hw03.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Homework 3: Tables and Charts\n",
    "Reading: Textbook chapters [5](http://www.inferentialthinking.com/chapters/05/tables.html) and [6](https://www.inferentialthinking.com/chapters/06/visualization.html).\n",
    "\n",
    "Please complete this notebook by filling in the cells provided. Before you begin, execute the following cell to load the provided tests. Each time you start your server, you will need to execute this cell again to load the tests."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=====================================================================\n",
      "Assignment: Homework 3: Tables and Charts\n",
      "OK, version v1.12.5\n",
      "=====================================================================\n",
      "\n",
      "Successfully logged in as kcs1992@berkeley.edu\n"
     ]
    }
   ],
   "source": [
    "# Don't change this cell; just run it. \n",
    "\n",
    "import numpy as np\n",
    "from datascience import *\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plots\n",
    "plots.style.use('fivethirtyeight')\n",
    "\n",
    "from client.api.notebook import Notebook\n",
    "ok = Notebook('hw03.ok')\n",
    "_ = ok.auth(inline=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color=\"#E74C3C\">**Important**: The `ok` tests don't usually tell you that your answer is correct. More often, they help catch careless mistakes. It's up to you to ensure that your answer is correct. If you're not sure, ask someone (not for the answer, but for some guidance about your approach).</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Differences between Universities, Part II\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 1.** Suppose you're choosing a university to attend, and you'd like to *quantify* how *dissimilar* any two universities are.  You rate each university you're considering on several numerical traits.  You decide on a very detailed list of 1000 traits, and you measure all of them!  Some examples:\n",
    "\n",
    "* The cost to attend (per year)\n",
    "* The average Yelp review of nearby Thai restaurants\n",
    "* The USA Today ranking of the Medical school\n",
    "* The USA Today ranking of the Engineering school\n",
    "\n",
    "You decide that the dissimilarity between two universities is the *total* of the differences in their traits.  That is, the dissimilarity is:\n",
    "\n",
    "* the **sum** of\n",
    "* the absolute values of\n",
    "* the 1000 differences in their trait values.\n",
    "\n",
    "In the next cell, we've loaded arrays containing the 1000 trait values for Stanford and Berkeley.  Compute the dissimilarity (according to the above method) between Stanford and Berkeley.  Call your answer `dissimilarity`.  Use a single line of code to compute the answer.\n",
    "\n",
    "*Note:* The data we're using aren't real -- we made them up for this exercise, except for the cost-of-attendance numbers, which we estimated for a student from a median-income family living in California using [this tool](http://college-tuition.startclass.com)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14060.558701067917"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stanford = Table.read_table(\"stanford.csv\").column(\"Trait value\")\n",
    "berkeley = Table.read_table(\"berkeley.csv\").column(\"Trait value\")\n",
    "\n",
    "dissimilarity = sum(abs(stanford-berkeley))\n",
    "dissimilarity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Running tests\n",
      "\n",
      "---------------------------------------------------------------------\n",
      "Test summary\n",
      "    Passed: 1\n",
      "    Failed: 0\n",
      "[ooooooooook] 100.0% passed\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = ok.grade('q1_1')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 2.** Identify all the subexpressions in your answer to the previous question, excluding the whole expression itself.  Write each on its own line.  Before each one, write a one-line comment describing the value of the subexpression, including what type of value it is.  We've written the first one for you.  (It should appear somewhere in your answer to the previous question!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "        -1.20945802e-01,   2.59027526e+01,  -6.88863749e+00,\n",
       "        -2.50838658e+01,  -7.08849091e-01,  -7.93207515e+00,\n",
       "        -1.42913658e+01,  -2.76057942e-01,  -4.52965480e-01,\n",
       "        -1.33538269e+00,  -2.01475037e+00,   1.73432569e+01,\n",
       "         2.18534418e+00,   6.24203262e-01,  -1.70345570e+00,\n",
       "        -3.84499191e+01,   4.30021655e-01,   1.96767688e+00,\n",
       "         1.96515305e+00,  -2.12413709e+01,  -1.98983759e+00,\n",
       "        -4.18538855e+01,   9.95450383e+00,  -1.79213904e+00,\n",
       "         7.84163945e-01,  -8.76632864e-01,   2.17972316e+01,\n",
       "        -1.82865771e+00,  -1.30580263e+01,  -4.68181379e+00,\n",
       "         2.79449720e+00,  -9.16168869e-01,  -1.54605774e+01,\n",
       "        -1.08307539e+01,  -1.88264801e+01,  -1.67800829e+00,\n",
       "        -3.08038062e-01,  -1.63204671e+00,  -6.89054950e-01,\n",
       "         4.08411836e+01,  -2.09289343e-01,  -2.42426507e+01,\n",
       "        -8.00731790e+00,   3.64442878e+01,  -2.70548994e+01,\n",
       "        -1.50442055e+00,  -1.08804493e+01,  -5.81672409e-01,\n",
       "         1.54058978e+01,  -1.24495197e-01,   3.38399309e+01,\n",
       "         5.47689759e-01,  -2.37537805e+00,  -3.12478538e+00,\n",
       "        -1.24564130e+01,   2.29876024e+00,   3.52772607e-01,\n",
       "         9.32473350e-01,   4.46813826e-02,  -1.62305828e+00,\n",
       "         1.84032236e+00,   1.37354133e+00,  -1.70998549e+01,\n",
       "        -2.18446928e-01,  -2.13424116e+01,   2.05730055e+01,\n",
       "        -3.03103370e+01,  -2.58406786e+01,   2.35471907e-01,\n",
       "         2.54345821e+00,  -5.84631254e-01,  -2.20600755e+01,\n",
       "        -2.12676510e+00,  -7.93968009e-01,  -9.73557052e+00,\n",
       "         4.31927765e+00,  -5.76336349e+00,  -7.46593823e-01,\n",
       "         2.99116209e-01,  -8.90945877e-01,  -1.64073889e+00,\n",
       "         8.19320788e+00,   6.00155989e-02,   3.31050737e+01,\n",
       "        -1.92693589e+01,   7.73439184e-02,   1.04661636e+00,\n",
       "         5.23465201e+00,   9.66405362e-01,  -2.34057943e-01,\n",
       "        -1.93664932e+01,   5.46869449e+00,  -5.84895245e+00,\n",
       "        -1.95350412e+01,   1.16880368e+00,   1.14361102e+00,\n",
       "         2.85444216e+01,  -3.92041943e+01,  -6.88080396e-01,\n",
       "         1.59848169e+00,  -1.09471761e+00,   6.99026233e-01,\n",
