s05_t01_sampling_methods.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "857001a9",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "# IT Academy - Data Science Itinerary\n",
    "\n",
    "$~$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad6e86cc",
   "metadata": {},
   "source": [
    "## S05 T01: Sampling Methods with pyhton\n",
    "__________\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "802ff245",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:57:31.032378Z",
     "start_time": "2022-03-10T14:57:31.026617Z"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import os\n",
    "import kaggle\n",
    "from IPython.display import display,HTML\n",
    "import seaborn as sns\n",
    "import matplotlib.image as mpimg\n",
    "from matplotlib import rcParams\n",
    "import matplotlib as mpl\n",
    "from matplotlib import cm\n",
    "from matplotlib import colors\n",
    "import squarify\n",
    "from sklearn.model_selection import train_test_split\n",
    "import imblearn\n",
    "from imblearn.over_sampling import SMOTE\n",
    "from sklearn import preprocessing\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "import random\n",
    "pd.options.mode.chained_assignment = None  #to avoid SettingWithCopyWarning"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7557656a",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "####  Simple random sample\n",
    "\n",
    "$~$\n",
    "\n",
    "Choose a sports-themed dataset you like. Perform a sampling of the data generating a simple random sample and a systematic sample.\n",
    "$~$\n",
    "___\n",
    "\n",
    "$~$\n",
    "##### finding a dataset\n",
    "\n",
    "$~$\n",
    "\n",
    "Let's find a dataset in Kaggle. Using de following line, we can search for \"sports\" datasets\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "99e311f6",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:46.723767Z",
     "start_time": "2022-03-10T14:55:45.180253Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ref                                                        title                                            size  lastUpdated          downloadCount  voteCount  usabilityRating  \r\n",
      "---------------------------------------------------------  ----------------------------------------------  -----  -------------------  -------------  ---------  ---------------  \r\n",
      "gpiosenka/sports-classification                            100 Sports Image Classification                 477MB  2022-01-13 16:08:31           1230         40  0.8235294        \r\n",
      "the-guardian/olympic-games                                 Olympic Sports and Medals, 1896-2014            483KB  2017-01-24 15:05:37          23095        208  0.7058824        \r\n",
      "ekrembayar/fifa-21-complete-player-dataset                 FIFA 21 COMPLETE PLAYER DATASET                   3MB  2020-10-05 06:21:30           2453         61  0.8235294        \r\n",
      "parulpandey/forbes-highest-paid-athletes-19902019          Forbes Highest Paid Athletes 1990-2020            4KB  2020-12-19 02:17:15           2825         41  0.8235294        \r\n",
      "artimous/complete-fifa-2017-player-dataset-global          Complete FIFA 2017 Player dataset (Global)       10MB  2017-04-13 08:37:43          14398        221  0.7647059        \r\n",
      "rishidamarla/toughest-sports-by-skill                      Toughest Sports by Skill                         11KB  2020-09-20 18:24:13            613         23  0.7647059        \r\n",
      "rahul253801/political-donations-by-american-sports-owners  Political Donations By American Sports Owners    34KB  2021-02-12 07:19:45            217         15  1.0              \r\n",
      "amananandrai/ag-news-classification-dataset                AG News Classification Dataset                   11MB  2020-04-20 07:55:38           4157         43  0.7058824        \r\n",
      "rishikeshkonapure/sports-image-dataset                     Sports Image Dataset                            466MB  2020-07-29 19:05:52            139          3  0.875            \r\n",
      "scottfree/sports-lines                                     Pro and College Sports Lines                     71KB  2017-11-08 15:00:12            815         26  0.64705884       \r\n",
      "yaswanthgali/sport-celebrity-image-classification          Sport Celebrity Image Classification             15MB  2021-11-26 11:34:15            151         22  0.875            \r\n",
      "maneesh99/sports-datasetbbc                                Sports Dataset(BBC)                             188KB  2020-10-11 07:40:22            176          7  0.64705884       \r\n",
      "erichqiu/nba-odds-and-scores                               NBA Odds and Scores                               2MB  2020-05-02 07:22:39            727         17  0.875            \r\n",
      "shitalgaikwad123/skills-required-for-different-sports      skills required for different sports             11KB  2021-07-23 17:37:57            167         11  0.7647059        \r\n",
      "zygmunt/betfair-sports                                     One week of Betfair data: 23 sports              81MB  2017-08-31 16:46:43            902         23  0.7647059        \r\n",
      "logandonaldson/sports-stadium-locations                    Sports Stadium Locations                          3KB  2022-01-15 22:01:16             44          5  0.9411765        \r\n",
      "harti28/independence-and-interdependence-in-sports         Independence and Interdependence in Sports        5KB  2021-03-02 17:07:15            109          4  1.0              \r\n",
      "shivagovindasamy/2020-tokyo-paralympics                    2020 Tokyo Paralympics                          116KB  2021-09-05 22:18:47            630         27  1.0              \r\n",
      "aryashah2k/beginners-sports-analytics-nfl-dataset          Beginners Sports Analytics NFL Dataset           21MB  2021-07-11 08:43:47            501          4  1.0              \r\n",
      "aalborguniversity/thermal-soccer-dataset                   Thermal soccer dataset                            2GB  2018-02-08 09:54:24            861         29  0.6875           \r\n"
