Detecting outliers with Z-score

Detecting Outliers with Z-score.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Method -1: Z-score\n",
    "\n",
    "### About the dataset\n",
    "\n",
    "The dataset is about consists of Placement data of MBA students of a B-school. It includes the following features:\n",
    "\n",
    "1. serial number (sl_no)\n",
    "2. gender(gender)\n",
    "3. secondary school percentage(ssc_p)\n",
    "4. secondary school specialization(ssc_b)\n",
    "5. higher secondary school percentage(hsc_p)\n",
    "6. higher secondary school specialization(hsc_b)\n",
    "7. degree percentage(degree_p)\n",
    "8. degree specialization(degree_t)\n",
    "9. workex(workex)\n",
    "10. competitive exam percentage(etest_p)\n",
    "11. Specialization(specialisation)\n",
    "12. mba percentage(mba_p)\n",
    "13. status(status)\n",
    "14. salary(salary)\n",
    "\n",
    "You can download the dataset from kaggle https://www.kaggle.com/benroshan/factors-affecting-campus-placement?select=Placement_Data_Full_Class.csv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Methods of Detecting Outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. Import the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"C:/Users/tkhan050/Documents/Blogs/Blog - 16 - Z-score/Placement.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sl_no</th>\n",
       "      <th>gender</th>\n",
       "      <th>ssc_p</th>\n",
       "      <th>ssc_b</th>\n",
       "      <th>hsc_p</th>\n",
       "      <th>hsc_b</th>\n",
       "      <th>hsc_s</th>\n",
       "      <th>degree_p</th>\n",
       "      <th>degree_t</th>\n",
       "      <th>workex</th>\n",
       "      <th>etest_p</th>\n",
       "      <th>specialisation</th>\n",
       "      <th>mba_p</th>\n",
       "      <th>status</th>\n",
       "      <th>salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>M</td>\n",
       "      <td>67.00</td>\n",
       "      <td>Others</td>\n",
       "      <td>91.00</td>\n",
       "      <td>Others</td>\n",
       "      <td>Commerce</td>\n",
       "      <td>58.00</td>\n",
       "      <td>Sci&amp;Tech</td>\n",
       "      <td>No</td>\n",
       "      <td>55.0</td>\n",
       "      <td>Mkt&amp;HR</td>\n",
       "      <td>58.80</td>\n",
       "      <td>Placed</td>\n",
       "      <td>270000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>M</td>\n",
       "      <td>79.33</td>\n",
       "      <td>Central</td>\n",
       "      <td>78.33</td>\n",
       "      <td>Others</td>\n",
       "      <td>Science</td>\n",
       "      <td>77.48</td>\n",
       "      <td>Sci&amp;Tech</td>\n",
       "      <td>Yes</td>\n",
       "      <td>86.5</td>\n",
       "      <td>Mkt&amp;Fin</td>\n",
       "      <td>66.28</td>\n",
       "      <td>Placed</td>\n",
       "      <td>200000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>M</td>\n",
       "      <td>65.00</td>\n",
       "      <td>Central</td>\n",
       "      <td>68.00</td>\n",
       "      <td>Central</td>\n",
       "      <td>Arts</td>\n",
       "      <td>64.00</td>\n",
       "      <td>Comm&amp;Mgmt</td>\n",
       "      <td>No</td>\n",
       "      <td>75.0</td>\n",
       "      <td>Mkt&amp;Fin</td>\n",
       "      <td>57.80</td>\n",
       "      <td>Placed</td>\n",
       "      <td>250000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>M</td>\n",
       "      <td>56.00</td>\n",
       "      <td>Central</td>\n",
       "      <td>52.00</td>\n",
       "      <td>Central</td>\n",
       "      <td>Science</td>\n",
       "      <td>52.00</td>\n",
       "      <td>Sci&amp;Tech</td>\n",
       "      <td>No</td>\n",
       "      <td>66.0</td>\n",
       "      <td>Mkt&amp;HR</td>\n",
       "      <td>59.43</td>\n",
       "      <td>Not Placed</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>M</td>\n",
       "      <td>85.80</td>\n",
       "      <td>Central</td>\n",
       "      <td>73.60</td>\n",
       "      <td>Central</td>\n",
       "      <td>Commerce</td>\n",
       "      <td>73.30</td>\n",
       "      <td>Comm&amp;Mgmt</td>\n",
       "      <td>No</td>\n",
       "      <td>96.8</td>\n",