       "        -9.32176005e-01,  -4.04742648e-01,  -3.80847341e+01,\n",
       "         1.49198298e+00,  -1.58050144e+01,  -2.14860302e+01,\n",
       "         7.31092704e+00,  -7.42401602e+00,   1.74788468e+00,\n",
       "        -1.67793535e+00,  -2.86767389e+00,  -2.92811569e+01,\n",
       "        -3.57795141e+01,   1.52853044e+01,  -7.08761883e+00,\n",
       "        -7.38839601e-01,  -2.25355344e+01,  -8.08128952e-01,\n",
       "        -6.13442082e+00,   6.60209508e-01,  -2.18090248e+00,\n",
       "        -4.26641062e-01,   4.93345347e+01,   1.07964445e+01,\n",
       "        -2.48693457e-02,   4.20224489e-02,   3.95155212e+01,\n",
       "         9.40879169e+00,  -3.13996041e-02,  -1.48193822e+00,\n",
       "         1.56008531e+01,  -2.60850582e+00,   4.90046976e-01,\n",
       "        -7.06855721e-01,   1.41619814e+01,   5.48053739e-01,\n",
       "         2.48332944e+01,   2.09114451e+01,  -3.11705081e+01,\n",
       "         1.01615302e+01,   2.17765743e+00,  -4.03006703e+00,\n",
       "        -2.40961181e+01,   1.69030162e+00,   2.54584763e+01,\n",
       "        -1.89717587e+00,  -1.82607266e+00,   4.51831104e+00,\n",
       "         8.45223551e-01,   2.70726438e-01,  -7.59992432e-02,\n",
       "        -2.43850862e+00,   1.14313956e+00,  -1.21143926e+01,\n",
       "         2.96016468e+01,   8.30657671e-01,   6.60029594e-01,\n",
       "        -7.55716553e-01,   3.13187716e+00,   3.58109490e+01,\n",
       "        -1.31221726e+00,  -4.73042389e+00,   1.97166475e+01,\n",
       "         3.82611771e+01,  -1.30382683e+01,   1.07155668e+00,\n",
       "        -6.27769169e-01,   2.36672266e+01,  -1.75933230e+01,\n",
       "        -1.17312836e+00,   1.51896851e+01,  -2.49950917e+01,\n",
       "         1.38338512e+00,  -7.23206053e+00,  -1.83700204e+00,\n",
       "        -1.51665656e+01,  -1.21268295e+00,  -1.99624406e+00,\n",
       "        -1.69631029e+00,  -4.36453156e+01,   1.14446729e+00,\n",
       "         1.00324210e-01,   5.00832244e-01,  -2.11361292e+01,\n",
       "         8.26468100e+00,  -2.38346521e+00,   2.11711221e+00,\n",
       "        -6.04140293e-01,   3.88989389e-01,  -2.95145033e+01,\n",
       "        -2.99705038e+00,   1.23933659e+01,   5.83931723e+00,\n",
       "        -2.93697523e+00,  -4.24904116e+00,  -1.24151066e+01,\n",
       "         1.84984859e+00,  -9.81482013e-01,   3.88642268e+01,\n",
       "         4.07850150e+01,  -3.91872565e+01,   3.72525178e-02,\n",
       "        -2.08198318e+00,   1.09437193e+00,   5.27212105e-01,\n",
       "         3.02464786e+01,  -1.98980307e+00,  -1.49085548e+00,\n",
       "         8.38421274e+00,   1.36519654e+00,  -9.77500282e+00,\n",
       "        -1.42974440e+00,  -5.52612863e-01,   6.35057248e-01,\n",
       "         7.32787527e+00,  -1.38355495e+01,   4.39212825e+00,\n",
       "         1.01280732e-01,   6.27056642e-01,  -1.41719189e+00,\n",
       "        -1.08557622e+01,  -1.90880448e+00,   5.60659280e+00,\n",
       "         7.88334727e+00,  -9.40391569e-01,  -3.05633886e-01,\n",
       "        -2.44879634e+00,  -1.09183317e+00,  -2.04657108e+00,\n",
       "        -2.32587813e+01,   7.32556600e-01,   1.28543880e+01,\n",
       "         5.39710015e+00,   1.18725898e+01,  -2.11806020e+00,\n",
       "         1.12519609e+00,  -1.65595678e+01,   2.32136908e+01,\n",
       "        -1.34892610e+01,   1.34333659e+00,   1.34562393e+01,\n",
       "        -7.42351739e-02,   3.66161333e+01,  -1.61501685e+00,\n",
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       "        -1.27786226e+00,  -4.46107852e+01,   6.76724524e-02,\n",
       "        -5.72342115e+00,  -5.92262205e+00,   2.49304498e+01,\n",
       "        -3.99422345e+00,  -1.75034367e+01,  -9.19798809e-01,\n",
       "        -5.34314842e-01,  -2.52792686e-01,   3.96557687e-01,\n",
       "        -1.68386298e+00,  -7.05462580e+00,   1.24115793e+00,\n",
       "        -2.51353666e+01,   1.06432484e+00,  -1.90746417e+00,\n",
       "        -2.48671072e+00,  -3.01451875e-01,   1.60088458e+01,\n",
       "         1.87844316e+01,  -1.55026952e+00,  -7.92387662e-01,\n",
       "         3.16998655e+00,   3.60242472e+00,   2.35987346e-01,\n",
       "        -1.50529756e+01,  -1.67764975e+01,   1.64514293e+01,\n",
       "         2.78827718e-01,  -3.14404223e-01,  -1.09529610e+01,\n",
       "         2.67105454e+01,  -4.67258932e+01,  -3.54764082e+01,\n",
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       "        -1.25864447e+01,  -1.20093605e-01,   1.76519248e+01,\n",
       "        -2.82273214e+00,  -2.89288992e-01,  -2.37138339e+00,\n",
       "         2.09524639e+00,  -1.28320747e+00,   1.71913221e+01,\n",
       "        -2.18137684e+00,  -5.30589581e+00,  -1.70779437e+00,\n",
       "         3.32471744e+01,  -4.41211786e+01,   1.14506109e+01,\n",
       "         1.92932377e+00,  -2.76150160e-02,  -1.56757914e+01,\n",
       "        -3.22018442e+01,   8.53138684e+00,  -5.10355683e+00,\n",
       "         2.85638550e+01,   1.56726595e-01,  -2.75729755e+00,\n",
       "        -1.06375388e+00,   1.04780701e+00,   6.62828980e+00,\n",
       "        -3.15564415e+00,   4.15015443e-01,   9.23969503e-01,\n",
       "         1.56956511e+00,   2.03670911e+00,   1.48472604e+01,\n",
       "         4.27121811e-01,   1.93803684e-01,  -1.20938652e+01,\n",
       "         1.81012768e+01,   3.06668514e+01,   1.52559193e+01,\n",
       "         7.79645498e+00,   2.14777195e+00,   2.34679895e+01,\n",
       "        -4.39594772e-01,  -1.39288125e-01,  -2.39724498e+00,\n",
       "         1.03116715e+00,  -4.16720922e-01,  -2.79356953e+01,\n",
       "         1.32944408e+00,  -1.70512133e+00,   1.76348926e+01,\n",
       "        -2.40239857e-01,  -8.35068861e+00,   2.46155064e+01,\n",
       "        -1.35405206e+00,   1.50641529e+00,   1.80097882e-01,\n",
       "         6.08267923e+00,   7.79103831e-02,  -1.90277046e+00,\n",
       "         1.34211469e+00,   1.28520861e+01,  -1.58645073e+00,\n",
       "        -2.54913498e+01,  -1.76137264e+00,  -7.49477720e+00,\n",
       "        -4.53190168e-01,   3.59246824e+00,  -1.68965313e+01,\n",
       "        -9.65257440e-01,  -5.54019094e-01,  -3.29938996e+01,\n",
       "         5.00599707e-01,   7.33324249e-01,  -1.76829314e+00,\n",
       "         1.07978996e+01,  -4.12408932e+00,   1.55683398e+00,\n",
       "         5.97774451e-01,   3.45778155e-01,  -2.91719587e+01,\n",
       "         2.57381885e+01,  -5.11391677e-02,  -1.81093425e+00,\n",
       "         3.60193896e+00,  -1.56370806e-01,   1.87578690e-01,\n",
       "        -1.01007418e+01,  -1.23176296e+00,   6.23607357e-01,\n",
       "        -9.69809441e+00,   2.01583497e+00,   9.53865467e+00,\n",
       "         5.70110959e-01,  -1.66128695e-01,  -2.90285673e-01,\n",
