Outliers.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Dealing with Outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Sometimes outliers can mess up an analysis; you usually don't want a handful of data points to skew the overall results. Let's revisit our example of income data, with Donald Trump thrown in:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x279597c5358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "\n",
    "incomes = np.random.normal(27000, 15000, 10000)\n",
    "incomes = np.append(incomes, [1000000000])\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.hist(incomes, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "That's not very helpful to look at. One billionaire ended up squeezing everybody else into a single line in my histogram. Plus it skewed my mean income significantly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "126713.54327205669"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "incomes.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "It's important to dig into what is causing your outliers, and understand where they are coming from. You also need to think about whether removing them is a valid thing to do, given the spirit of what it is you're trying to analyze. If I know I want to understand more about the incomes of \"typical Americans\", filtering out billionaires seems like a legitimate thing to do.\n",
    "\n",
    "Here's something a little more robust than filtering out billionaires - it filters out anything beyond two standard deviations of the median value in the data set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JiiT/mmRvkvuTvL3VL05yZ/u93pnkkqFzZu35O0d9XJTkq0k+21Pfklyc5Lb2d7YvyVU9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\n9JLUuf8HxDzT6rZ6sbQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2795b8394e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def reject_outliers(data):\n",
    "    u = np.median(data)\n",
    "    s = np.std(data)\n",
    "    filtered = [e for e in data if (u - 2 * s < e < u + 2 * s)]\n",
    "    return filtered\n",
    "\n",
    "filtered = reject_outliers(incomes)\n",
    "\n",
    "plt.hist(filtered, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "That looks better. And, our mean is more, well, meangingful now as well:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26726.214626383888"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(filtered)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Activity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Instead of a single outlier, add several randomly-generated outliers to the data. Experiment with different values of the multiple of the standard deviation to identify outliers, and see what effect it has on the final results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qYDOwu3XbDVzT2puBu6vqpap6EpgCrkhyMXBBVe2vqgLuGhojSRqDBbnmkGQN8GPAQ8DK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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15b92a46198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "\n",
    "incomes = np.random.normal(27000, 15000, 15000)\n",
    "incomes = np.append(incomes, [1000000000])\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.hist(incomes, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "93534.3363436082"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "incomes.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wx236ZOC0casFWA08DDy/3d8KvGXc6nhOXbO9gBP4xd4CvAp4hIMhsAnYNNTnDuA8Bv/k\n3xlqfxPwieE+bfokBidmZLhPe+wTwJtmsZ4/AG4c9zqOU+N5wB1D9w+pc6H8ALcxuE7VbmBFa1sB\n7J7p12eW1n8VsB34bQ6GwNjVAryEwZtnDmsfq1oYfAD7brs9CbidwQfAsarj8J953RyUZB2wr6q+\nedhDR7q8xMr2s/cI7YfMU1XPAD8GfukYzzVb3sYg2Q9Zp8OWPQ51HMtCWpcjasPoVwN3Acuran97\n6HFgeZueyddnNnwEeC/ws6G2caxlDTAJ/E3btHVDkheOWy1V9STwYeD7wH7gx1X1pXGr43Czfoho\nki8Dv3yEhz4AvJ9Bki54x6qjqm5rfT4APAPcOJfrpkMleRHweeBdVfVU29wKQFVVkgV/SFySS4ED\nVXVPkvOP1GdcamHwPvMa4B1VdVeSjzLYbPL/xqGWJC8H3s0g1H4EfC7Jm4f7jEMdh5v1EKiq3zlS\ne5JfZ/DL/Gb7J10FfCPJORz98hL72vTh7QzNszfJSQyGoD9s7ecfNs9XZ6qOoXreAlwKXFBtLLcQ\n65ghJ3T5j/mQ5HkMAuDGqrq1NT+RZEVV7U+yAjjQ2mfy9ZlprwfemORi4FTgxUk+M6a17AX2VtVd\n7f4tDEJg3GqZAL5WVZMASW4FXjeGdRxqNrc1TXF72yMc3CdwNofuUHmIo+9Qubi1X8WhO1S2Dm3H\ne5jBztSlbfr0GV73ixhcDnvZYe1jVccU6j2p1bKGgzuGz14Af0MBPg185LD2D3HojrsPzvTrM8t1\nnc/BfQJjWQvwb8Ar2vSftzrGqhbgN4CdwAva8rcA7xi3Op5T12wvYAq/4EdoIdDuf4DB3vTdtD3n\nrX0CuL899pccPOHtVOBzwJ72C37Z0Dxva+17gLfOwrrvYbAd77728/FxrGOKNV/MYCfZ9xhsElsI\nf0O/BRTwraHX4mIG21S3Aw8CX2YoPGfy9ZnFus7nYAiMZS0M3kB3tNfmHxl8kBm7WoD3MfjAdz/w\ndwze4MeujuEfzxiWpI4tiJPFJEnzwxCQpI4ZApLUMUNAkjpmCEhSxwwBSeqYISBJHTMEJKlj/weL\n/QJqwT4YFAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15b92caf1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def reject_outliers(data):\n",
    "    u = np.median(data)\n",
    "    s = np.std(data)\n",
    "    filtered = [e for e in data if (u - 2 * s < e < u + 2 * s)]\n",
    "    return filtered\n",
    "\n",
    "filtered = reject_outliers(incomes)\n",
    "\n",
    "plt.hist(filtered, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26873.905299364447"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(filtered)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}