S02c_Exercise1_solution.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Execute before using this notebook if using google colab\n",
    "\n",
    "kernel = str(get_ipython())\n",
    "\n",
    "if 'google.colab' in kernel:    \n",
    "    !wget https://raw.githubusercontent.com/fredzett/rmqa/master/utils.py -P local_modules -nc \n",
    "    !npx degit fredzett/rmqa/data data\n",
    "    import sys\n",
    "    sys.path.append('local_modules')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from utils import Datasets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 1 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Show (with an example) that the median and the $50^{th}$ percentile are the same"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numbers = [1022,23,23,21,31,5,5,7,8,9,0,0,3,12,325,46]\n",
    "np.median(numbers) == np.percentile(numbers,50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 2\n",
    "\n",
    "The **HR Statistics Inc.** has gathered a sample of salary data. The data includes three groups`\n",
    "\n",
    "- `low`: salary from workers with work experience $<=5yrs$\n",
    "- `medium`: salary from workers with work experience $>5yrs$ and $<=10yrs$\n",
    "- `high`: salary from workers with work experience $>10yrs$\n",
    "\n",
    "For the consulting service the company wants to understand if and how salaries differe by work experience. \n",
    "\n",
    "Please help them and calculate for each group:\n",
    "\n",
    "- location parameter\n",
    "- variance parameter\n",
    "\n",
    "**Important**: try to avoid code repetition\n",
    "\n",
    "What are your conclusions?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "low, medium,  high = Datasets.salaries()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Solution 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are various way how to do this. Here is one way..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_summary(groups):\n",
    "    for i in range(len(groups)):\n",
    "        print()\n",
    "        print(\"Summary for Group\", i + 1)\n",
    "        print(\"---------------------\")\n",
    "        print(\"Mean:\", np.mean(groups[i]))\n",
    "        print(\"Median:\", np.median(groups[i]))\n",
    "        print(\"Stdev:\", np.std(groups[i]))\n",
    "        print(\"Quartiles:\", np.quantile(groups[i],[0.25,0.5,0.75]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Summary for Group 1\n",
      "---------------------\n",
      "Mean: 40309.09\n",
      "Median: 41136.0\n",
      "Stdev: 10347.90371533771\n",
      "Quartiles: [32402.  41136.  47939.5]\n",
      "\n",
      "Summary for Group 2\n",
      "---------------------\n",
      "Mean: 60262.01\n",
      "Median: 59846.5\n",
      "Stdev: 18997.284195113254\n",
      "Quartiles: [45898.   59846.5  73902.25]\n",
      "\n",
      "Summary for Group 3\n",
      "---------------------\n",
      "Mean: 81353.41\n",
      "Median: 80339.5\n",
      "Stdev: 13146.482363046778\n",
      "Quartiles: [72708.25 80339.5  88513.75]\n"
     ]
    }
   ],
   "source": [
    "make_summary([low,medium,high])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solutions 2 (outlook)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using other modules it is even easiere to achieve similar things"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "#plt.style.use(\"ggplot\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "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>low</th>\n",
       "      <th>high</th>\n",
       "      <th>medium</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>40309.090000</td>\n",
       "      <td>81353.410000</td>\n",
       "      <td>60262.010000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>10400.034543</td>\n",
       "      <td>13212.711913</td>\n",
       "      <td>19092.989003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>18140.000000</td>\n",
       "      <td>47800.000000</td>\n",
       "      <td>25384.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>32402.000000</td>\n",
       "      <td>72708.250000</td>\n",
       "      <td>45898.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>41136.000000</td>\n",
       "      <td>80339.500000</td>\n",
       "      <td>59846.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>47939.500000</td>\n",
       "      <td>88513.750000</td>\n",
       "      <td>73902.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>61488.000000</td>\n",
       "      <td>121011.000000</td>\n",
       "      <td>119261.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                low           high         medium\n",
       "count    100.000000     100.000000     100.000000\n",
       "mean   40309.090000   81353.410000   60262.010000\n",
       "std    10400.034543   13212.711913   19092.989003\n",
       "min    18140.000000   47800.000000   25384.000000\n",
       "25%    32402.000000   72708.250000   45898.000000\n",
       "50%    41136.000000   80339.500000   59846.500000\n",
       "75%    47939.500000   88513.750000   73902.250000\n",
       "max    61488.000000  121011.000000  119261.000000"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = {\"low\":low, \"high\":high, \"medium\":medium}\n",
    "df = pd.DataFrame(data)\n",
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x396 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[[\"low\",\"high\"]].hist();\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.8.3"
  },
  "toc-autonumbering": true
 },
 "nbformat": 4,
 "nbformat_minor": 4
}