     ]
    }
   ],
   "source": [
    "!kaggle datasets list -s \"sports\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "615d98e0",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "for this exercice we are going to use [Olympic Sports and Medals, 1896-2014](https://www.kaggle.com/the-guardian/olympic-games?select=summer.csv) from Kaggle.\n",
    "$~$ \n",
    "\n",
    "\"the-guardian/olympic-games\"\n",
    "$~$ \n",
    "_____\n",
    "\n",
    "$~$ \n",
    "\n",
    "##### downloading a dataset from kaggle\n",
    "\n",
    "$~$ \n",
    "\n",
    "_____\n",
    "\n",
    "$~$ \n",
    "\n",
    "We use the following code to download the dataset from kagggle:\n",
    "\n",
    "$~$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6f8a14c7",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:48.269505Z",
     "start_time": "2022-03-10T14:55:46.727293Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading olympic-games.zip to ./data\n",
      "100%|████████████████████████████████████████| 483k/483k [00:00<00:00, 3.45MB/s]\n",
      "100%|████████████████████████████████████████| 483k/483k [00:00<00:00, 3.43MB/s]\n"
     ]
    }
   ],
   "source": [
    "PATH = \"./data\"\n",
    "\n",
    "if not os.path.exists(PATH):\n",
    "    os.makedirs(PATH)\n",
    "if not os.listdir(PATH):\n",
    "        !kaggle datasets download -d \"the-guardian/olympic-games\" --unzip -p $PATH  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a42efb16",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:48.285495Z",
     "start_time": "2022-03-10T14:55:48.277531Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "./data/winter.csv\n",
      "./data/summer.csv\n",
      "./data/dictionary.csv\n"
     ]
    }
   ],
   "source": [
    "files = [os.path.join(PATH,f) for f in os.listdir(PATH)]\n",
    "\n",
    "for f in files:\n",
    "    print(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a38f9a54",
   "metadata": {},
   "source": [
    "\n",
    "$~$ \n",
    "\n",
    "as we have downloaded three files, let's work with the file: \"summer.csv\"\n",
    "\n",
    "\n",
    "$~$\n",
    "___\n",
    "\n",
    "\n",
    "$~$\n",
    "\n",
    "##### reading the file\n",
    "\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "19fe347e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:48.409466Z",
     "start_time": "2022-03-10T14:55:48.288611Z"
    }
   },
   "outputs": [],
   "source": [
    "df = pd.read_csv(files[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7db1a834",
   "metadata": {},
   "source": [
    "$~$\n",
    "____\n",
    "##### getting information from the dataset\n",
    "\n",
    "\n",
    "$~$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5d232ea4",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:48.502045Z",
     "start_time": "2022-03-10T14:55:48.416636Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 31165 entries, 0 to 31164\n",
      "Data columns (total 9 columns):\n",
      " #   Column      Non-Null Count  Dtype \n",
      "---  ------      --------------  ----- \n",
      " 0   Year        31165 non-null  int64 \n",
      " 1   City        31165 non-null  object\n",
      " 2   Sport       31165 non-null  object\n",
      " 3   Discipline  31165 non-null  object\n",
      " 4   Athlete     31165 non-null  object\n",
      " 5   Country     31161 non-null  object\n",
      " 6   Gender      31165 non-null  object\n",
      " 7   Event       31165 non-null  object\n",
      " 8   Medal       31165 non-null  object\n",
      "dtypes: int64(1), object(8)\n",
      "memory usage: 2.1+ MB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "54cb1a42",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:48.594181Z",
     "start_time": "2022-03-10T14:55:48.504809Z"
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   },
   "outputs": [
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       "      <td>31165</td>\n",
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       "      <th>top</th>\n",
       "      <td>London</td>\n",
       "      <td>Aquatics</td>\n",
       "      <td>Athletics</td>\n",
       "      <td>PHELPS, Michael</td>\n",
       "      <td>USA</td>\n",
       "      <td>Men</td>\n",
       "      <td>Football</td>\n",
       "      <td>Gold</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\n",
       "      <td>3567</td>\n",
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       "      <td>3638</td>\n",
       "      <td>22</td>\n",
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       "      <td>22746</td>\n",
       "      <td>1497</td>\n",
       "      <td>10486</td>\n",
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      "text/plain": [
       "          City     Sport Discipline          Athlete Country Gender     Event  \\\n",
       "count    31165     31165      31165            31165   31161  31165     31165   \n",
       "unique      22        43         67            22762     147      2       666   \n",
       "top     London  Aquatics  Athletics  PHELPS, Michael     USA    Men  Football   \n",
       "freq      3567      4170       3638               22    4585  22746      1497   \n",
       "\n",
       "        Medal  \n",
       "count   31165  \n",
       "unique      3  \n",
       "top      Gold  \n",
       "freq    10486  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe(include=[object])  "
   ]
  },
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   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>City</th>\n",
       "      <th>Sport</th>\n",
       "      <th>Discipline</th>\n",
       "      <th>Athlete</th>\n",
       "      <th>Country</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Event</th>\n",
       "      <th>Medal</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1896</td>\n",
       "      <td>Athens</td>\n",
       "      <td>Aquatics</td>\n",
       "      <td>Swimming</td>\n",
       "      <td>HAJOS, Alfred</td>\n",
       "      <td>HUN</td>\n",
       "      <td>Men</td>\n",
       "      <td>100M Freestyle</td>\n",
