basic statistics1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import scipy\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "from scipy import stats\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Q7)Calculate Mean, Median, Mode, Variance, Standard Deviation, Range &     comment about the values / draw inferences, for the given dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"Q7.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>Unnamed: 0</th>\n",
       "      <th>Points</th>\n",
       "      <th>Score</th>\n",
       "      <th>Weigh</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mazda RX4</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.620</td>\n",
       "      <td>16.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Mazda RX4 Wag</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.875</td>\n",
       "      <td>17.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Datsun 710</td>\n",
       "      <td>3.85</td>\n",
       "      <td>2.320</td>\n",
       "      <td>18.61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Hornet 4 Drive</td>\n",
       "      <td>3.08</td>\n",
       "      <td>3.215</td>\n",
       "      <td>19.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Hornet Sportabout</td>\n",
       "      <td>3.15</td>\n",
       "      <td>3.440</td>\n",
       "      <td>17.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Valiant</td>\n",
       "      <td>2.76</td>\n",
       "      <td>3.460</td>\n",
       "      <td>20.22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Duster 360</td>\n",
       "      <td>3.21</td>\n",
       "      <td>3.570</td>\n",
       "      <td>15.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Merc 240D</td>\n",
       "      <td>3.69</td>\n",
       "      <td>3.190</td>\n",
       "      <td>20.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Merc 230</td>\n",
       "      <td>3.92</td>\n",
       "      <td>3.150</td>\n",
       "      <td>22.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Merc 280</td>\n",
       "      <td>3.92</td>\n",
       "      <td>3.440</td>\n",
       "      <td>18.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Merc 280C</td>\n",
       "      <td>3.92</td>\n",
       "      <td>3.440</td>\n",
       "      <td>18.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Merc 450SE</td>\n",
       "      <td>3.07</td>\n",
       "      <td>4.070</td>\n",
       "      <td>17.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>Merc 450SL</td>\n",
       "      <td>3.07</td>\n",
       "      <td>3.730</td>\n",
       "      <td>17.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>Merc 450SLC</td>\n",
       "      <td>3.07</td>\n",
       "      <td>3.780</td>\n",
       "      <td>18.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>Cadillac Fleetwood</td>\n",
       "      <td>2.93</td>\n",
       "      <td>5.250</td>\n",
       "      <td>17.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>Lincoln Continental</td>\n",
       "      <td>3.00</td>\n",
       "      <td>5.424</td>\n",
       "      <td>17.82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Chrysler Imperial</td>\n",
       "      <td>3.23</td>\n",
       "      <td>5.345</td>\n",
       "      <td>17.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Fiat 128</td>\n",
       "      <td>4.08</td>\n",
       "      <td>2.200</td>\n",
       "      <td>19.47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Honda Civic</td>\n",
       "      <td>4.93</td>\n",
       "      <td>1.615</td>\n",
       "      <td>18.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Toyota Corolla</td>\n",
       "      <td>4.22</td>\n",
       "      <td>1.835</td>\n",
       "      <td>19.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Toyota Corona</td>\n",
       "      <td>3.70</td>\n",
       "      <td>2.465</td>\n",
       "      <td>20.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>Dodge Challenger</td>\n",
       "      <td>2.76</td>\n",
       "      <td>3.520</td>\n",
       "      <td>16.87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>AMC Javelin</td>\n",
       "      <td>3.15</td>\n",
       "      <td>3.435</td>\n",
       "      <td>17.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>Camaro Z28</td>\n",
       "      <td>3.73</td>\n",
       "      <td>3.840</td>\n",
       "      <td>15.41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>Pontiac Firebird</td>\n",
       "      <td>3.08</td>\n",
       "      <td>3.845</td>\n",
       "      <td>17.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>Fiat X1-9</td>\n",
       "      <td>4.08</td>\n",
       "      <td>1.935</td>\n",
       "      <td>18.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>Porsche 914-2</td>\n",
       "      <td>4.43</td>\n",
       "      <td>2.140</td>\n",
       "      <td>16.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>Lotus Europa</td>\n",
       "      <td>3.77</td>\n",
       "      <td>1.513</td>\n",
       "      <td>16.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>Ford Pantera L</td>\n",
       "      <td>4.22</td>\n",
       "      <td>3.170</td>\n",
       "      <td>14.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>Ferrari Dino</td>\n",
       "      <td>3.62</td>\n",
       "      <td>2.770</td>\n",
       "      <td>15.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>Maserati Bora</td>\n",
       "      <td>3.54</td>\n",
       "      <td>3.570</td>\n",
       "      <td>14.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>Volvo 142E</td>\n",
       "      <td>4.11</td>\n",
       "      <td>2.780</td>\n",
       "      <td>18.60</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Unnamed: 0  Points  Score  Weigh\n",
       "0             Mazda RX4    3.90  2.620  16.46\n",
       "1         Mazda RX4 Wag    3.90  2.875  17.02\n",
       "2            Datsun 710    3.85  2.320  18.61\n",
       "3        Hornet 4 Drive    3.08  3.215  19.44\n",
