02. Working-with-Outliers.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'C:\\\\Users\\\\Mohan\\\\Desktop\\\\Remote Internship-2020\\\\Python codes'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import os\n",
    "os.getcwd()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "os.chdir(\"C:/Users/Mohan/Desktop/Remote Internship-2020/Data Sets\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>crim</th>\n",
       "      <th>zn</th>\n",
       "      <th>indus</th>\n",
       "      <th>chas</th>\n",
       "      <th>nox</th>\n",
       "      <th>rm</th>\n",
       "      <th>age</th>\n",
       "      <th>dis</th>\n",
       "      <th>rad</th>\n",
       "      <th>tax</th>\n",
       "      <th>ptratio</th>\n",
       "      <th>black</th>\n",
       "      <th>lstat</th>\n",
       "      <th>medv</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.00632</td>\n",
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       "      <td>0.538</td>\n",
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       "      <td>4.9671</td>\n",
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       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
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       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
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       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
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       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
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       "      <td>3</td>\n",
       "      <td>0.03237</td>\n",
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       "      <td>2.94</td>\n",
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       "      <td>4</td>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
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       "      <td>...</td>\n",
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       "      <td>501</td>\n",
       "      <td>0.06263</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.593</td>\n",
       "      <td>69.1</td>\n",
       "      <td>2.4786</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>391.99</td>\n",
       "      <td>9.67</td>\n",
       "      <td>22.4</td>\n",
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       "    <tr>\n",
       "      <td>502</td>\n",
       "      <td>0.04527</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.120</td>\n",
       "      <td>76.7</td>\n",
       "      <td>2.2875</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.08</td>\n",
       "      <td>20.6</td>\n",
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       "      <td>503</td>\n",
       "      <td>0.06076</td>\n",
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       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.64</td>\n",
       "      <td>23.9</td>\n",
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       "      <td>504</td>\n",
       "      <td>0.10959</td>\n",
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       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.794</td>\n",
       "      <td>89.3</td>\n",
       "      <td>2.3889</td>\n",
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       "      <td>393.45</td>\n",
       "      <td>6.48</td>\n",
       "      <td>22.0</td>\n",
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       "      <td>505</td>\n",
       "      <td>0.04741</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.030</td>\n",
       "      <td>80.8</td>\n",
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       "      <td>273</td>\n",
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       "      <td>396.90</td>\n",
       "      <td>7.88</td>\n",
       "      <td>11.9</td>\n",
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       "<p>506 rows × 14 columns</p>\n",
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      ],
      "text/plain": [
       "        crim    zn  indus  chas    nox     rm   age     dis  rad  tax  \\\n",
       "0    0.00632  18.0   2.31     0  0.538  6.575  65.2  4.0900    1  296   \n",
       "1    0.02731   0.0   7.07     0  0.469  6.421  78.9  4.9671    2  242   \n",
       "2    0.02729   0.0   7.07     0  0.469  7.185  61.1  4.9671    2  242   \n",
       "3    0.03237   0.0   2.18     0  0.458  6.998  45.8  6.0622    3  222   \n",
       "4    0.06905   0.0   2.18     0  0.458  7.147  54.2  6.0622    3  222   \n",
       "..       ...   ...    ...   ...    ...    ...   ...     ...  ...  ...   \n",
       "501  0.06263   0.0  11.93     0  0.573  6.593  69.1  2.4786    1  273   \n",
       "502  0.04527   0.0  11.93     0  0.573  6.120  76.7  2.2875    1  273   \n",
       "503  0.06076   0.0  11.93     0  0.573  6.976  91.0  2.1675    1  273   \n",
       "504  0.10959   0.0  11.93     0  0.573  6.794  89.3  2.3889    1  273   \n",
       "505  0.04741   0.0  11.93     0  0.573  6.030  80.8  2.5050    1  273   \n",
       "\n",
       "     ptratio   black  lstat  medv  \n",
       "0       15.3  396.90   4.98  24.0  \n",
       "1       17.8  396.90   9.14  21.6  \n",
       "2       17.8  392.83   4.03  34.7  \n",
       "3       18.7  394.63   2.94  33.4  \n",
       "4       18.7  396.90   5.33  36.2  \n",