       "         2.16613160e+01,  -8.71868523e-02,  -2.16171643e+00,\n",
       "        -5.55161844e-01,   1.45131985e+01,  -7.94541135e-01,\n",
       "        -1.10959298e+01,  -2.52718251e+01,   5.25944270e-01,\n",
       "         7.95084037e-02,  -2.95907442e+01,  -3.58665109e-01,\n",
       "        -4.79265595e-01,   1.66974716e+00,   5.26149289e+00,\n",
       "         4.44683410e+00,  -4.09395512e-01,   3.30562842e+01,\n",
       "         2.74206245e+01,   1.16549535e+01,  -9.22417134e+00,\n",
       "        -1.22021862e+00,  -4.04369197e-02,   9.13013800e-02,\n",
       "         3.56001538e+01,   9.17811579e-02,  -1.16079894e+01,\n",
       "         7.26784223e-01,   1.81126019e+00,   8.20449516e-01,\n",
       "         9.59524009e-01,  -6.32900987e+00,   3.71487914e-01,\n",
       "        -2.82920371e+00,  -4.57624720e+01,  -2.77769565e+01,\n",
       "        -7.22165383e-01,   1.39172584e+00,   4.25164900e+00,\n",
       "         7.39457252e+00,  -1.29054091e+00,  -8.65232874e-01,\n",
       "         7.20842624e-01,   1.86838454e-01,   2.16198985e+00,\n",
       "        -4.84800044e+00,   3.12580317e-02,   1.04907541e+00,\n",
       "        -1.19303788e+00,   1.72495977e+00,  -2.60129548e+00,\n",
       "         2.90536220e-01,   1.10971453e+01,  -6.32906060e-01,\n",
       "        -3.49015594e-01,  -1.66795670e+00,  -1.73327403e-01,\n",
       "         1.29814971e-01,   5.88282519e-02,  -2.75236907e+01,\n",
       "         1.57485072e+00,  -2.30754197e+00,  -9.69976164e-01,\n",
       "         8.47211134e-02,  -3.16985706e+01,   1.49867081e+00,\n",
       "         1.49992667e+01,  -4.09282831e-01,  -8.98600432e-01,\n",
       "         1.91979711e+00,   3.37287091e+00,  -2.46440145e+01,\n",
       "         3.78382267e+01,   6.75098110e-01,  -4.31109946e-01,\n",
       "        -3.76378619e-01,   4.90704459e-01,   3.06599806e+01,\n",
       "         2.34523364e+01,  -6.38520949e-01,  -3.77880377e-01,\n",
       "        -7.38155694e-01,  -1.05313209e-01,  -6.11263012e-02,\n",
       "        -1.08792695e+01,   1.94733636e+00,   1.21405659e+00,\n",
       "         1.93003365e+01,   7.23899453e-01,  -2.90093302e+01,\n",
       "         1.38113622e+01,   1.41804444e-01,   2.15489268e+01,\n",
       "        -1.43710743e+01,  -2.03637024e+01,  -4.04527109e-01,\n",
       "         3.53835261e+00,  -9.55420552e+00,   3.65626547e+01,\n",
       "         3.05051876e+00,   1.57384118e-01,   2.22125346e+01,\n",
       "        -6.60156120e-01,  -1.21098664e+00,  -1.82168031e+01,\n",
       "        -2.85897609e+00,  -3.99834443e+01,   1.87125788e+01,\n",
       "         8.80009549e-01,  -1.14171068e+00,   3.57459545e+01,\n",
       "         3.63836995e+01,  -2.00140466e+01,  -1.38050648e+01,\n",
       "         2.32630887e-01])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stanford-berkeley\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "for_assignment_type": "student"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# An array of 1000 numbers, each a different measured trait of Stanford University.\n",
    "stanford # whole expressions\n",
    "berkeley # whole expressions\n",
    "stanford-berkeley #the 1000 differences in their trait values.\n",
    "abs(stanford-berkeley)#abs value of 1000 differences\n",
    "sum(abs(stanford-berkeley))# sum up the 1000 differences\n",
    "\n",
    "\n",
    "type(stanford) #numpy.ndarray\n",
    "type(berkeley) #numpy.ndarray\n",
    " \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 3.** Why do we sum up the absolute values of the differences in trait values, rather than just summing up the differences?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "manual_grade": true,
    "manual_problem_id": "more_universities_3"
   },
   "source": [
    "*Without the absolute values, the number could become negative and it might not be meaningful.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Weighing the traits\n",
    "After computing dissimilarities between several schools, you notice a problem with your method: the scale of the traits matters a lot.\n",
    "\n",
    "Since schools cost tens of thousands of dollars to attend, the cost-to-attend trait is always a much bigger *number* than most other traits.  That makes it affect the dissimilarity a lot more than other traits.  Two schools that differ in cost-to-attend by \\$900, but are otherwise identical, get a dissimilarity of 900.  But two schools that differ in graduation rate by .9 (a huge difference!), but are otherwise identical, get a dissimilarity of only .9.\n",
    "\n",
    "One way to fix this problem is to assign different \"weights\" to different traits.  For example, we could fix the problem above by multiplying the difference in the cost-to-attend traits by .001, so that a difference of \\$900 in cost-to-attend results in a dissimilarity of $900 \\times .001$, or $.9$.\n",
    "\n",
    "Here's a revised method that does that for every trait:\n",
    "\n",
    "1. For each trait, subtract the two schools' trait values.\n",
    "2. Then take the absolute value of that difference.\n",
    "3. *Now multiply that absolute value by a trait-specific number, like .001 or 2.*\n",
    "4. Now sum the 1000 resulting numbers.\n",
    "\n",
    "**Question 4.** Suppose you've already decided on a weight for each trait.  These are loaded into an array called `weights` in the cell below.  `weights.item(0)` is the weight for the first trait, `weights.item(1)` is the weight for the second trait, and so on.  Use the revised method to compute a revised dissimilarity between Berkeley and Stanford.\n",
    "\n",
    "*Hint:* Using array arithmetic, your answer should be almost as short as in question 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "505.98313211458805"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights = Table.read_table(\"weights.csv\").column(\"Weight\")\n",
    "\n",
    "revised_dissimilarity = sum(abs(stanford-berkeley)*weights)\n",
    "revised_dissimilarity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Running tests\n",
      "\n",
      "---------------------------------------------------------------------\n",
      "Test summary\n",
      "    Passed: 1\n",
      "    Failed: 0\n",
      "[ooooooooook] 100.0% passed\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = ok.grade('q1_4')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Unemployment\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Federal Reserve Bank of St. Louis publishes data about jobs in the US.  Below we've loaded data on unemployment in the United States.  There are many ways of defining unemployment, and our dataset includes two notions of the unemployment rate:\n",
    "\n",