       "      <td>Gold</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1896</td>\n",
       "      <td>Athens</td>\n",
       "      <td>Aquatics</td>\n",
       "      <td>Swimming</td>\n",
       "      <td>HERSCHMANN, Otto</td>\n",
       "      <td>AUT</td>\n",
       "      <td>Men</td>\n",
       "      <td>100M Freestyle</td>\n",
       "      <td>Silver</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1896</td>\n",
       "      <td>Athens</td>\n",
       "      <td>Aquatics</td>\n",
       "      <td>Swimming</td>\n",
       "      <td>DRIVAS, Dimitrios</td>\n",
       "      <td>GRE</td>\n",
       "      <td>Men</td>\n",
       "      <td>100M Freestyle For Sailors</td>\n",
       "      <td>Bronze</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1896</td>\n",
       "      <td>Athens</td>\n",
       "      <td>Aquatics</td>\n",
       "      <td>Swimming</td>\n",
       "      <td>MALOKINIS, Ioannis</td>\n",
       "      <td>GRE</td>\n",
       "      <td>Men</td>\n",
       "      <td>100M Freestyle For Sailors</td>\n",
       "      <td>Gold</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1896</td>\n",
       "      <td>Athens</td>\n",
       "      <td>Aquatics</td>\n",
       "      <td>Swimming</td>\n",
       "      <td>CHASAPIS, Spiridon</td>\n",
       "      <td>GRE</td>\n",
       "      <td>Men</td>\n",
       "      <td>100M Freestyle For Sailors</td>\n",
       "      <td>Silver</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Year    City     Sport Discipline             Athlete Country Gender  \\\n",
       "0  1896  Athens  Aquatics   Swimming       HAJOS, Alfred     HUN    Men   \n",
       "1  1896  Athens  Aquatics   Swimming    HERSCHMANN, Otto     AUT    Men   \n",
       "2  1896  Athens  Aquatics   Swimming   DRIVAS, Dimitrios     GRE    Men   \n",
       "3  1896  Athens  Aquatics   Swimming  MALOKINIS, Ioannis     GRE    Men   \n",
       "4  1896  Athens  Aquatics   Swimming  CHASAPIS, Spiridon     GRE    Men   \n",
       "\n",
       "                        Event   Medal  \n",
       "0              100M Freestyle    Gold  \n",
       "1              100M Freestyle  Silver  \n",
       "2  100M Freestyle For Sailors  Bronze  \n",
       "3  100M Freestyle For Sailors    Gold  \n",
       "4  100M Freestyle For Sailors  Silver  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7800d8f6",
   "metadata": {},
   "source": [
    "\n",
    "$~$\n",
    "____\n",
    "\n",
    "##### working on the dataset\n",
    "\n",
    "\n",
    "$~$\n",
    "\n",
    "we are going to analyze how many medals each country has, for them let's execute the following code:\n",
    "\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "dd7f54eb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:48.630544Z",
     "start_time": "2022-03-10T14:55:48.616841Z"
    }
   },
   "outputs": [],
   "source": [
    "medal_count = df.groupby(\"Country\")[\"Medal\"].agg([\"count\"]).sort_values(by=\"count\", ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0d0b4cfe",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:48.642161Z",
     "start_time": "2022-03-10T14:55:48.636006Z"
    }
   },
   "outputs": [],
   "source": [
    "medal_count[\"proportion\"]= medal_count[\"count\"] / medal_count[\"count\"].sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "39ad46ba",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:48.656027Z",
     "start_time": "2022-03-10T14:55:48.645231Z"
    }
   },
   "outputs": [
    {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>proportion</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Country</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>USA</th>\n",
       "      <td>4585</td>\n",
       "      <td>0.147139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>URS</th>\n",
       "      <td>2049</td>\n",
       "      <td>0.065755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GBR</th>\n",
       "      <td>1720</td>\n",
       "      <td>0.055197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FRA</th>\n",
       "      <td>1396</td>\n",
       "      <td>0.044800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GER</th>\n",
       "      <td>1305</td>\n",
       "      <td>0.041879</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ITA</th>\n",
       "      <td>1296</td>\n",
       "      <td>0.041590</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AUS</th>\n",
       "      <td>1189</td>\n",
       "      <td>0.038157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HUN</th>\n",
       "      <td>1079</td>\n",
       "      <td>0.034627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SWE</th>\n",
       "      <td>1044</td>\n",
       "      <td>0.033503</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NED</th>\n",
       "      <td>851</td>\n",
       "      <td>0.027310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GDR</th>\n",
       "      <td>825</td>\n",
       "      <td>0.026475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHN</th>\n",
       "      <td>807</td>\n",
       "      <td>0.025898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>JPN</th>\n",
       "      <td>788</td>\n",
       "      <td>0.025288</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RUS</th>\n",
       "      <td>768</td>\n",
       "      <td>0.024646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CAN</th>\n",
       "      <td>649</td>\n",
       "      <td>0.020827</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ROU</th>\n",
       "      <td>640</td>\n",
       "      <td>0.020538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOR</th>\n",
       "      <td>554</td>\n",
       "      <td>0.017779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KOR</th>\n",
       "      <td>529</td>\n",
       "      <td>0.016976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>POL</th>\n",
       "      <td>511</td>\n",
       "      <td>0.016399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DEN</th>\n",
       "      <td>507</td>\n",