       "..       ...     ...    ...   ...  \n",
       "501     21.0  391.99   9.67  22.4  \n",
       "502     21.0  396.90   9.08  20.6  \n",
       "503     21.0  396.90   5.64  23.9  \n",
       "504     21.0  393.45   6.48  22.0  \n",
       "505     21.0  396.90   7.88  11.9  \n",
       "\n",
       "[506 rows x 14 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Import the data\n",
    "df=pd.read_csv(\"Boston.csv\")\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>lstat</th>\n",
       "      <th>medv</th>\n",
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       "      <td>0</td>\n",
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       "      <td>9.14</td>\n",
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       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
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       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
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      "text/plain": [
       "      crim    zn  indus  chas    nox     rm   age     dis  rad  tax  ptratio  \\\n",
       "0  0.00632  18.0   2.31     0  0.538  6.575  65.2  4.0900    1  296     15.3   \n",
       "1  0.02731   0.0   7.07     0  0.469  6.421  78.9  4.9671    2  242     17.8   \n",
       "2  0.02729   0.0   7.07     0  0.469  7.185  61.1  4.9671    2  242     17.8   \n",
       "3  0.03237   0.0   2.18     0  0.458  6.998  45.8  6.0622    3  222     18.7   \n",
       "4  0.06905   0.0   2.18     0  0.458  7.147  54.2  6.0622    3  222     18.7   \n",
       "\n",
       "    black  lstat  medv  \n",
       "0  396.90   4.98  24.0  \n",
       "1  396.90   9.14  21.6  \n",
       "2  392.83   4.03  34.7  \n",
       "3  394.63   2.94  33.4  \n",
       "4  396.90   5.33  36.2  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x20ade28fd88>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Discover outliers with visualzation tools\n",
    "#Create a boxplot for 'dis'\n",
    "import seaborn as sns\n",
    "sns.boxplot(x=df['dis'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Observation\n",
    "The plot shows three points between 10 to 12. These are outliers as these are not included in the box of other observations(no where near the quartiles).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Create a scatter plot for two variables 'indus' & 'tax'\n",
    "fig, ax = plt.subplots(figsize=(16,8))\n",
    "ax.scatter(df['indus'], df['tax'])\n",
    "ax.set_xlabel('Proportion of non-retail business acres per town')\n",
    "ax.set_ylabel('Full-value property-tax rate per $10,000')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Observation\n",
    "Most of the data points are lying bottom left side but there are points which are far from the population like top right corner."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.41978194 0.28482986 1.2879095  ... 0.44105193 1.0755623  0.15968566]\n",
      " [0.41733926 0.48772236 0.59338101 ... 0.44105193 0.49243937 0.10152429]\n",
      " [0.41734159 0.48772236 0.59338101 ... 0.39642699 1.2087274  1.32424667]\n",
      " ...\n",
      " [0.41344658 0.48772236 0.11573841 ... 0.44105193 0.98304761 0.14880191]\n",
      " [0.40776407 0.48772236 0.11573841 ... 0.4032249  0.86530163 0.0579893 ]\n",
      " [0.41500016 0.48772236 0.11573841 ... 0.44105193 0.66905833 1.15724782]]\n"
     ]
    }
   ],
   "source": [
    "#Get Z-scores of Boston data\n",
    "from scipy import stats\n",
    "import numpy as np\n",
    "z = np.abs(stats.zscore(df))\n",
    "print(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Observation\n",
    "It is difficult to say which data point is an outlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([ 55,  56,  57, 102, 141, 142, 152, 154, 155, 160, 162, 163, 199,\n",
      "       200, 201, 202, 203, 204, 208, 209, 210, 211, 212, 216, 218, 219,\n",
      "       220, 221, 222, 225, 234, 236, 256, 257, 262, 269, 273, 274, 276,\n",
      "       277, 282, 283, 283, 284, 347, 351, 352, 353, 353, 354, 355, 356,\n",
      "       357, 358, 363, 364, 364, 365, 367, 369, 370, 372, 373, 374, 374,\n",
      "       380, 398, 404, 405, 406, 410, 410, 411, 412, 412, 414, 414, 415,\n",
      "       416, 418, 418, 419, 423, 424, 425, 426, 427, 427, 429, 431, 436,\n",
      "       437, 438, 445, 450, 454, 455, 456, 457, 466], dtype=int64), array([ 1,  1,  1, 11, 12,  3,  3,  3,  3,  3,  3,  3,  1,  1,  1,  1,  1,\n",
      "        1,  3,  3,  3,  3,  3,  3,  3,  3,  3,  3,  3,  5,  3,  3,  1,  5,\n",
      "        5,  3,  3,  3,  3,  3,  3,  1,  3,  1,  1,  7,  7,  1,  7,  7,  7,\n",
      "        3,  3,  3,  3,  3,  5,  5,  5,  3,  3,  3, 12,  5, 12,  0,  0,  0,\n",
      "        0,  5,  0, 11, 11, 11, 12,  0, 12, 11, 11,  0, 11, 11, 11, 11, 11,\n",
      "       11,  0, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11],\n",
      "      dtype=int64))\n"
     ]
    }
   ],
   "source": [
    "# Define a threshold to identify an outlier.\n",
    "threshold = 3\n",
    "print(np.where(z > 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Observations\n",
    "1. The above are datapoint with z-score greater than 3.\n",
    "2.The first array contains the list of row numbers and second array respective column numbers, which mean z[55][1] have a z-score higher than 3.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.375038763517294\n"