       "4     Hornet Sportabout    3.15  3.440  17.02\n",
       "5               Valiant    2.76  3.460  20.22\n",
       "6            Duster 360    3.21  3.570  15.84\n",
       "7             Merc 240D    3.69  3.190  20.00\n",
       "8              Merc 230    3.92  3.150  22.90\n",
       "9              Merc 280    3.92  3.440  18.30\n",
       "10            Merc 280C    3.92  3.440  18.90\n",
       "11           Merc 450SE    3.07  4.070  17.40\n",
       "12           Merc 450SL    3.07  3.730  17.60\n",
       "13          Merc 450SLC    3.07  3.780  18.00\n",
       "14   Cadillac Fleetwood    2.93  5.250  17.98\n",
       "15  Lincoln Continental    3.00  5.424  17.82\n",
       "16    Chrysler Imperial    3.23  5.345  17.42\n",
       "17             Fiat 128    4.08  2.200  19.47\n",
       "18          Honda Civic    4.93  1.615  18.52\n",
       "19       Toyota Corolla    4.22  1.835  19.90\n",
       "20        Toyota Corona    3.70  2.465  20.01\n",
       "21     Dodge Challenger    2.76  3.520  16.87\n",
       "22          AMC Javelin    3.15  3.435  17.30\n",
       "23           Camaro Z28    3.73  3.840  15.41\n",
       "24     Pontiac Firebird    3.08  3.845  17.05\n",
       "25            Fiat X1-9    4.08  1.935  18.90\n",
       "26        Porsche 914-2    4.43  2.140  16.70\n",
       "27         Lotus Europa    3.77  1.513  16.90\n",
       "28       Ford Pantera L    4.22  3.170  14.50\n",
       "29         Ferrari Dino    3.62  2.770  15.50\n",
       "30        Maserati Bora    3.54  3.570  14.60\n",
       "31           Volvo 142E    4.11  2.780  18.60"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>Points</th>\n",
       "      <th>Score</th>\n",
       "      <th>Weigh</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>32.000000</td>\n",
       "      <td>32.000000</td>\n",
       "      <td>32.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.596563</td>\n",
       "      <td>3.217250</td>\n",
       "      <td>17.848750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.534679</td>\n",
       "      <td>0.978457</td>\n",
       "      <td>1.786943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>2.760000</td>\n",
       "      <td>1.513000</td>\n",
       "      <td>14.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>3.080000</td>\n",
       "      <td>2.581250</td>\n",
       "      <td>16.892500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>3.695000</td>\n",
       "      <td>3.325000</td>\n",
       "      <td>17.710000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.920000</td>\n",
       "      <td>3.610000</td>\n",
       "      <td>18.900000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>4.930000</td>\n",
       "      <td>5.424000</td>\n",
       "      <td>22.900000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "          Points      Score      Weigh\n",
       "count  32.000000  32.000000  32.000000\n",
       "mean    3.596563   3.217250  17.848750\n",
       "std     0.534679   0.978457   1.786943\n",
       "min     2.760000   1.513000  14.500000\n",
       "25%     3.080000   2.581250  16.892500\n",
       "50%     3.695000   3.325000  17.710000\n",
       "75%     3.920000   3.610000  18.900000\n",
       "max     4.930000   5.424000  22.900000"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    3.07\n",
       "1    3.92\n",
       "dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Points'].mode()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    3.44\n",
       "dtype: float64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Score'].mode()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    17.02\n",
       "1    18.90\n",
       "dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Weigh'].mode()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Points</th>\n",
       "      <th>Score</th>\n",
       "      <th>Weigh</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mazda RX4</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.620</td>\n",
       "      <td>16.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Mazda RX4 Wag</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.875</td>\n",
       "      <td>17.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Datsun 710</td>\n",
       "      <td>3.85</td>\n",
       "      <td>2.320</td>\n",
       "      <td>18.61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Hornet 4 Drive</td>\n",
       "      <td>3.08</td>\n",
       "      <td>3.215</td>\n",
       "      <td>19.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Hornet Sportabout</td>\n",
       "      <td>3.15</td>\n",
       "      <td>3.440</td>\n",
       "      <td>17.02</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Unnamed: 0  Points  Score  Weigh\n",
       "0          Mazda RX4    3.90  2.620  16.46\n",
       "1      Mazda RX4 Wag    3.90  2.875  17.02\n",
       "2         Datsun 710    3.85  2.320  18.61\n",
       "3     Hornet 4 Drive    3.08  3.215  19.44\n",
       "4  Hornet Sportabout    3.15  3.440  17.02"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Points    0.285881\n",
       "Score     0.957379\n",
       "Weigh     3.193166\n",
       "dtype: float64"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Unnamed: 0    Volvo 142E\n",
       "Points              4.93\n",
       "Score              5.424\n",
       "Weigh               22.9\n",
       "dtype: object"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Unnamed: 0    AMC Javelin\n",
       "Points               2.76\n",
       "Score               1.513\n",
       "Weigh                14.5\n",
       "dtype: object"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.min()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Q9)(a)Calculate Skewness, Kurtosis & draw inferences on the following data Cars speed and distance \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "d1 = pd.read_csv('Q9_a.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>Index</th>\n",