    "1. Among people who are able to work and are looking for a full-time job, the percentage who can't find a job.  This is called the Non-Employment Index, or NEI.\n",
    "2. Among people who are able to work and are looking for a full-time job, the percentage who can't find any job *or* are only working at a part-time job.  The latter group is called \"Part-Time for Economic Reasons\", so the acronym for this index is NEI-PTER.  (Economists are great at marketing.)\n",
    "\n",
    "The source of the data is [here](https://fred.stlouisfed.org/categories/33509)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 1.** The data are in a CSV file called `unemployment.csv`.  Load that file into a table called `unemployment`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Date</th> <th>NEI</th> <th>NEI-PTER</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>1994-01-01</td> <td>10.0974</td> <td>11.172  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1994-04-01</td> <td>9.6239 </td> <td>10.7883 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1994-07-01</td> <td>9.3276 </td> <td>10.4831 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1994-10-01</td> <td>9.1071 </td> <td>10.2361 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1995-01-01</td> <td>8.9693 </td> <td>10.1832 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1995-04-01</td> <td>9.0314 </td> <td>10.1071 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1995-07-01</td> <td>8.9802 </td> <td>10.1084 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1995-10-01</td> <td>8.9932 </td> <td>10.1046 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1996-01-01</td> <td>9.0002 </td> <td>10.0531 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1996-04-01</td> <td>8.9038 </td> <td>9.9782  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (80 rows omitted)</p"
      ],
      "text/plain": [
       "Date       | NEI     | NEI-PTER\n",
       "1994-01-01 | 10.0974 | 11.172\n",
       "1994-04-01 | 9.6239  | 10.7883\n",
       "1994-07-01 | 9.3276  | 10.4831\n",
       "1994-10-01 | 9.1071  | 10.2361\n",
       "1995-01-01 | 8.9693  | 10.1832\n",
       "1995-04-01 | 9.0314  | 10.1071\n",
       "1995-07-01 | 8.9802  | 10.1084\n",
       "1995-10-01 | 8.9932  | 10.1046\n",
       "1996-01-01 | 9.0002  | 10.0531\n",
       "1996-04-01 | 8.9038  | 9.9782\n",
       "... (80 rows omitted)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unemployment = Table.read_table('unemployment.csv')\n",
    "\n",
    "unemployment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Running tests\n",
      "\n",
      "---------------------------------------------------------------------\n",
      "Test summary\n",
      "    Passed: 1\n",
      "    Failed: 0\n",
      "[ooooooooook] 100.0% passed\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = ok.grade('q2_1')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 2.** Sort the data in decreasing order by NEI, naming the sorted table `by_nei`.  Create another table called `by_nei_pter` that's sorted in decreasing order by NEI-PTER instead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Date</th> <th>NEI</th> <th>NEI-PTER</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>2009-10-01</td> <td>10.9698</td> <td>12.8557 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2009-07-01</td> <td>10.8089</td> <td>12.7404 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2010-01-01</td> <td>10.9054</td> <td>12.7311 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2010-04-01</td> <td>10.6597</td> <td>12.5664 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2009-04-01</td> <td>10.7082</td> <td>12.5497 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2010-10-01</td> <td>10.5856</td> <td>12.4329 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2010-07-01</td> <td>10.5521</td> <td>12.3897 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2011-01-01</td> <td>10.5024</td> <td>12.3017 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2011-07-01</td> <td>10.4856</td> <td>12.2507 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2011-04-01</td> <td>10.4409</td> <td>12.247  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (80 rows omitted)</p"
      ],
      "text/plain": [
       "Date       | NEI     | NEI-PTER\n",
       "2009-10-01 | 10.9698 | 12.8557\n",
       "2009-07-01 | 10.8089 | 12.7404\n",
       "2010-01-01 | 10.9054 | 12.7311\n",
       "2010-04-01 | 10.6597 | 12.5664\n",
       "2009-04-01 | 10.7082 | 12.5497\n",
       "2010-10-01 | 10.5856 | 12.4329\n",
       "2010-07-01 | 10.5521 | 12.3897\n",
       "2011-01-01 | 10.5024 | 12.3017\n",
       "2011-07-01 | 10.4856 | 12.2507\n",
       "2011-04-01 | 10.4409 | 12.247\n",
       "... (80 rows omitted)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "by_nei = unemployment.sort('NEI',descending=True)\n",
    "by_nei\n",
    "by_nei_pter = unemployment.sort('NEI-PTER', descending=True)\n",
    "by_nei_pter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Running tests\n",
      "\n",
      "---------------------------------------------------------------------\n",
      "Test summary\n",
      "    Passed: 1\n",
      "    Failed: 0\n",
      "[ooooooooook] 100.0% passed\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = ok.grade('q2_2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 3.** Use `take` to make a table containing the data for the 10 quarters when NEI was greatest.  Call that table `greatest_nei`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Date</th> <th>NEI</th> <th>NEI-PTER</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>2009-10-01</td> <td>10.9698</td> <td>12.8557 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2010-01-01</td> <td>10.9054</td> <td>12.7311 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2009-07-01</td> <td>10.8089</td> <td>12.7404 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2009-04-01</td> <td>10.7082</td> <td>12.5497 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2010-04-01</td> <td>10.6597</td> <td>12.5664 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2010-10-01</td> <td>10.5856</td> <td>12.4329 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2010-07-01</td> <td>10.5521</td> <td>12.3897 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2011-01-01</td> <td>10.5024</td> <td>12.3017 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2011-07-01</td> <td>10.4856</td> <td>12.2507 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2011-04-01</td> <td>10.4409</td> <td>12.247  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "Date       | NEI     | NEI-PTER\n",
       "2009-10-01 | 10.9698 | 12.8557\n",
       "2010-01-01 | 10.9054 | 12.7311\n",
       "2009-07-01 | 10.8089 | 12.7404\n",