     ]
    }
   ],
   "source": [
    "print(z[55][1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Observation\n",
    "The data point — 55th record on column ZN is an outlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "crim         3.595037\n",
      "zn          12.500000\n",
      "indus       12.910000\n",
      "chas         0.000000\n",
      "nox          0.175000\n",
      "rm           0.738000\n",
      "age         49.050000\n",
      "dis          3.088250\n",
      "rad         20.000000\n",
      "tax        387.000000\n",
      "ptratio      2.800000\n",
      "black       20.847500\n",
      "lstat       10.005000\n",
      "medv         7.975000\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "#Find outliers using IQR Score(i.e. IQR=Q3-Q1) \n",
    "Q1 = df.quantile(0.25)\n",
    "Q3 = df.quantile(0.75)\n",
    "IQR = Q3 - Q1\n",
    "print(IQR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      crim     zn  indus   chas    nox     rm    age    dis    rad    tax  \\\n",
      "0    False  False  False  False  False  False  False  False  False  False   \n",
      "1    False  False  False  False  False  False  False  False  False  False   \n",
      "2    False  False  False  False  False  False  False  False  False  False   \n",
      "3    False  False  False  False  False  False  False  False  False  False   \n",
      "4    False  False  False  False  False  False  False  False  False  False   \n",
      "..     ...    ...    ...    ...    ...    ...    ...    ...    ...    ...   \n",
      "501  False  False  False  False  False  False  False  False  False  False   \n",
      "502  False  False  False  False  False  False  False  False  False  False   \n",
      "503  False  False  False  False  False  False  False  False  False  False   \n",
      "504  False  False  False  False  False  False  False  False  False  False   \n",
      "505  False  False  False  False  False  False  False  False  False  False   \n",
      "\n",
      "     ptratio  black  lstat   medv  \n",
      "0      False  False  False  False  \n",
      "1      False  False  False  False  \n",
      "2      False  False  False  False  \n",
      "3      False  False  False  False  \n",
      "4      False  False  False  False  \n",
      "..       ...    ...    ...    ...  \n",
      "501    False  False  False  False  \n",
      "502    False  False  False  False  \n",
      "503    False  False  False  False  \n",
      "504    False  False  False  False  \n",
      "505    False  False  False  False  \n",
      "\n",
      "[506 rows x 14 columns]\n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "cannot compare a dtyped [bool] array with a scalar of type [NoneType]",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m~\\anacond3\\lib\\site-packages\\pandas\\core\\ops\\__init__.py\u001b[0m in \u001b[0;36mna_op\u001b[1;34m(x, y)\u001b[0m\n\u001b[0;32m   1253\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1254\u001b[1;33m             \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mop\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1255\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anacond3\\lib\\site-packages\\pandas\\core\\ops\\roperator.py\u001b[0m in \u001b[0;36mror_\u001b[1;34m(left, right)\u001b[0m\n\u001b[0;32m     56\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mror_\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mleft\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mright\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 57\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0moperator\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mor_\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mright\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mleft\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     58\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mTypeError\u001b[0m: unsupported operand type(s) for |: 'NoneType' and 'bool'",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m~\\anacond3\\lib\\site-packages\\pandas\\core\\ops\\__init__.py\u001b[0m in \u001b[0;36mna_op\u001b[1;34m(x, y)\u001b[0m\n\u001b[0;32m   1268\u001b[0m                 \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1269\u001b[1;33m                     \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlibops\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mscalar_binop\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mop\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1270\u001b[0m                 except (\n",