       "      <th>speed</th>\n",
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       "      <td>46</td>\n",
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       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>38</td>\n",
       "      <td>19</td>\n",
       "      <td>68</td>\n",
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       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>39</td>\n",
       "      <td>20</td>\n",
       "      <td>32</td>\n",
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       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>40</td>\n",
       "      <td>20</td>\n",
       "      <td>48</td>\n",
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       "    <tr>\n",
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       "      <td>20</td>\n",
       "      <td>52</td>\n",
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       "    <tr>\n",
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       "      <th>42</th>\n",
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       "      <td>20</td>\n",
       "      <td>64</td>\n",
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       "    <tr>\n",
       "      <th>43</th>\n",
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       "      <td>22</td>\n",
       "      <td>66</td>\n",
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       "    <tr>\n",
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       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>46</td>\n",
       "      <td>24</td>\n",
       "      <td>70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>47</td>\n",
       "      <td>24</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>48</td>\n",
       "      <td>24</td>\n",
       "      <td>93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>49</td>\n",
       "      <td>24</td>\n",
       "      <td>120</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>50</td>\n",
       "      <td>25</td>\n",
       "      <td>85</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Index  speed  dist\n",
       "0       1      4     2\n",
       "1       2      4    10\n",
       "2       3      7     4\n",
       "3       4      7    22\n",
       "4       5      8    16\n",
       "5       6      9    10\n",
       "6       7     10    18\n",
       "7       8     10    26\n",
       "8       9     10    34\n",
       "9      10     11    17\n",
       "10     11     11    28\n",
       "11     12     12    14\n",
       "12     13     12    20\n",
       "13     14     12    24\n",
       "14     15     12    28\n",
       "15     16     13    26\n",
       "16     17     13    34\n",
       "17     18     13    34\n",
       "18     19     13    46\n",
       "19     20     14    26\n",
       "20     21     14    36\n",
       "21     22     14    60\n",
       "22     23     14    80\n",
       "23     24     15    20\n",
       "24     25     15    26\n",
       "25     26     15    54\n",
       "26     27     16    32\n",
       "27     28     16    40\n",
       "28     29     17    32\n",
       "29     30     17    40\n",
       "30     31     17    50\n",
       "31     32     18    42\n",
       "32     33     18    56\n",
       "33     34     18    76\n",
       "34     35     18    84\n",
       "35     36     19    36\n",
       "36     37     19    46\n",
       "37     38     19    68\n",
       "38     39     20    32\n",
       "39     40     20    48\n",
       "40     41     20    52\n",
       "41     42     20    56\n",
       "42     43     20    64\n",
       "43     44     22    66\n",
       "44     45     23    54\n",
       "45     46     24    70\n",
       "46     47     24    92\n",
       "47     48     24    93\n",
       "48     49     24   120\n",
       "49     50     25    85"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.11750986144663393"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d1['speed'].skew()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.5089944204057617"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d1['speed'].kurt()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8068949601674215"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d1['dist'].skew()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4050525816795765"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d1['dist'].kurt()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "d2= pd.read_csv('Q9_b.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>7</th>\n",
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       "      <td>16.359484</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10</td>\n",
       "      <td>115.645204</td>\n",
       "      <td>30.920154</td>\n",
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       "      <th>10</th>\n",
       "      <td>11</td>\n",
       "      <td>111.185353</td>\n",
       "      <td>29.363341</td>\n",
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       "      <th>12</th>\n",
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       "      <td>122.105055</td>\n",
       "      <td>32.813592</td>\n",
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       "      <th>13</th>\n",
       "      <td>14</td>\n",
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       "      <td>29.378436</td>\n",
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       "      <th>14</th>\n",
       "      <td>15</td>\n",
       "      <td>108.185353</td>\n",
       "      <td>29.347279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>16</td>\n",
       "      <td>111.185353</td>\n",
       "      <td>29.604527</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>17</td>\n",
       "      <td>114.369293</td>\n",
       "      <td>29.535784</td>\n",
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       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>18</td>\n",
       "      <td>117.598513</td>\n",