       "2009-04-01 | 10.7082 | 12.5497\n",
       "2010-04-01 | 10.6597 | 12.5664\n",
       "2010-10-01 | 10.5856 | 12.4329\n",
       "2010-07-01 | 10.5521 | 12.3897\n",
       "2011-01-01 | 10.5024 | 12.3017\n",
       "2011-07-01 | 10.4856 | 12.2507\n",
       "2011-04-01 | 10.4409 | 12.247"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "greatest_nei = (unemployment.sort('NEI', descending=True)).take(np.arange(0,10,1))\n",
    "greatest_nei"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Running tests\n",
      "\n",
      "---------------------------------------------------------------------\n",
      "Test summary\n",
      "    Passed: 1\n",
      "    Failed: 0\n",
      "[ooooooooook] 100.0% passed\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = ok.grade('q2_3')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 4.** It's believed that many people became PTER (recall: \"Part-Time for Economic Reasons\") in the \"Great Recession\" of 2008-2009.  NEI-PTER is the percentage of people who are unemployed (and counted in the NEI) plus the percentage of people who are PTER.  Compute an array containing the percentage of people who were PTER in each quarter.  (The first element of the array should correspond to the first row of `unemployment`, and so on.)\n",
    "\n",
    "*Note:* Use the original `unemployment` table for this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.0746,  1.1644,  1.1555,  1.129 ,  1.2139,  1.0757,  1.1282,\n",
       "        1.1114,  1.0529,  1.0744,  1.1004,  1.0747,  1.0705,  1.0455,\n",
       "        1.008 ,  0.9734,  0.9753,  0.8931,  0.9451,  0.8367,  0.8208,\n",
       "        0.8105,  0.8248,  0.7578,  0.7251,  0.7445,  0.7543,  0.7423,\n",
       "        0.7399,  0.7687,  0.8418,  0.9923,  0.9181,  0.9629,  0.9703,\n",
       "        0.9575,  1.0333,  1.0781,  1.0675,  1.0354,  1.0601,  1.01  ,\n",
       "        1.0042,  1.0368,  0.9704,  0.923 ,  0.9759,  0.93  ,  0.889 ,\n",
       "        0.821 ,  0.9409,  0.955 ,  0.898 ,  0.8948,  0.9523,  0.9579,\n",
       "        1.0149,  1.0762,  1.2873,  1.4335,  1.7446,  1.8415,  1.9315,\n",
       "        1.8859,  1.8257,  1.9067,  1.8376,  1.8473,  1.7993,  1.8061,\n",
       "        1.7651,  1.7927,  1.7286,  1.6387,  1.6808,  1.6805,  1.6629,\n",
       "        1.6253,  1.6477,  1.6298,  1.4796,  1.5131,  1.4866,  1.4345,\n",
       "        1.3675,  1.3097,  1.2319,  1.1735,  1.1844,  1.1746])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pter = unemployment.column(\"NEI-PTER\")-unemployment.column(\"NEI\")\n",
    "pter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Running tests\n",
      "\n",
      "---------------------------------------------------------------------\n",
      "Test summary\n",
      "    Passed: 1\n",
      "    Failed: 0\n",
      "[ooooooooook] 100.0% passed\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = ok.grade('q2_4')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 5.** Add `pter` as a column to `unemployment` (named \"PTER\") and sort the resulting table by that column in decreasing order.  Call the table `by_pter`.\n",
    "\n",
    "Try to do this with a single line of code, if you can."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Date</th> <th>NEI</th> <th>NEI-PTER</th> <th>PTER</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>2009-07-01</td> <td>10.8089</td> <td>12.7404 </td> <td>1.9315</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2010-04-01</td> <td>10.6597</td> <td>12.5664 </td> <td>1.9067</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2009-10-01</td> <td>10.9698</td> <td>12.8557 </td> <td>1.8859</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2010-10-01</td> <td>10.5856</td> <td>12.4329 </td> <td>1.8473</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2009-04-01</td> <td>10.7082</td> <td>12.5497 </td> <td>1.8415</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2010-07-01</td> <td>10.5521</td> <td>12.3897 </td> <td>1.8376</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2010-01-01</td> <td>10.9054</td> <td>12.7311 </td> <td>1.8257</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2011-04-01</td> <td>10.4409</td> <td>12.247  </td> <td>1.8061</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2011-01-01</td> <td>10.5024</td> <td>12.3017 </td> <td>1.7993</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2011-10-01</td> <td>10.3287</td> <td>12.1214 </td> <td>1.7927</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (80 rows omitted)</p"
      ],
      "text/plain": [
       "Date       | NEI     | NEI-PTER | PTER\n",
       "2009-07-01 | 10.8089 | 12.7404  | 1.9315\n",
       "2010-04-01 | 10.6597 | 12.5664  | 1.9067\n",
       "2009-10-01 | 10.9698 | 12.8557  | 1.8859\n",
       "2010-10-01 | 10.5856 | 12.4329  | 1.8473\n",
       "2009-04-01 | 10.7082 | 12.5497  | 1.8415\n",
       "2010-07-01 | 10.5521 | 12.3897  | 1.8376\n",
       "2010-01-01 | 10.9054 | 12.7311  | 1.8257\n",
       "2011-04-01 | 10.4409 | 12.247   | 1.8061\n",
       "2011-01-01 | 10.5024 | 12.3017  | 1.7993\n",
       "2011-10-01 | 10.3287 | 12.1214  | 1.7927\n",
       "... (80 rows omitted)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "by_pter = unemployment.with_columns(\"PTER\", pter).sort(\"PTER\", descending=True)\n",
    "by_pter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Running tests\n",
      "\n",
      "---------------------------------------------------------------------\n",
      "Test summary\n",
      "    Passed: 1\n",
      "    Failed: 0\n",
      "[ooooooooook] 100.0% passed\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = ok.grade('q2_5')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 6.** Does it seem true that the PTER rate was very high during the Great Recession, compared to other periods in the dataset? Justify your answer by referring to specific values in the table or by generating a chart."