       "      <td>Mkt&amp;Fin</td>\n",
       "      <td>55.50</td>\n",
       "      <td>Placed</td>\n",
       "      <td>425000.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sl_no gender  ssc_p    ssc_b  hsc_p    hsc_b     hsc_s  degree_p  \\\n",
       "0      1      M  67.00   Others  91.00   Others  Commerce     58.00   \n",
       "1      2      M  79.33  Central  78.33   Others   Science     77.48   \n",
       "2      3      M  65.00  Central  68.00  Central      Arts     64.00   \n",
       "3      4      M  56.00  Central  52.00  Central   Science     52.00   \n",
       "4      5      M  85.80  Central  73.60  Central  Commerce     73.30   \n",
       "\n",
       "    degree_t workex  etest_p specialisation  mba_p      status    salary  \n",
       "0   Sci&Tech     No     55.0         Mkt&HR  58.80      Placed  270000.0  \n",
       "1   Sci&Tech    Yes     86.5        Mkt&Fin  66.28      Placed  200000.0  \n",
       "2  Comm&Mgmt     No     75.0        Mkt&Fin  57.80      Placed  250000.0  \n",
       "3   Sci&Tech     No     66.0         Mkt&HR  59.43  Not Placed       NaN  \n",
       "4  Comm&Mgmt     No     96.8        Mkt&Fin  55.50      Placed  425000.0  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. Check if there are any \"na\" values present"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sl_no              0\n",
       "gender             0\n",
       "ssc_p              0\n",
       "ssc_b              0\n",
       "hsc_p              0\n",
       "hsc_b              0\n",
       "hsc_s              0\n",
       "degree_p           0\n",
       "degree_t           0\n",
       "workex             0\n",
       "etest_p            0\n",
       "specialisation     0\n",
       "mba_p              0\n",
       "status             0\n",
       "salary            67\n",
       "dtype: int64"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isna().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3. Drop all the \"na\" values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "datadrop = df.dropna()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4. Create a function for Z-score using the below formula\n",
    "\n",
    "<img src = 'http://ai-ml-analytics.com/wp-content/uploads/2020/06/sample-z-score.png'>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "outliers =[]\n",
    "def outliers_zscore(data):\n",
    "    max_dev = 3\n",
    "    mean = np.mean(data)\n",
    "    std = np.std(data)\n",
    "    for i in data:\n",
    "        Z_score = (i-mean)/std\n",
    "        if np.abs(Z_score)>max_dev:\n",
    "            outliers.append(i)\n",
    "    return outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 5. Pass the column from the dataframe to show the outlier which are basically 3 standard deviations away from the mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "z_score_outlier = outliers_zscore(datadrop['salary'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 6. Showing the outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[940000.0, 690000.0, 650000.0]"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z_score_outlier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Method 2: Using Quantiles\n",
    "\n",
    "Let's say we have a set of data and we want to determine what are the possible outliers. Before understanding the method of detecting outliers, we need to understand what **Outliers** are and how are they important or not important in different cases.\n",
    "\n",
    "An **outlier** is basically an extremely high or extremely low value in our dataset.\n",
    "\n",
    "Ex.,\n",
    "1. Suppose the normal salary of a person is \\\\$5k per month. \n",
    "But one month he received a salary of $10k. This can be treated as an outlier which might be because of the annual bonus he would have got.\n",
    "\n",
    "2. Another example we could think of is in case of fraudelent credit card transaction. Suppose a person credic card transactions have always been within the range of \\\\$150-\\\\$200, however there were couple of transactions which were more than \\\\$2000. This is clearly an outlier, which could be regarded as a fraudelent transaction."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Quantiles**: These are basically measures/segments in which the data can be shown. These include percentiles, quartiles, deciles and so on. We calculate these data after arranging them in ascending order.\n",