       "      <td>16.194122</td>\n",
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       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>19</td>\n",
       "      <td>114.369293</td>\n",
       "      <td>29.929394</td>\n",
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       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>20</td>\n",
       "      <td>118.472936</td>\n",
       "      <td>33.516974</td>\n",
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       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>21</td>\n",
       "      <td>119.105055</td>\n",
       "      <td>32.324650</td>\n",
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       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>22</td>\n",
       "      <td>110.840817</td>\n",
       "      <td>34.908211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>23</td>\n",
       "      <td>120.288996</td>\n",
       "      <td>32.675828</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>24</td>\n",
       "      <td>113.829145</td>\n",
       "      <td>31.837122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>25</td>\n",
       "      <td>119.185353</td>\n",
       "      <td>28.781728</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>26</td>\n",
       "      <td>114.598513</td>\n",
       "      <td>16.043175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>27</td>\n",
       "      <td>120.760520</td>\n",
       "      <td>38.062823</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>28</td>\n",
       "      <td>119.105055</td>\n",
       "      <td>32.835069</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>29</td>\n",
       "      <td>99.564907</td>\n",
       "      <td>34.483207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>30</td>\n",
       "      <td>121.840817</td>\n",
       "      <td>35.549360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>52</td>\n",
       "      <td>118.288996</td>\n",
       "      <td>33.436711</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>53</td>\n",
       "      <td>120.404312</td>\n",
       "      <td>40.398164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>54</td>\n",
       "      <td>143.392639</td>\n",
       "      <td>37.620695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>55</td>\n",
       "      <td>135.392639</td>\n",
       "      <td>37.254392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>56</td>\n",
       "      <td>126.404312</td>\n",
       "      <td>40.589068</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>57</td>\n",
       "      <td>110.461264</td>\n",
       "      <td>30.147543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>58</td>\n",
       "      <td>118.288996</td>\n",
       "      <td>32.734518</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>59</td>\n",
       "      <td>112.645204</td>\n",
       "      <td>30.615283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>60</td>\n",
       "      <td>115.576579</td>\n",
       "      <td>37.662874</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>61</td>\n",
       "      <td>130.208698</td>\n",
       "      <td>36.888153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>62</td>\n",
       "      <td>117.668550</td>\n",
       "      <td>37.860411</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>63</td>\n",
       "      <td>126.048103</td>\n",
       "      <td>43.390988</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>63</th>\n",
       "      <td>64</td>\n",
       "      <td>125.312342</td>\n",
       "      <td>40.722831</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64</th>\n",
       "      <td>65</td>\n",
       "      <td>128.128401</td>\n",
       "      <td>40.159482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>65</th>\n",
       "      <td>66</td>\n",
       "      <td>126.598513</td>\n",
       "      <td>15.712859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>67</td>\n",
       "      <td>132.484609</td>\n",
       "      <td>37.979956</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>68</td>\n",
       "      <td>133.680223</td>\n",
       "      <td>41.573975</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>69</td>\n",
       "      <td>133.312342</td>\n",
       "      <td>40.472042</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>70</td>\n",
       "      <td>158.300669</td>\n",
       "      <td>37.141733</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>71</td>\n",
       "      <td>164.598513</td>\n",
       "      <td>15.823060</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>72</td>\n",
       "      <td>133.415985</td>\n",
       "      <td>44.013139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>73</td>\n",
       "      <td>133.140074</td>\n",
       "      <td>43.353123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>74</td>\n",
       "      <td>124.715241</td>\n",
       "      <td>52.997752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>75</td>\n",
       "      <td>121.864163</td>\n",
       "      <td>42.618698</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>76</td>\n",
       "      <td>132.864163</td>\n",
       "      <td>42.778219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>77</td>\n",
       "      <td>169.598513</td>\n",
       "      <td>16.132947</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>78</td>\n",
       "      <td>150.576579</td>\n",
       "      <td>37.923113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>79</td>\n",
       "      <td>151.598513</td>\n",
       "      <td>15.769625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>80</td>\n",
       "      <td>167.944460</td>\n",
       "      <td>39.423099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>81</td>\n",
       "      <td>139.840817</td>\n",
       "      <td>34.948615</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>81 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Unnamed: 0          SP         WT\n",
