Basic Statistics1_Ass_Q20.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-09-19T05:17:37.931714Z",
     "start_time": "2021-09-19T05:17:37.919748Z"
    }
   },
   "source": [
    "# # Q20) Basic Statistics1- Assignment 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-09-19T05:18:02.529416Z",
     "start_time": "2021-09-19T05:18:02.516452Z"
    }
   },
   "source": [
    "Calculate probability from the given dataset for the below cases\n",
    "\n",
    "Data _set: Cars.csv\n",
    "\n",
    "Calculate the probability of MPG  of Cars for the below cases.\n",
    "\n",
    "MPG <- Cars$MPG\n",
    "\n",
    "a.\tP(MPG>38)\n",
    "\n",
    "b.\tP(MPG<40)\n",
    "\n",
    "c.  P(20<MPG<50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-09-19T05:18:30.402446Z",
     "start_time": "2021-09-19T05:18:24.337846Z"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sn\n",
    "from scipy import stats\n",
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-09-19T05:18:32.615063Z",
     "start_time": "2021-09-19T05:18:32.242101Z"
    }
   },
   "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>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",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>322</td>\n",
       "      <td>36.900000</td>\n",
       "      <td>50</td>\n",
       "      <td>169.598513</td>\n",
       "      <td>16.132947</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>238</td>\n",
       "      <td>19.197888</td>\n",
       "      <td>115</td>\n",
       "      <td>150.576579</td>\n",
       "      <td>37.923113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>263</td>\n",
       "      <td>34.000000</td>\n",
       "      <td>50</td>\n",
       "      <td>151.598513</td>\n",
       "      <td>15.769625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>295</td>\n",
       "      <td>19.833733</td>\n",
       "      <td>119</td>\n",
       "      <td>167.944460</td>\n",
       "      <td>39.423099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>236</td>\n",
       "      <td>12.101263</td>\n",
       "      <td>107</td>\n",
       "      <td>139.840817</td>\n",
       "      <td>34.948615</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>81 rows × 5 columns</p>\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\n",
       "..  ...        ...  ...         ...        ...\n",
       "76  322  36.900000   50  169.598513  16.132947\n",
       "77  238  19.197888  115  150.576579  37.923113\n",
       "78  263  34.000000   50  151.598513  15.769625\n",
       "79  295  19.833733  119  167.944460  39.423099\n",
       "80  236  12.101263  107  139.840817  34.948615\n",
       "\n",
       "[81 rows x 5 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crs=pd.read_csv('Cars.csv') #Reading the file\n",
    "crs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-09-19T05:18:47.150476Z",
     "start_time": "2021-09-19T05:18:47.075330Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: 34.4221\n",
      "Std Dev: 9.1314\n"
     ]
    }
   ],
   "source": [
    "crs['MPG'].mean()\n",
    "print('Mean:', round(crs.MPG.mean(), 4)) #Rounding mean off to 4 decimal places\n",
    "print('Std Dev:', round(crs.MPG.std(), 4)) #Rounding standard dev off to 4 decimal places"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-09-19T05:19:01.227294Z",
     "start_time": "2021-09-19T05:18:58.706995Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Chetana\\anaconda3\\lib\\site-packages\\seaborn\\distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#sn.histplot(crs.MPG)\n",
    "sn.distplot(crs.MPG, label = 'CARS');\n",
    "plt.xlabel('CARS');\n",
    "plt.ylabel('Density');\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-09-19T05:19:26.193209Z",
     "start_time": "2021-09-19T05:19:26.111400Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3475939251582705"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# P(MPG>38) #Since the sample size is large than 38\n",
    "1-stats.norm.cdf(38,crs.MPG.mean(),crs.MPG.std()) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-09-19T05:19:36.906403Z",
     "start_time": "2021-09-19T05:19:36.887451Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7293498762151616"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# P(MPG<40) #Since the sample size is less than 40\n",
    "stats.norm.cdf(40,crs.MPG.mean(),crs.MPG.std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-09-19T05:19:46.139710Z",
     "start_time": "2021-09-19T05:19:46.043633Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2430968797327613e-05"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# P (20<MPG<50)\n",
    "stats.norm.cdf(0.50,crs.MPG.mean(),crs.MPG.std())-stats.norm.cdf(0.20,crs.MPG.mean(),crs.MPG.std())          "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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  "varInspector": {
   "cols": {
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    "lenVar": 40
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   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
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   "window_display": false
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 "nbformat": 4,
 "nbformat_minor": 4
}