
    "iqr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the CDF to look up the percentile rank of a particular value.  For example, my second daughter was 10.2 pounds at birth, which is near the 99th percentile."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "98.827174153573807"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "live_cdf.PercentileRank(10.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we draw a random sample from the observed weights and map each weigh to its percentile rank."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sample = np.random.choice(weights, 100, replace=True)\n",
    "ranks = [live_cdf.PercentileRank(x) for x in sample]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting list of ranks should be approximately uniform from 0-1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xd17a630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rank_cdf = thinkstats2.Cdf(ranks)\n",
    "thinkplot.Cdf(rank_cdf)\n",
    "thinkplot.Config(xlabel='Percentile rank', ylabel='CDF')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That observation is the basis of `Cdf.Sample`, which generates a random sample from a Cdf.  Here's an example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hhjoaT5BCl2RS2AgcGLtdHp6LawC2uvsHwAdm9iQwDXgVkTy27JHabJnseLeRxhOk0CXZ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\nNxPv7QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd16bf60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "resample = live_cdf.Sample(1000)\n",
    "thinkplot.Cdf(live_cdf)\n",
    "thinkplot.Cdf(thinkstats2.Cdf(resample, label='resample'))\n",
    "thinkplot.Config(xlabel='Birth weight (pounds)', ylabel='CDF')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This confirms that the random sample has the same distribution as the original data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Exercise:** How much did you weigh at birth? If you don’t know, call your mother or someone else who knows. Using the NSFG data (all live births), compute the distribution of birth weights and use it to find your percentile rank. If you were a first baby, find your percentile rank in the distribution for first babies. Otherwise use the distribution for others. If you are in the 90th percentile or higher, call your mother back and apologize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.021862702229995628"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution goes here\n",
    "cdf.PercentileRank(7.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "55.871657754010698"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution goes here\n",
    "other_cdf.PercentileRank(7.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Exercise:** The numbers generated by `numpy.random.random` are supposed to be uniform between 0 and 1; that is, every value in the range should have the same probability.\n",
    "\n",
    "Generate 1000 numbers from `numpy.random.random` and plot their PMF.  What goes wrong?\n",
    "\n",
    "Now plot the CDF. Is the distribution uniform?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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uISFJGjg9HlFk5uGIuANYBjQB92Xmmoi4rdq+CFgKXAd0APuBW0pjq13fCTwYEbcCG4GP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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc7defd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution goes here\n",
    "paul = np.random.random(1000)\n",
    "pk2 = thinkstats2.Pmf(paul)\n",
    "thinkplot.Pmf(pk2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'xscale': 'linear', 'yscale': 'linear'}"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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snZdSt06tgDsSSQ2Fu4RGYWExXW+IDPZ7Bp3PoQfunYKORFJH4S6h8M3y1Vz/tykR44/f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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe1817b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution goes here\n",
    "pk3 = thinkstats2.Cdf(paul)\n",
    "thinkplot.Cdf(pk3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}