       "0            1  104.185353  28.762059\n",
       "1            2  105.461264  30.466833\n",
       "2            3  105.461264  30.193597\n",
       "3            4  113.461264  30.632114\n",
       "4            5  104.461264  29.889149\n",
       "5            6  113.185353  29.591768\n",
       "6            7  105.461264  30.308480\n",
       "7            8  102.598513  15.847758\n",
       "8            9  102.598513  16.359484\n",
       "9           10  115.645204  30.920154\n",
       "10          11  111.185353  29.363341\n",
       "11          12  117.598513  15.753535\n",
       "12          13  122.105055  32.813592\n",
       "13          14  111.185353  29.378436\n",
       "14          15  108.185353  29.347279\n",
       "15          16  111.185353  29.604527\n",
       "16          17  114.369293  29.535784\n",
       "17          18  117.598513  16.194122\n",
       "18          19  114.369293  29.929394\n",
       "19          20  118.472936  33.516974\n",
       "20          21  119.105055  32.324650\n",
       "21          22  110.840817  34.908211\n",
       "22          23  120.288996  32.675828\n",
       "23          24  113.829145  31.837122\n",
       "24          25  119.185353  28.781728\n",
       "25          26  114.598513  16.043175\n",
       "26          27  120.760520  38.062823\n",
       "27          28  119.105055  32.835069\n",
       "28          29   99.564907  34.483207\n",
       "29          30  121.840817  35.549360\n",
       "..         ...         ...        ...\n",
       "51          52  118.288996  33.436711\n",
       "52          53  120.404312  40.398164\n",
       "53          54  143.392639  37.620695\n",
       "54          55  135.392639  37.254392\n",
       "55          56  126.404312  40.589068\n",
       "56          57  110.461264  30.147543\n",
       "57          58  118.288996  32.734518\n",
       "58          59  112.645204  30.615283\n",
       "59          60  115.576579  37.662874\n",
       "60          61  130.208698  36.888153\n",
       "61          62  117.668550  37.860411\n",
       "62          63  126.048103  43.390988\n",
       "63          64  125.312342  40.722831\n",
       "64          65  128.128401  40.159482\n",
       "65          66  126.598513  15.712859\n",
       "66          67  132.484609  37.979956\n",
       "67          68  133.680223  41.573975\n",
       "68          69  133.312342  40.472042\n",
       "69          70  158.300669  37.141733\n",
       "70          71  164.598513  15.823060\n",
       "71          72  133.415985  44.013139\n",
       "72          73  133.140074  43.353123\n",
       "73          74  124.715241  52.997752\n",
       "74          75  121.864163  42.618698\n",
       "75          76  132.864163  42.778219\n",
       "76          77  169.598513  16.132947\n",
       "77          78  150.576579  37.923113\n",
       "78          79  151.598513  15.769625\n",
       "79          80  167.944460  39.423099\n",
       "80          81  139.840817  34.948615\n",
       "\n",
       "[81 rows x 3 columns]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6114501961773555"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2['SP'].skew()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.9773289437871764"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2['SP'].kurt()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.6147533255357768"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2['WT'].skew()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9502914910300326"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2['WT'].kurt()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Q11)  Suppose we want to estimate the average weight of an adult male in    Mexico. We draw a random sample of 2,000 men from a population of 3,000,000 men and weigh them. We find that the average person in our sample weighs 200 pounds, and the standard deviation of the sample is 30 pounds. Calculate 94%,98%,96% confidence interval?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(143.54417173267188, 256.4558282673281)"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " stats. t .interval(0.94,2000,200,30)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(130.1535847418068, 269.8464152581932)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " stats. t .interval(0.98,2000,200,30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(138.34732124381935, 261.65267875618065)"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " stats. t .interval(0.96,2000,200,30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Q12)  Below are the scores obtained by a student in tests \n",
    "# 34,36,36,38,38,39,39,40,40,41,41,41,41,42,42,45,49,56\n",
    "# 1)\tFind mean, median, variance, standard deviation.\n",
    "# 2)\tWhat can we say about the student marks? \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = [34,36,36,38,38,39,39,40,40,41,41,41,41,42,42,45,49,56]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_script = pd.DataFrame(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>49</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>56</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0\n",
       "0   34\n",
       "1   36\n",
       "2   36\n",
       "3   38\n",
       "4   38\n",
       "5   39\n",
       "6   39\n",
       "7   40\n",
       "8   40\n",
       "9   41\n",
       "10  41\n",
       "11  41\n",
       "12  41\n",
       "13  42\n",
       "14  42\n",
       "15  45\n",
       "16  49\n",
       "17  56"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_script"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    41.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_script.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    40.5\n",
       "dtype: float64"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_script.median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    25.529412\n",