    "\n",
    "\n",
    "**i. Percentile**: Percentile is defined as the percentage of data that is present below the value of the original value. For example if someone scores a percentile of 90 then the number of students below that are 90 percent of the students.\n",
    "\n",
    "\n",
    "**ii. Decile**: Decile is defined as the 10th percentile, which means the data points that are present below decile is 10 percent of the whole data set.\n",
    "\n",
    "\n",
    "**iii. Quartile**: Quartile is defined as 1/4th of the data or the 25th percentile and can be categorized into 3 quartiles:\n",
    "1st Quartile consists of 25 percent of the data, 2nd Quartile is 50 percent of the data and 3rd quartile is 75 percent of the data. We also call the 2nd quartile as the median or 50th percentile or 5th decile.\n",
    "\n",
    "\n",
    "**iv. Interquartile Range(IQR)**: Interquartile range is defined as the difference between the third quartile and the first quartile and can be effective in figuring out the outliers in the dataset.\n",
    "\n",
    "Our data contains outliers if it is outside **Q1(first quartile) or Q3(3rd Quartile)**. The **3rd quartile** is the **Upper Bound** and the **First Quartile** is **the Lower Bound**\n",
    "\n",
    "**Upper Bound = Q3(third quartile) + 1.5(IQR)** \n",
    "**lower than Q1(first quartile) - 1.5(IQR)**\n",
    "\n",
    "Now that we have understood what all these means, let’s pull it back together and calculate it using an example:\n",
    "\n",
    "Ex: 71, 70, 90, 70, 70, 60, 70, 72, 72, 320, 71, 69\n",
    "\n",
    "1. Rearrange the numbers in order:\n",
    "\n",
    "    60, 69, 70, 70, 70, 70, 71, 71, 72, 72, 90, 320\n",
    "    \n",
    "\n",
    "2. Calculate the median(Q2) : (70+71)/2 = 70.5\n",
    "\n",
    "3. Split the range into 2 halves with the first half less than 70.5 and the 2nd half greater than 70.5\n",
    "\n",
    "4. 1st half = 60, 69, 70, 70, 70, 70\n",
    "\n",
    "5. 2nd half = 71, 71, 72, 72, 90, 320\n",
    "\n",
    "6. Q1 = calculate the median of the 1st half = (70 + 70)/2 = 70\n",
    "\n",
    "7. Q3 = calculate the median of the 2nd half = (72 + 72)/2 =72\n",
    "\n",
    "\n",
    "**The interquartile range is : Q3-Q1** = 72 - 70 = 2\n",
    "\n",
    "**Upper Bound = Q3(third quartile) + 1.5(IQR)** = 72 + 1.5(2) = 75\n",
    "\n",
    "\n",
    "**lower Bound = Q1(first quartile) - 1.5(IQR)** = 70 - 1.5(2) = 67\n",
    "\n",
    "Anything outside the Upper Bound and Lower Bound is considered an Outlier. So in our example the outliers would be 90, 320\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. Calculate the Q1(First Quartile) and Q3(Third Quartile) for the 'salary' column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "quartile1,quartile3=np.percentile(datadrop['salary'],[25,75])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "240000.0 300000.0\n"
     ]
    }
   ],
   "source": [
    "print(quartile1,quartile3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. Calculate the Interquartile Range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "60000.0\n"
     ]
    }
   ],
   "source": [
    "interquartile_range = quartile3-quartile1\n",
    "print(interquartile_range)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3. Calculate the Lower bound and Upper bound. Anything outside the upper and lower bound is an outlier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "lower_bound = quartile1 -(1.5*interquartile_range)\n",
    "upper_bound = quartile3 +(1.5*interquartile_range)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "150000.0 390000.0\n"
     ]
    }
   ],
   "source": [
    "print(lower_bound,upper_bound)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4. Boxplot showing the Outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.boxplot(datadrop['salary'])\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}