       "      <td>0.016270</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         count  proportion\n",
       "Country                   \n",
       "USA       4585    0.147139\n",
       "URS       2049    0.065755\n",
       "GBR       1720    0.055197\n",
       "FRA       1396    0.044800\n",
       "GER       1305    0.041879\n",
       "ITA       1296    0.041590\n",
       "AUS       1189    0.038157\n",
       "HUN       1079    0.034627\n",
       "SWE       1044    0.033503\n",
       "NED        851    0.027310\n",
       "GDR        825    0.026475\n",
       "CHN        807    0.025898\n",
       "JPN        788    0.025288\n",
       "RUS        768    0.024646\n",
       "CAN        649    0.020827\n",
       "ROU        640    0.020538\n",
       "NOR        554    0.017779\n",
       "KOR        529    0.016976\n",
       "POL        511    0.016399\n",
       "DEN        507    0.016270"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "medal_count.head(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93874659",
   "metadata": {},
   "source": [
    "\n",
    "$~$\n",
    "\n",
    "As we can see, the country that has the most medals in total is USA.\n",
    "\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80792823",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T11:40:32.689429Z",
     "start_time": "2022-03-10T11:40:32.597315Z"
    }
   },
   "source": [
    "##### ploting the distribution\n",
    "\n",
    "____\n",
    "$~$\n",
    "\n",
    "let's see graphically how is the distribution of total medals by country \n",
    "\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e9193bff",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:48.966217Z",
     "start_time": "2022-03-10T14:55:48.659193Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10,5))\n",
    "fig = sns.kdeplot(medal_count[\"proportion\"],bw_method=.10, shade=True)\n",
    "\n",
    "fig.spines['top'].set_visible(False)\n",
    "fig.spines['right'].set_visible(False)\n",
    "fig.set_title(\"Distribution of total medal by country\")\n",
    "\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45072437",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "##### a simple sample\n",
    "___\n",
    "\n",
    "Once we have seen how the proportion of medals in our dataset is, let's proceed to obtain a simple random sample by executing the following code:\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "8bcf3a61",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:48.975252Z",
     "start_time": "2022-03-10T14:55:48.968823Z"
    }
   },
   "outputs": [],
   "source": [
    "df_sample = df.sample(n=1000,random_state=2021)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89088018",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "now, we are going to transform the sample to be able to make comparisons with our original data\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "cdf02d36",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:48.984022Z",
     "start_time": "2022-03-10T14:55:48.978416Z"
    }
   },
   "outputs": [],
   "source": [
    "medal_count_sample = df_sample.groupby(\"Country\")[\"Medal\"]\\\n",
    "                    .agg([\"count\"]).sort_values(by=\"count\", ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "9e0b4fa5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:48.995288Z",
     "start_time": "2022-03-10T14:55:48.986470Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\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>count</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Country</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>USA</th>\n",
       "      <td>135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>URS</th>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GBR</th>\n",
       "      <td>57</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ITA</th>\n",
       "      <td>56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FRA</th>\n",
       "      <td>52</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         count\n",
       "Country       \n",
       "USA        135\n",
       "URS         75\n",
       "GBR         57\n",
       "ITA         56\n",
       "FRA         52"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "medal_count_sample.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "6b9f1784",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:49.002017Z",
     "start_time": "2022-03-10T14:55:48.997821Z"
    }
   },
   "outputs": [],
   "source": [
    "medal_count_sample[\"proportion\"]= medal_count_sample[\"count\"]\\\n",
    "                                / medal_count_sample[\"count\"].sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1033ec3e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:49.013448Z",
     "start_time": "2022-03-10T14:55:49.004616Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\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>count</th>\n",
       "      <th>proportion</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Country</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>USA</th>\n",
       "      <td>135</td>\n",
       "      <td>0.135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>URS</th>\n",
       "      <td>75</td>\n",
       "      <td>0.075</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GBR</th>\n",
       "      <td>57</td>\n",
       "      <td>0.057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ITA</th>\n",
       "      <td>56</td>\n",
       "      <td>0.056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FRA</th>\n",
       "      <td>52</td>\n",
       "      <td>0.052</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         count  proportion\n",
       "Country                   \n",
       "USA        135       0.135\n",
       "URS         75       0.075\n",
       "GBR         57       0.057\n",
       "ITA         56       0.056\n",
       "FRA         52       0.052"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "medal_count_sample.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f8f37497",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:49.032829Z",