      "\u001b[1;32mpandas\\_libs\\ops.pyx\u001b[0m in \u001b[0;36mpandas._libs.ops.scalar_binop\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: Does not understand character buffer dtype format string ('?')",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-16-a02a94f243ef>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdf\u001b[0m \u001b[1;33m<\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mQ1\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m1.5\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mIQR\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m|\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdf\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mQ3\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;36m1.5\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mIQR\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m~\\anacond3\\lib\\site-packages\\pandas\\core\\ops\\__init__.py\u001b[0m in \u001b[0;36mf\u001b[1;34m(self, other, axis, level, fill_value)\u001b[0m\n\u001b[0;32m   1504\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1505\u001b[0m             \u001b[1;32massert\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mother\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1506\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_combine_const\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mother\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mop\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1507\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1508\u001b[0m     \u001b[0mf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mop_name\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anacond3\\lib\\site-packages\\pandas\\core\\frame.py\u001b[0m in \u001b[0;36m_combine_const\u001b[1;34m(self, other, func)\u001b[0m\n\u001b[0;32m   5401\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m_combine_const\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mother\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   5402\u001b[0m         \u001b[1;32massert\u001b[0m \u001b[0mlib\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_scalar\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mother\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mother\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 5403\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mops\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdispatch_to_series\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mother\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   5404\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   5405\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mcombine\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mother\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfill_value\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0moverwrite\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anacond3\\lib\\site-packages\\pandas\\core\\ops\\__init__.py\u001b[0m in \u001b[0;36mdispatch_to_series\u001b[1;34m(left, right, func, str_rep, axis)\u001b[0m\n\u001b[0;32m    594\u001b[0m         \u001b[1;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mright\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    595\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 596\u001b[1;33m     \u001b[0mnew_data\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mexpressions\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevaluate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcolumn_op\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstr_rep\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mleft\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mright\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    597\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    598\u001b[0m     \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mleft\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_constructor\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnew_data\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mindex\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mleft\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mFalse\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anacond3\\lib\\site-packages\\pandas\\core\\computation\\expressions.py\u001b[0m in \u001b[0;36mevaluate\u001b[1;34m(op, op_str, a, b, use_numexpr, **eval_kwargs)\u001b[0m\n\u001b[0;32m    219\u001b[0m     \u001b[0muse_numexpr\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0muse_numexpr\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0m_bool_arith_check\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mop_str\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    220\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0muse_numexpr\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 221\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0m_evaluate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mop\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mop_str\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0meval_kwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    222\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0m_evaluate_standard\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mop\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mop_str\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    223\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anacond3\\lib\\site-packages\\pandas\\core\\computation\\expressions.py\u001b[0m in \u001b[0;36m_evaluate_numexpr\u001b[1;34m(op, op_str, a, b, truediv, reversed, **eval_kwargs)\u001b[0m\n\u001b[0;32m    125\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    126\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 127\u001b[1;33m         \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_evaluate_standard\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mop\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mop_str\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    