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Date</th> <th>NEI</th> <th>NEI-PTER</th> <th>PTER</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>2010-10-01</td> <td>10.5856</td> <td>12.4329 </td> <td>1.8473</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2010-07-01</td> <td>10.5521</td> <td>12.3897 </td> <td>1.8376</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2010-04-01</td> <td>10.6597</td> <td>12.5664 </td> <td>1.9067</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2010-01-01</td> <td>10.9054</td> <td>12.7311 </td> <td>1.8257</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2009-10-01</td> <td>10.9698</td> <td>12.8557 </td> <td>1.8859</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2009-07-01</td> <td>10.8089</td> <td>12.7404 </td> <td>1.9315</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2009-04-01</td> <td>10.7082</td> <td>12.5497 </td> <td>1.8415</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2009-01-01</td> <td>10.2693</td> <td>12.0139 </td> <td>1.7446</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2008-10-01</td> <td>9.2555 </td> <td>10.689  </td> <td>1.4335</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2008-07-01</td> <td>8.884  </td> <td>10.1713 </td> <td>1.2873</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2008-04-01</td> <td>8.5176 </td> <td>9.5938  </td> <td>1.0762</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2008-01-01</td> <td>8.3326 </td> <td>9.3475  </td> <td>1.0149</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2007-10-01</td> <td>8.2687 </td> <td>9.2266  </td> <td>0.9579</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2007-07-01</td> <td>8.1828 </td> <td>9.1351  </td> <td>0.9523</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2007-04-01</td> <td>8.2629 </td> <td>9.1577  </td> <td>0.8948</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2007-01-01</td> <td>8.1203 </td> <td>9.0183  </td> <td>0.898 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2006-10-01</td> <td>8.1316 </td> <td>9.0866  </td> <td>0.955 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2006-07-01</td> <td>8.2011 </td> <td>9.142   </td> <td>0.9409</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2006-04-01</td> <td>8.3396 </td> <td>9.1606  </td> <td>0.821 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2006-01-01</td> <td>8.289  </td> <td>9.178   </td> <td>0.889 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2005-10-01</td> <td>8.3971 </td> <td>9.3271  </td> <td>0.93  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2005-07-01</td> <td>8.3727 </td> <td>9.3486  </td> <td>0.9759</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2005-04-01</td> <td>8.5138 </td> <td>9.4368  </td> <td>0.923 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2005-01-01</td> <td>8.5683 </td> <td>9.5387  </td> <td>0.9704</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2004-10-01</td> <td>8.6651 </td> <td>9.7019  </td> <td>1.0368</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2004-07-01</td> <td>8.6804 </td> <td>9.6846  </td> <td>1.0042</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2004-04-01</td> <td>8.7244 </td> <td>9.7344  </td> <td>1.01  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2004-01-01</td> <td>8.791  </td> <td>9.8511  </td> <td>1.0601</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2003-10-01</td> <td>8.9607 </td> <td>9.9961  </td> <td>1.0354</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2003-07-01</td> <td>9.0202 </td> <td>10.0877 </td> <td>1.0675</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2003-04-01</td> <td>8.944  </td> <td>10.0221 </td> <td>1.0781</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2003-01-01</td> <td>8.8809 </td> <td>9.9142  </td> <td>1.0333</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2002-10-01</td> <td>8.7184 </td> <td>9.6759  </td> <td>0.9575</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2002-07-01</td> <td>8.8508 </td> <td>9.8211  </td> <td>0.9703</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2002-04-01</td> <td>8.9295 </td> <td>9.8924  </td> <td>0.9629</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2002-01-01</td> <td>9.0119 </td> <td>9.93    </td> <td>0.9181</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2001-10-01</td> <td>8.6782 </td> <td>9.6705  </td> <td>0.9923</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2001-07-01</td> <td>8.1444 </td> <td>8.9862  </td> <td>0.8418</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2001-04-01</td> <td>8.0353 </td> <td>8.804   </td> <td>0.7687</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2001-01-01</td> <td>7.757  </td> <td>8.4969  </td> <td>0.7399</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2000-10-01</td> <td>7.6769 </td> <td>8.4192  </td> <td>0.7423</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2000-07-01</td> <td>7.6915 </td> <td>8.4458  </td> <td>0.7543</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2000-04-01</td> <td>7.6754 </td> <td>8.4199  </td> <td>0.7445</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2000-01-01</td> <td>7.6128 </td> <td>8.3379  </td> <td>0.7251</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1999-10-01</td> <td>7.7832 </td> <td>8.541   </td> <td>0.7578</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1999-07-01</td> <td>7.8956 </td> <td>8.7204  </td> <td>0.8248</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1999-04-01</td> <td>8.1083 </td> <td>8.9188  </td> <td>0.8105</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1999-01-01</td> <td>7.8933 </td> <td>8.7141  </td> <td>0.8208</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1998-10-01</td> <td>8.0568 </td> <td>8.8935  </td> <td>0.8367</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1998-07-01</td> <td>8.1194 </td> <td>9.0645  </td> <td>0.9451</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1998-04-01</td> <td>7.9992 </td> <td>8.8923  </td> <td>0.8931</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1998-01-01</td> <td>8.1216 </td> <td>9.0969  </td> <td>0.9753</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1997-10-01</td> <td>8.2335 </td> <td>9.2069  </td> <td>0.9734</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1997-07-01</td> <td>8.2957 </td> <td>9.3037  </td> <td>1.008 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1997-04-01</td> <td>8.4915 </td> <td>9.537   </td> <td>1.0455</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1997-01-01</td> <td>8.6661 </td> <td>9.7366  </td> <td>1.0705</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1996-10-01</td> <td>8.6554 </td> <td>9.7301  </td> <td>1.0747</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1996-07-01</td> <td>8.7627 </td> <td>9.8631  </td> <td>1.1004</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1996-04-01</td> <td>8.9038 </td> <td>9.9782  </td> <td>1.0744</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1996-01-01</td> <td>9.0002 </td> <td>10.0531 </td> <td>1.0529</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1995-10-01</td> <td>8.9932 </td> <td>10.1046 </td> <td>1.1114</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1995-07-01</td> <td>8.9802 </td> <td>10.1084 </td> <td>1.1282</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1995-04-01</td> <td>9.0314 </td> <td>10.1071 </td> <td>1.0757</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1995-01-01</td> <td>8.9693 </td> <td>10.1832 </td> <td>1.2139</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1994-10-01</td> <td>9.1071 </td> <td>10.2361 </td> <td>1.129 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1994-07-01</td> <td>9.3276 </td> <td>10.4831 </td> <td>1.1555</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1994-04-01</td> <td>9.6239 </td> <td>10.7883 </td> <td>1.1644</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1994-01-01</td> <td>10.0974</td> <td>11.172  </td> <td>1.0746</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#by_pter.show().sort(\"Date\", descending=True)\n",