     "start_time": "2022-03-10T14:55:49.015984Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count_total</th>\n",
       "      <th>proportion_total</th>\n",
       "      <th>count_sample</th>\n",
       "      <th>proportion_sample</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Country</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>USA</th>\n",
       "      <td>4585</td>\n",
       "      <td>0.147139</td>\n",
       "      <td>135</td>\n",
       "      <td>0.135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>URS</th>\n",
       "      <td>2049</td>\n",
       "      <td>0.065755</td>\n",
       "      <td>75</td>\n",
       "      <td>0.075</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GBR</th>\n",
       "      <td>1720</td>\n",
       "      <td>0.055197</td>\n",
       "      <td>57</td>\n",
       "      <td>0.057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FRA</th>\n",
       "      <td>1396</td>\n",
       "      <td>0.044800</td>\n",
       "      <td>52</td>\n",
       "      <td>0.052</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GER</th>\n",
       "      <td>1305</td>\n",
       "      <td>0.041879</td>\n",
       "      <td>41</td>\n",
       "      <td>0.041</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ITA</th>\n",
       "      <td>1296</td>\n",
       "      <td>0.041590</td>\n",
       "      <td>56</td>\n",
       "      <td>0.056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AUS</th>\n",
       "      <td>1189</td>\n",
       "      <td>0.038157</td>\n",
       "      <td>38</td>\n",
       "      <td>0.038</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HUN</th>\n",
       "      <td>1079</td>\n",
       "      <td>0.034627</td>\n",
       "      <td>38</td>\n",
       "      <td>0.038</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SWE</th>\n",
       "      <td>1044</td>\n",
       "      <td>0.033503</td>\n",
       "      <td>30</td>\n",
       "      <td>0.030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NED</th>\n",
       "      <td>851</td>\n",
       "      <td>0.027310</td>\n",
       "      <td>31</td>\n",
       "      <td>0.031</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GDR</th>\n",
       "      <td>825</td>\n",
       "      <td>0.026475</td>\n",
       "      <td>16</td>\n",
       "      <td>0.016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHN</th>\n",
       "      <td>807</td>\n",
       "      <td>0.025898</td>\n",
       "      <td>23</td>\n",
       "      <td>0.023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>JPN</th>\n",
       "      <td>788</td>\n",
       "      <td>0.025288</td>\n",
       "      <td>29</td>\n",
       "      <td>0.029</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RUS</th>\n",
       "      <td>768</td>\n",
       "      <td>0.024646</td>\n",
       "      <td>34</td>\n",
       "      <td>0.034</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CAN</th>\n",
       "      <td>649</td>\n",
       "      <td>0.020827</td>\n",
       "      <td>20</td>\n",
       "      <td>0.020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ROU</th>\n",
       "      <td>640</td>\n",
       "      <td>0.020538</td>\n",
       "      <td>16</td>\n",
       "      <td>0.016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOR</th>\n",
       "      <td>554</td>\n",
       "      <td>0.017779</td>\n",
       "      <td>17</td>\n",
       "      <td>0.017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KOR</th>\n",
       "      <td>529</td>\n",
       "      <td>0.016976</td>\n",
       "      <td>18</td>\n",
       "      <td>0.018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>POL</th>\n",
       "      <td>511</td>\n",
       "      <td>0.016399</td>\n",
       "      <td>12</td>\n",
       "      <td>0.012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DEN</th>\n",
       "      <td>507</td>\n",
       "      <td>0.016270</td>\n",
       "      <td>17</td>\n",
       "      <td>0.017</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         count_total  proportion_total  count_sample  proportion_sample\n",
       "Country                                                                \n",
       "USA             4585          0.147139           135              0.135\n",
       "URS             2049          0.065755            75              0.075\n",
       "GBR             1720          0.055197            57              0.057\n",
       "FRA             1396          0.044800            52              0.052\n",
       "GER             1305          0.041879            41              0.041\n",
       "ITA             1296          0.041590            56              0.056\n",
       "AUS             1189          0.038157            38              0.038\n",
       "HUN             1079          0.034627            38              0.038\n",
       "SWE             1044          0.033503            30              0.030\n",
       "NED              851          0.027310            31              0.031\n",
       "GDR              825          0.026475            16              0.016\n",
       "CHN              807          0.025898            23              0.023\n",
       "JPN              788          0.025288            29              0.029\n",
       "RUS              768          0.024646            34              0.034\n",
       "CAN              649          0.020827            20              0.020\n",
       "ROU              640          0.020538            16              0.016\n",
       "NOR              554          0.017779            17              0.017\n",
       "KOR              529          0.016976            18              0.018\n",
       "POL              511          0.016399            12              0.012\n",
       "DEN              507          0.016270            17              0.017"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "medal_count.merge(medal_count_sample, left_on='Country', right_on='Country', \n",