128\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    129\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anacond3\\lib\\site-packages\\pandas\\core\\computation\\expressions.py\u001b[0m in \u001b[0;36m_evaluate_standard\u001b[1;34m(op, op_str, a, b, **eval_kwargs)\u001b[0m\n\u001b[0;32m     68\u001b[0m         \u001b[0m_store_test_result\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mFalse\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     69\u001b[0m     \u001b[1;32mwith\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0merrstate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mall\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m\"ignore\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 70\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mop\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     71\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     72\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anacond3\\lib\\site-packages\\pandas\\core\\ops\\__init__.py\u001b[0m in \u001b[0;36mcolumn_op\u001b[1;34m(a, b)\u001b[0m\n\u001b[0;32m    568\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    569\u001b[0m         \u001b[1;32mdef\u001b[0m \u001b[0mcolumn_op\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 570\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[1;33m{\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0miloc\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcolumns\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m}\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    571\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    572\u001b[0m     \u001b[1;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mright\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mABCDataFrame\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anacond3\\lib\\site-packages\\pandas\\core\\ops\\__init__.py\u001b[0m in \u001b[0;36m<dictcomp>\u001b[1;34m(.0)\u001b[0m\n\u001b[0;32m    568\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    569\u001b[0m         \u001b[1;32mdef\u001b[0m \u001b[0mcolumn_op\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 570\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[1;33m{\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0miloc\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcolumns\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m}\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    571\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    572\u001b[0m     \u001b[1;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mright\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mABCDataFrame\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anacond3\\lib\\site-packages\\pandas\\core\\ops\\roperator.py\u001b[0m in \u001b[0;36mror_\u001b[1;34m(left, right)\u001b[0m\n\u001b[0;32m     55\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     56\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mror_\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mleft\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mright\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 57\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0moperator\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mor_\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mright\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mleft\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     58\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     59\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anacond3\\lib\\site-packages\\pandas\\core\\ops\\__init__.py\u001b[0m in \u001b[0;36mwrapper\u001b[1;34m(self, other)\u001b[0m\n\u001b[0;32m   1319\u001b[0m         \u001b[1;31m#   integer dtypes.  Otherwise these are boolean ops\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1320\u001b[0m         \u001b[0mfiller\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfill_int\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mis_self_int_dtype\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0mis_other_int_dtype\u001b[0m \u001b[1;32melse\u001b[0m \u001b[0mfill_bool\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1321\u001b[1;33m         \u001b[0mres_values\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mna_op\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0movalues\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1322\u001b[0m         \u001b[0munfilled\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_constructor\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mres_values\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mindex\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mname\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mres_name\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1323\u001b[0m         \u001b[0mfilled\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfiller\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0munfilled\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anacond3\\lib\\site-packages\\pandas\\core\\ops\\__init__.py\u001b[0m in \u001b[0;36mna_op\u001b[1;34m(x, y)\u001b[0m\n\u001b[0;32m   1278\u001b[0m                         \u001b[1;34m\"cannot compare a dtyped [{dtype}] array \"\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1279\u001b[0m                         \"with a scalar of type [{typ}]\".format(\n\u001b[1;32m-> 1280\u001b[1;33m                             \u001b[0mdtype\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtyp\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mtype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1281\u001b[0m                         )\n\u001b[0;32m   1282\u001b[0m                     )\n",