    "\n",
    "#type(by_pter.column(\"Date\").item(0))\n",
    "by_pter.where(\"Date\", are.below(\"2010-12-30\")).sort(\"Date\", descending=True).show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "manual_grade": true,
    "manual_problem_id": "basic_sorting_6"
   },
   "source": [
    "*As i look at the table for PTER during Great Recession was high becuase right before 2008,\n",
    "it was about 1.00 and becomes 1.93 by the end of the Recession*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Birth Rates\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following table gives census-based population estimates for each state on July 1, 2015 and July 1, 2016. The last four columns describe the components of the estimated change in population during this time interval. *For all questions below, assume that the word \"states\" refers to all 52 rows including Puerto Rico & the District of Columbia.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>REGION</th> <th>NAME</th> <th>2015</th> <th>2016</th> <th>BIRTHS</th> <th>DEATHS</th> <th>MIGRATION</th> <th>OTHER</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>3     </td> <td>Alabama   </td> <td>4,853,875 </td> <td>4,863,300 </td> <td>58,556 </td> <td>52,405 </td> <td>3,874    </td> <td>-600  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>4     </td> <td>Alaska    </td> <td>737,709   </td> <td>741,894   </td> <td>11,255 </td> <td>4,511  </td> <td>-2,557   </td> <td>-2    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>4     </td> <td>Arizona   </td> <td>6,817,565 </td> <td>6,931,071 </td> <td>87,204 </td> <td>56,564 </td> <td>76,405   </td> <td>6,461 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>3     </td> <td>Arkansas  </td> <td>2,977,853 </td> <td>2,988,248 </td> <td>37,936 </td> <td>30,581 </td> <td>3,530    </td> <td>-490  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>4     </td> <td>California</td> <td>38,993,940</td> <td>39,250,017</td> <td>502,848</td> <td>273,850</td> <td>33,530   </td> <td>-6,451</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (47 rows omitted)</p"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Don't change this cell; just run it.\n",
    "# From http://www2.census.gov/programs-surveys/popest/datasets/2010-2016/national/totals/nst-est2016-alldata.csv\n",
    "# See http://www2.census.gov/programs-surveys/popest/datasets/2010-2015/national/totals/nst-est2015-alldata.pdf\n",
    "#     for column descriptions. (As of Feb 2017, no descriptions were posted for 2010-2016.)\n",
    "pop = Table.read_table('nst-est2016-alldata.csv').where('SUMLEV', 40).select([1, 4, 12, 13, 27, 34, 62, 69])\n",
    "pop = pop.relabeled(2, '2015').relabeled(3, '2016')\n",
    "pop = pop.relabeled(4, 'BIRTHS').relabeled(5, 'DEATHS')\n",
    "pop = pop.relabeled(6, 'MIGRATION').relabeled(7, 'OTHER')\n",
    "pop.set_format([2, 3, 4, 5, 6, 7], NumberFormatter(decimals=0)).show(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 1.** Assign `us_birth_rate` to the total US annual birth rate during this time interval. The annual birth rate for a year-long period is the number of births in that period as a proportion of the population at the start of the period."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.012358536498646102"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "us_birth_rate = sum(pop.column(\"BIRTHS\"))/sum(pop.column('2015'))\n",
    "us_birth_rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Running tests\n",
      "\n",
      "---------------------------------------------------------------------\n",
      "Test summary\n",
      "    Passed: 1\n",
      "    Failed: 0\n",
      "[ooooooooook] 100.0% passed\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = ok.grade('q3_1')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 2.** Assign `fastest_growth` to an array of the names of the five states with the fastest population growth rates in *descending order of growth rate*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Utah', 'Nevada', 'Idaho', 'Florida', 'Washington'], \n",
       "      dtype='<U20')"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "growth = (pop.column(\"2016\")-pop.column(\"2015\"))/pop.column(\"2015\")\n",
    "fastest_growth = (\n",
    "    pop.with_columns(\"Growth\",growth).sort(\"Growth\", descending=True).\n",
    "    take(np.arange(0,5,1)).column(\"NAME\"))\n",
    "        \n",
    "        \n",
    "                                                          \n",
    "\n",
    "\n",
    "fastest_growth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Running tests\n",
      "\n",
      "---------------------------------------------------------------------\n",
      "Test summary\n",
      "    Passed: 1\n",
      "    Failed: 0\n",
      "[ooooooooook] 100.0% passed\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = ok.grade('q3_2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 3.** Assign `movers` to the number of states for which the absolute annual rate of migration was higher than 1%. The annual rate of migration for a year-long period is the net number of migrations (in and out) as a proportion of the population at the start of the period. The `MIGRATION` column contains estimated annual net migration counts by state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mi_growth = abs(pop.column(\"MIGRATION\"))/pop.column(\"2015\")\n",
    "movers = (\n",
    "    pop.with_columns(\"MI_GROWTH\",mi_growth).\n",
    "    where(\"MI_GROWTH\",are.above(0.01)).column(\"NAME\")\n",
    ")\n",
    "\n",
    "movers = len(movers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Running tests\n",
      "\n",
      "---------------------------------------------------------------------\n",
      "Test summary\n",
      "    Passed: 1\n",
      "    Failed: 0\n",
      "[ooooooooook] 100.0% passed\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = ok.grade('q3_3')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 4.** Assign `west_births` to the total number of births that occurred in region 4 (the Western US). *Hint:* Make sure you double check the type of the values in the region column."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "979657"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(pop.column(\"REGION\").item(0))\n",
    "\n",
    "\n",