    "                  suffixes=('_total', '_sample')).head(20)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82b116c5",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "##### total populations vs simple sample\n",
    "\n",
    "$~$\n",
    "\n",
    "As can be seen in the table above, the simple sample benefits the countries that have more medals, but disadvantages the countries with fewer medals. This can be a problem if we work with data with subgroups.\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c02ccdfc",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "##### graphic point of view: total populations vs simple sample\n",
    "\n",
    "$~$\n",
    "\n",
    "A quick way to see what our sampling is like is to make some plots. Let's see some:\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "0aa73f7c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:49.324184Z",
     "start_time": "2022-03-10T14:55:49.035219Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axes = plt.subplots(1,2, figsize=(10,5))\n",
    "\n",
    "\n",
    "\n",
    "sns.kdeplot(medal_count[\"proportion\"],bw_method=.10, shade=True,ax=axes[0])\n",
    "\n",
    "axes[0].spines['top'].set_visible(False)\n",
    "axes[0].spines['right'].set_visible(False)\n",
    "axes[0].set_title(\"fig 1. Distribution of total medal by country (population) \",fontsize=8)\n",
    "\n",
    "\n",
    "sns.kdeplot(medal_count_sample[\"proportion\"],bw_method=.10, shade=True,ax=axes[1])\n",
    "axes[1].set_title(\"fig 2. Distribution of total medal by country(simple random sample)\",fontsize=8)\n",
    "\n",
    "axes[1].spines['top'].set_visible(False)\n",
    "axes[1].spines['right'].set_visible(False)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16810ceb",
   "metadata": {},
   "source": [
    "\n",
    "$~$\n",
    "\n",
    "we can also see the effect of sampling in a Treemaps of the distribution\n",
    "\n",
    "$~$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "5d848796",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:49.935747Z",
     "start_time": "2022-03-10T14:55:49.326965Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1152x324 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "medal_count_plot = medal_count[medal_count[\"count\"] > 20]\n",
    "\n",
    "normdata = mpl.colors.Normalize(min(medal_count_plot[\"count\"].values\n",
    "), max(medal_count_plot[\"count\"].values\n",
    "))  \n",
    "colormap = mpl.cm.Blues #this line allows us to change the colors\n",
    "colors =colormap(normdata(medal_count_plot[\"count\"].values\n",
    "))\n",
    "\n",
    "\n",
    "fig = plt.gcf()\n",
    "ax = fig.add_subplot()\n",
    "fig.set_size_inches(16, 4.5)\n",
    "\n",
    "squarify.plot(sizes=medal_count_plot[\"count\"].values\n",
    ", alpha=0.8, label=medal_count_plot.index,color = colors,\n",
    "              text_kwargs={'fontsize':10, 'fontname':\"helvetica\",'weight':'bold'})\n",
    "plt.title(\"Total medals distribution\",fontsize=23,fontweight=\"bold\")\n",
    "plt.axis('off')\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "bd8cf81d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.085973Z",
     "start_time": "2022-03-10T14:55:49.939976Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1152x324 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "medal_count_sample_plot = medal_count_sample[medal_count_sample[\"count\"] > 20]\n",
    "\n",
    "normdata = mpl.colors.Normalize(min(medal_count_sample_plot[\"count\"].values\n",
    "), max(medal_count_sample_plot[\"count\"].values\n",
    "))  \n",
    "colormap = mpl.cm.Blues #this line allows us to change the colors\n",
    "colors =colormap(normdata(medal_count_sample_plot[\"count\"].values\n",
    "))\n",
    "\n",
    "\n",
    "fig = plt.gcf()\n",
    "ax = fig.add_subplot()\n",
    "fig.set_size_inches(16, 4.5)\n",
    "\n",
    "squarify.plot(sizes=medal_count_sample_plot[\"count\"].values\n",
    ", alpha=0.8, label=medal_count_sample_plot.index,color = colors,\n",
    "              text_kwargs={'fontsize':10, 'fontname':\"helvetica\",'weight':'bold'})\n",
    "plt.title(\"Total medals distribution(simple sample)\",fontsize=23,fontweight=\"bold\")\n",
    "plt.axis('off')\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89413adc",
   "metadata": {},
   "source": [
    "___\n",
    "$~$\n",
    "\n",
    "\n",
    "####  Systematic Sample\n",
    "\n",
    "$~$\n",
    "___\n",
    "\n",
    "\n",
    "The first thing we will do is define the interval:\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "1783e4a0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.092203Z",
     "start_time": "2022-03-10T14:55:50.088422Z"
    }
   },
   "outputs": [],
   "source": [
    "sample_size= 1000\n",
    "\n",
    "pop_size = len(df)\n",
    "\n",
    "interval = pop_size // sample_size\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d2f103e",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "let's randomly shuffle the rows and reset the index in case there is a built-in order that could bias the results.\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "9c1f214e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.119342Z",
     "start_time": "2022-03-10T14:55:50.095843Z"
    }
   },
   "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>Year</th>\n",
       "      <th>City</th>\n",
       "      <th>Sport</th>\n",
       "      <th>Discipline</th>\n",
       "      <th>Athlete</th>\n",
       "      <th>Country</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Event</th>\n",
       "      <th>Medal</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2012</td>\n",
       "      <td>London</td>\n",
       "      <td>Wrestling</td>\n",
       "      <td>Wrestling Freestyle</td>\n",
       "      <td>EBRAHIM, Karam Mohamed Gaber</td>\n",
       "      <td>EGY</td>\n",
       "      <td>Men</td>\n",
       "      <td>Wg 84 KG</td>\n",
       "      <td>Silver</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1924</td>\n",
       "      <td>Paris</td>\n",
       "      <td>Football</td>\n",
       "      <td>Football</td>\n",
       "      <td>SOMMA, P.</td>\n",
       "      <td>URU</td>\n",
       "      <td>Men</td>\n",