       "dtype: float64"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_script.var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    5.052664\n",
       "dtype: float64"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_script.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Q 20) Calculate probability from the given dataset for the below cases\n",
    "\n",
    " \n",
    "Calculate the probability of MPG  of Cars for the below cases.\n",
    "       MPG <- Cars$MPG\n",
    "a.\tP(MPG>38)\n",
    "b.\tP(MPG<40)\n",
    "c.    P (20<MPG<50)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "data1 = pd.read_csv('Cars.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>HP</th>\n",
       "      <th>MPG</th>\n",
       "      <th>VOL</th>\n",
       "      <th>SP</th>\n",
       "      <th>WT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>49</td>\n",
       "      <td>53.700681</td>\n",
       "      <td>89</td>\n",
       "      <td>104.185353</td>\n",
       "      <td>28.762059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>55</td>\n",
       "      <td>50.013401</td>\n",
       "      <td>92</td>\n",
       "      <td>105.461264</td>\n",
       "      <td>30.466833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>55</td>\n",
       "      <td>50.013401</td>\n",
       "      <td>92</td>\n",
       "      <td>105.461264</td>\n",
       "      <td>30.193597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>70</td>\n",
       "      <td>45.696322</td>\n",
       "      <td>92</td>\n",
       "      <td>113.461264</td>\n",
       "      <td>30.632114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>53</td>\n",
       "      <td>50.504232</td>\n",
       "      <td>92</td>\n",
       "      <td>104.461264</td>\n",
       "      <td>29.889149</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   HP        MPG  VOL          SP         WT\n",
       "0  49  53.700681   89  104.185353  28.762059\n",
       "1  55  50.013401   92  105.461264  30.466833\n",
       "2  55  50.013401   92  105.461264  30.193597\n",
       "3  70  45.696322   92  113.461264  30.632114\n",
       "4  53  50.504232   92  104.461264  29.889149"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data1.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# P(MPG>38)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3475939251582705"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1-stats.norm.cdf(38,data1.MPG.mean(),data1.MPG.std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# \tP(MPG<40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7293498762151616"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.cdf(40,data1.MPG.mean(),data1.MPG.std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# P (20<MPG<50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8988689169682046"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.cdf(50,data1.MPG.mean(),data1.MPG.std())-stats.norm.cdf(20,data1.MPG.mean(),data1.MPG.std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Q 21) Check whether the data follows normal distribution\n",
    "# a)\tCheck whether the MPG of Cars follows Normal Distribution \n",
    "       \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MPG</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>53.700681</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>50.013401</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>50.013401</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>45.696322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>50.504232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>45.696322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>50.013401</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>46.716554</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>46.716554</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>42.299078</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>44.652834</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>39.354094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>39.354094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>44.652834</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>45.734893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>44.652834</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>42.789909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>39.354094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>42.789909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>38.901834</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>38.411003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>42.828479</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>38.310606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>40.474723</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>38.310606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>38.411003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>38.411003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>38.411003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>43.469434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>35.404192</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>29.629936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>29.629936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>24.487367</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>26.852279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>27.856252</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>31.113584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>29.629936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>30.131923</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>28.860225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>27.354265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>24.609132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>23.515917</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>63</th>\n",
       "      <td>23.515917</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64</th>\n",