      "\u001b[1;31mTypeError\u001b[0m: cannot compare a dtyped [bool] array with a scalar of type [NoneType]"
     ]
    }
   ],
   "source": [
    "print(df < (Q1 - 1.5 * IQR)) |(df > (Q3 + 1.5 * IQR))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Working with Outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Get clean data by removing or filtering the outliers\n",
    "boston_df_o = df[(z < 3).all(axis=1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>0.06905</td>\n",
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       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
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       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
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       "      <td>6.593</td>\n",
       "      <td>69.1</td>\n",
       "      <td>2.4786</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>391.99</td>\n",
       "      <td>9.67</td>\n",
       "      <td>22.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>502</td>\n",
       "      <td>0.04527</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.120</td>\n",
       "      <td>76.7</td>\n",
       "      <td>2.2875</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.08</td>\n",
       "      <td>20.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>503</td>\n",
       "      <td>0.06076</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.976</td>\n",
       "      <td>91.0</td>\n",
       "      <td>2.1675</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.64</td>\n",
       "      <td>23.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>504</td>\n",
       "      <td>0.10959</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.794</td>\n",
       "      <td>89.3</td>\n",
       "      <td>2.3889</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>393.45</td>\n",
       "      <td>6.48</td>\n",
       "      <td>22.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>505</td>\n",
       "      <td>0.04741</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.030</td>\n",
       "      <td>80.8</td>\n",
       "      <td>2.5050</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>7.88</td>\n",
       "      <td>11.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>415 rows × 14 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        crim    zn  indus  chas    nox     rm   age     dis  rad  tax  \\\n",
       "0    0.00632  18.0   2.31     0  0.538  6.575  65.2  4.0900    1  296   \n",
       "1    0.02731   0.0   7.07     0  0.469  6.421  78.9  4.9671    2  242   \n",
       "2    0.02729   0.0   7.07     0  0.469  7.185  61.1  4.9671    2  242   \n",
       "3    0.03237   0.0   2.18     0  0.458  6.998  45.8  6.0622    3  222   \n",
       "4    0.06905   0.0   2.18     0  0.458  7.147  54.2  6.0622    3  222   \n",
       "..       ...   ...    ...   ...    ...    ...   ...     ...  ...  ...   \n",
       "501  0.06263   0.0  11.93     0  0.573  6.593  69.1  2.4786    1  273   \n",
       "502  0.04527   0.0  11.93     0  0.573  6.120  76.7  2.2875    1  273   \n",
       "503  0.06076   0.0  11.93     0  0.573  6.976  91.0  2.1675    1  273   \n",
       "504  0.10959   0.0  11.93     0  0.573  6.794  89.3  2.3889    1  273   \n",
       "505  0.04741   0.0  11.93     0  0.573  6.030  80.8  2.5050    1  273   \n",
       "\n",
       "     ptratio   black  lstat  medv  \n",
       "0       15.3  396.90   4.98  24.0  \n",
       "1       17.8  396.90   9.14  21.6  \n",
       "2       17.8  392.83   4.03  34.7  \n",
       "3       18.7  394.63   2.94  33.4  \n",
       "4       18.7  396.90   5.33  36.2  \n",
       "..       ...     ...    ...   ...  \n",
       "501     21.0  391.99   9.67  22.4  \n",
       "502     21.0  396.90   9.08  20.6  \n",
       "503     21.0  396.90   5.64  23.9  \n",
       "504     21.0  393.45   6.48  22.0  \n",
       "505     21.0  396.90   7.88  11.9  \n",
       "\n",
       "[415 rows x 14 columns]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston_df_o"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506, 14)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(415, 14)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston_df_o.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Observation\n",
    "90+ rows containing outliers in the dataset have been removed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Use IQR score to filterout the outliers to keep only valid values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(268, 14)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston_df_out = df[~((df < (Q1 - 1.5 * IQR)) |(df > (Q3 + 1.5 * IQR))).any(axis=1)]\n",
    "boston_df_out.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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