       "      <td>Football</td>\n",
       "      <td>Gold</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1988</td>\n",
       "      <td>Seoul</td>\n",
       "      <td>Handball</td>\n",
       "      <td>Handball</td>\n",
       "      <td>TURCHINA, Zinaida</td>\n",
       "      <td>URS</td>\n",
       "      <td>Women</td>\n",
       "      <td>Handball</td>\n",
       "      <td>Bronze</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2004</td>\n",
       "      <td>Athens</td>\n",
       "      <td>Handball</td>\n",
       "      <td>Handball</td>\n",
       "      <td>BROEDSGAARD, Karen</td>\n",
       "      <td>DEN</td>\n",
       "      <td>Women</td>\n",
       "      <td>Handball</td>\n",
       "      <td>Gold</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1996</td>\n",
       "      <td>Atlanta</td>\n",
       "      <td>Aquatics</td>\n",
       "      <td>Swimming</td>\n",
       "      <td>HAN, Xue</td>\n",
       "      <td>CHN</td>\n",
       "      <td>Women</td>\n",
       "      <td>4X100M Medley Relay</td>\n",
       "      <td>Bronze</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Year     City      Sport           Discipline  \\\n",
       "0  2012   London  Wrestling  Wrestling Freestyle   \n",
       "1  1924    Paris   Football             Football   \n",
       "2  1988    Seoul   Handball             Handball   \n",
       "3  2004   Athens   Handball             Handball   \n",
       "4  1996  Atlanta   Aquatics             Swimming   \n",
       "\n",
       "                        Athlete Country Gender                Event   Medal  \n",
       "0  EBRAHIM, Karam Mohamed Gaber     EGY    Men             Wg 84 KG  Silver  \n",
       "1                     SOMMA, P.     URU    Men             Football    Gold  \n",
       "2             TURCHINA, Zinaida     URS  Women             Handball  Bronze  \n",
       "3            BROEDSGAARD, Karen     DEN  Women             Handball    Gold  \n",
       "4                      HAN, Xue     CHN  Women  4X100M Medley Relay  Bronze  "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shuffled= df.sample(frac=1,ignore_index=True)\n",
    "shuffled.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "867dbea5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.131428Z",
     "start_time": "2022-03-10T14:55:50.121977Z"
    }
   },
   "outputs": [],
   "source": [
    "sys_sample = shuffled.iloc[::interval].reset_index(drop=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "04376aae",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.151669Z",
     "start_time": "2022-03-10T14:55:50.135017Z"
    },
    "scrolled": true
   },
   "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",
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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>Year</th>\n",
       "      <th>City</th>\n",
       "      <th>Sport</th>\n",
       "      <th>Discipline</th>\n",
       "      <th>Athlete</th>\n",
       "      <th>Country</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Event</th>\n",
       "      <th>Medal</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2012</td>\n",
       "      <td>London</td>\n",
       "      <td>Wrestling</td>\n",
       "      <td>Wrestling Freestyle</td>\n",
       "      <td>EBRAHIM, Karam Mohamed Gaber</td>\n",
       "      <td>EGY</td>\n",
       "      <td>Men</td>\n",
       "      <td>Wg 84 KG</td>\n",
       "      <td>Silver</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1928</td>\n",
       "      <td>Amsterdam</td>\n",
       "      <td>Football</td>\n",
       "      <td>Football</td>\n",
       "      <td>BOSIO, Angel</td>\n",
       "      <td>ARG</td>\n",
       "      <td>Men</td>\n",
       "      <td>Football</td>\n",
       "      <td>Silver</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2012</td>\n",
       "      <td>London</td>\n",
       "      <td>Aquatics</td>\n",
       "      <td>Water Polo</td>\n",
       "      <td>SMITH, Sophie</td>\n",
       "      <td>AUS</td>\n",
       "      <td>Women</td>\n",
       "      <td>Water Polo</td>\n",
       "      <td>Bronze</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1996</td>\n",
       "      <td>Atlanta</td>\n",
       "      <td>Handball</td>\n",
       "      <td>Handball</td>\n",
       "      <td>MATYAS, Auguszta</td>\n",
       "      <td>HUN</td>\n",
       "      <td>Women</td>\n",
       "      <td>Handball</td>\n",
       "      <td>Bronze</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1988</td>\n",
       "      <td>Seoul</td>\n",
       "      <td>Gymnastics</td>\n",
       "      <td>Artistic G.</td>\n",
       "      <td>LIOUKINE, Valeri</td>\n",
       "      <td>URS</td>\n",
       "      <td>Men</td>\n",
       "      <td>Parallel Bars</td>\n",
       "      <td>Silver</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Year       City       Sport           Discipline  \\\n",
       "0  2012     London   Wrestling  Wrestling Freestyle   \n",
       "1  1928  Amsterdam    Football             Football   \n",
       "2  2012     London    Aquatics           Water Polo   \n",
       "3  1996    Atlanta    Handball             Handball   \n",
       "4  1988      Seoul  Gymnastics          Artistic G.   \n",
       "\n",
       "                        Athlete Country Gender          Event   Medal  \n",
       "0  EBRAHIM, Karam Mohamed Gaber     EGY    Men       Wg 84 KG  Silver  \n",
       "1                  BOSIO, Angel     ARG    Men       Football  Silver  \n",
       "2                 SMITH, Sophie     AUS  Women     Water Polo  Bronze  \n",
       "3              MATYAS, Auguszta     HUN  Women       Handball  Bronze  \n",
       "4              LIOUKINE, Valeri     URS    Men  Parallel Bars  Silver  "
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys_sample.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b4fb875",
   "metadata": {},
   "source": [
    "\n",
    "##### working on the dataset\n",
    "\n",
    "\n",
    "$~$\n",
    "\n",