       "      <td>23.605158</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>65</th>\n",
       "      <td>40.050000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>23.103172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>23.103172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>23.103172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>21.273708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>19.678507</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>23.203569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>23.203569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>19.086341</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>19.086341</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>18.762837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>36.900000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>19.197888</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>34.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>19.833733</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>12.101263</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>81 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          MPG\n",
       "0   53.700681\n",
       "1   50.013401\n",
       "2   50.013401\n",
       "3   45.696322\n",
       "4   50.504232\n",
       "5   45.696322\n",
       "6   50.013401\n",
       "7   46.716554\n",
       "8   46.716554\n",
       "9   42.299078\n",
       "10  44.652834\n",
       "11  39.354094\n",
       "12  39.354094\n",
       "13  44.652834\n",
       "14  45.734893\n",
       "15  44.652834\n",
       "16  42.789909\n",
       "17  39.354094\n",
       "18  42.789909\n",
       "19  38.901834\n",
       "20  38.411003\n",
       "21  42.828479\n",
       "22  38.310606\n",
       "23  40.474723\n",
       "24  38.310606\n",
       "25  38.411003\n",
       "26  38.411003\n",
       "27  38.411003\n",
       "28  43.469434\n",
       "29  35.404192\n",
       "..        ...\n",
       "51  29.629936\n",
       "52  29.629936\n",
       "53  24.487367\n",
       "54  26.852279\n",
       "55  27.856252\n",
       "56  31.113584\n",
       "57  29.629936\n",
       "58  30.131923\n",
       "59  28.860225\n",
       "60  27.354265\n",
       "61  24.609132\n",
       "62  23.515917\n",
       "63  23.515917\n",
       "64  23.605158\n",
       "65  40.050000\n",
       "66  23.103172\n",
       "67  23.103172\n",
       "68  23.103172\n",
       "69  21.273708\n",
       "70  19.678507\n",
       "71  23.203569\n",
       "72  23.203569\n",
       "73  19.086341\n",
       "74  19.086341\n",
       "75  18.762837\n",
       "76  36.900000\n",
       "77  19.197888\n",
       "78  34.000000\n",
       "79  19.833733\n",
       "80  12.101263\n",
       "\n",
       "[81 rows x 1 columns]"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data1[['MPG']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "34.422075728024666"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data1.MPG.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "35.15272697"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data1.MPG.median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    29.629936\n",
       "dtype: float64"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data1.MPG.mode()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# b)\tCheck Whether the Adipose Tissue (AT) and Waist Circumference(Waist)  from wc-at data set  follows Normal Distribution "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "data2 = pd.read_csv('wc-at.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Waist</th>\n",
       "      <th>AT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>74.75</td>\n",
       "      <td>25.72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>72.60</td>\n",
       "      <td>25.89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>81.80</td>\n",
       "      <td>42.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>83.95</td>\n",
       "      <td>42.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>74.65</td>\n",
       "      <td>29.84</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Waist     AT\n",
       "0  74.75  25.72\n",
       "1  72.60  25.89\n",
       "2  81.80  42.60\n",
       "3  83.95  42.80\n",
       "4  74.65  29.84"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "91.90183486238533"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2.Waist.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     94.5\n",
       "1    106.0\n",
       "2    108.5\n",
       "dtype: float64"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2.Waist.mode()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "90.8"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2.Waist.median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "101.89403669724771"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2.AT.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "96.54"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2.AT.median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    121.0\n",
       "1    123.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2.AT.mode()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Q 24)   A Government  company claims that an average light bulb lasts 270 days. A researcher randomly selects 18 bulbs for testing. The sampled bulbs last an average of 260 days, with a standard deviation of 90 days. If the CEO's claim were true, what is the probability that 18 randomly selected bulbs would have an average life of no more than 260 days"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = (260-270)/(90/(pow(18,0.5)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.4714045207910317"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.32167253567098364"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.t.cdf(t,df=17)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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