    "west_births = sum(pop.where(\"REGION\", are.equal_to(\"4\")).column(\"BIRTHS\"))\n",
    "west_births"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Running tests\n",
      "\n",
      "---------------------------------------------------------------------\n",
      "Test summary\n",
      "    Passed: 1\n",
      "    Failed: 0\n",
      "[ooooooooook] 100.0% passed\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = ok.grade('q3_4')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 5.** Assign `less_than_west_births` to the number of states that had a total population in 2016 that was smaller than the *number of babies born in region 4 (the Western US)* during this time interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "less_than_west_births=pop.where(\"2016\", are.below(west_births)).num_rows\n",
    "#less_than_west_births = (pop.where(\"NAME\", are.below(west_births)))\n",
    "less_than_west_births"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Running tests\n",
      "\n",
      "---------------------------------------------------------------------\n",
      "Test summary\n",
      "    Passed: 1\n",
      "    Failed: 0\n",
      "[ooooooooook] 100.0% passed\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = ok.grade('q3_5')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 6.** Was there an association between birth rate and death rate during this time interval? Use the code cell below to support your conclusion with a chart. If an association exists, what might explain it?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "manual_grade": true,
    "manual_problem_id": "births_6"
   },
   "source": [
    "*Write your answer here, replacing this text.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>REGION</th> <th>NAME</th> <th>2015</th> <th>2016</th> <th>BIRTHS</th> <th>DEATHS</th> <th>MIGRATION</th> <th>OTHER</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>4     </td> <td>Alaska              </td> <td>737,709</td> <td>741,894</td> <td>11,255</td> <td>4,511 </td> <td>-2,557   </td> <td>-2   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>3     </td> <td>Delaware            </td> <td>944,076</td> <td>952,065</td> <td>10,922</td> <td>8,945 </td> <td>5,583    </td> <td>429  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>3     </td> <td>District of Columbia</td> <td>670,377</td> <td>681,170</td> <td>9,779 </td> <td>5,455 </td> <td>6,392    </td> <td>77   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2     </td> <td>North Dakota        </td> <td>756,835</td> <td>757,952</td> <td>11,824</td> <td>6,172 </td> <td>-4,684   </td> <td>149  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2     </td> <td>South Dakota        </td> <td>857,919</td> <td>865,454</td> <td>12,114</td> <td>7,296 </td> <td>2,573    </td> <td>144  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>1     </td> <td>Vermont             </td> <td>626,088</td> <td>624,594</td> <td>6,035 </td> <td>5,547 </td> <td>-1,910   </td> <td>-72  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>4     </td> <td>Wyoming             </td> <td>586,555</td> <td>585,501</td> <td>7,590 </td> <td>4,838 </td> <td>-3,823   </td> <td>17   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "REGION | NAME                 | 2015    | 2016    | BIRTHS | DEATHS | MIGRATION | OTHER\n",
       "4      | Alaska               | 737,709 | 741,894 | 11,255 | 4,511  | -2,557    | -2\n",
       "3      | Delaware             | 944,076 | 952,065 | 10,922 | 8,945  | 5,583     | 429\n",
       "3      | District of Columbia | 670,377 | 681,170 | 9,779  | 5,455  | 6,392     | 77\n",
       "2      | North Dakota         | 756,835 | 757,952 | 11,824 | 6,172  | -4,684    | 149\n",
       "2      | South Dakota         | 857,919 | 865,454 | 12,114 | 7,296  | 2,573     | 144\n",
       "1      | Vermont              | 626,088 | 624,594 | 6,035  | 5,547  | -1,910    | -72\n",
       "4      | Wyoming              | 586,555 | 585,501 | 7,590  | 4,838  | -3,823    | 17"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pop.where(\"2016\", are.below(west_births))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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y5QoWL16MS5cu4cyZM/Dw8MDKlSsbLFEiImr66iw6ly9fRteuXQ227du3D97e3nj77bcB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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2fdae81a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate a chart here to support your conclusion\n",
    "pop.scatter('BIRTHS', 'DEATHS') #Since it's linearly increasing, there's an positive association between them."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Marginal Histograms\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the following scatter plot: ![](scatter.png)\n",
    "\n",
    "The axes of the plot represent values of two variables: $x$ and $y$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose we have a table called `t` that has two columns in it:\n",
    "\n",
    "- `x`: a column containing the x-values of the points in the scatter plot\n",
    "- `y`: a column containing the y-values of the points in the scatter plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 1:** Match each of the following histograms to the code that produced them. Explain your reasoning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Histogram A:** ![](var1.png)\n",
    "**Histogram B:** ![](var2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "for_assignment_type": "student"
   },
   "source": [
    "**Line 1:** `t.hist('x')`\n",
    "\n",
    "**Histogram for Line 1:**\n",
    "Histogram B\n",
    "\n",
    "**Explanation:**\n",
    "According to the scatter plot, its range for x-values is -2 to 3 and Hist B represents the range of x-values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "for_assignment_type": "student"
   },
   "source": [
    "**Line 2:** `t.hist('y')`\n",
    "\n",
    "**Histogram for Line 2:**\n",
    "Histogram A\n",
    "**Explanation:**\n",
    "According to the scatter plot, there's a gap for y inbetween -0.5 and 0.5 and Histogram A\n",
    "indicates there's no values inbetween -0.5 and 0.5."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Submission\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Once you're finished, select \"Save and Checkpoint\" in the File menu and then execute the `submit` cell below. The result will contain a link that you can use to check that your assignment has been submitted successfully. If you submit more than once before the deadline, we will only grade your final submission."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "_ = ok.submit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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