    "once we have the systematic sample, let's work a little with the data so we can make comparisons. \n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "dd201379",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.173561Z",
     "start_time": "2022-03-10T14:55:50.154355Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "        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>count</th>\n",
       "      <th>proportion</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Country</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>USA</th>\n",
       "      <td>150</td>\n",
       "      <td>0.149105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GBR</th>\n",
       "      <td>75</td>\n",
       "      <td>0.074553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>URS</th>\n",
       "      <td>47</td>\n",
       "      <td>0.046720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AUS</th>\n",
       "      <td>47</td>\n",
       "      <td>0.046720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ITA</th>\n",
       "      <td>47</td>\n",
       "      <td>0.046720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GER</th>\n",
       "      <td>44</td>\n",
       "      <td>0.043738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HUN</th>\n",
       "      <td>36</td>\n",
       "      <td>0.035785</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>JPN</th>\n",
       "      <td>32</td>\n",
       "      <td>0.031809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SWE</th>\n",
       "      <td>32</td>\n",
       "      <td>0.031809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FRA</th>\n",
       "      <td>32</td>\n",
       "      <td>0.031809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NED</th>\n",
       "      <td>30</td>\n",
       "      <td>0.029821</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GDR</th>\n",
       "      <td>26</td>\n",
       "      <td>0.025845</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHN</th>\n",
       "      <td>24</td>\n",
       "      <td>0.023857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FRG</th>\n",
       "      <td>21</td>\n",
       "      <td>0.020875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RUS</th>\n",
       "      <td>21</td>\n",
       "      <td>0.020875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>POL</th>\n",
       "      <td>20</td>\n",
       "      <td>0.019881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KOR</th>\n",
       "      <td>18</td>\n",
       "      <td>0.017893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BRA</th>\n",
       "      <td>18</td>\n",
       "      <td>0.017893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ROU</th>\n",
       "      <td>17</td>\n",
       "      <td>0.016899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FIN</th>\n",
       "      <td>17</td>\n",
       "      <td>0.016899</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         count  proportion\n",
       "Country                   \n",
       "USA        150    0.149105\n",
       "GBR         75    0.074553\n",
       "URS         47    0.046720\n",
       "AUS         47    0.046720\n",
       "ITA         47    0.046720\n",
       "GER         44    0.043738\n",
       "HUN         36    0.035785\n",
       "JPN         32    0.031809\n",
       "SWE         32    0.031809\n",
       "FRA         32    0.031809\n",
       "NED         30    0.029821\n",
       "GDR         26    0.025845\n",
       "CHN         24    0.023857\n",
       "FRG         21    0.020875\n",
       "RUS         21    0.020875\n",
       "POL         20    0.019881\n",
       "KOR         18    0.017893\n",
       "BRA         18    0.017893\n",
       "ROU         17    0.016899\n",
       "FIN         17    0.016899"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "medal_count_sys_sample = sys_sample.groupby(\"Country\")[\"Medal\"]\\\n",
    "                    .agg([\"count\"]).sort_values(by=\"count\", ascending=False)\n",
    "\n",
    "medal_count_sys_sample[\"proportion\"]= medal_count_sys_sample[\"count\"]\\\n",
    "                                / medal_count_sys_sample[\"count\"].sum()\n",
    "\n",
    "medal_count_sys_sample.head(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1529ce22",
   "metadata": {},
   "source": [
    "\n",
    "##### compare population vs systematic sample\n",
    "\n",
    "_____\n",
    "$~$\n",
    "\n",
    "now we can compare our population with the systematic sample\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "3e2d77a1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.193308Z",
     "start_time": "2022-03-10T14:55:50.176185Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count_total</th>\n",
       "      <th>proportion_total</th>\n",
       "      <th>count_sys_sample</th>\n",
       "      <th>proportion_sys_sample</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Country</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>USA</th>\n",
       "      <td>4585</td>\n",
       "      <td>0.147139</td>\n",
       "      <td>150</td>\n",
       "      <td>0.149105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>URS</th>\n",
       "      <td>2049</td>\n",
       "      <td>0.065755</td>\n",
       "      <td>47</td>\n",
       "      <td>0.046720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GBR</th>\n",
       "      <td>1720</td>\n",
       "      <td>0.055197</td>\n",
       "      <td>75</td>\n",
       "      <td>0.074553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FRA</th>\n",
       "      <td>1396</td>\n",
       "      <td>0.044800</td>\n",
       "      <td>32</td>\n",
       "      <td>0.031809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GER</th>\n",
       "      <td>1305</td>\n",
       "      <td>0.041879</td>\n",
       "      <td>44</td>\n",
       "      <td>0.043738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ITA</th>\n",
       "      <td>1296</td>\n",
       "      <td>0.041590</td>\n",
       "      <td>47</td>\n",
       "      <td>0.046720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AUS</th>\n",
       "      <td>1189</td>\n",
       "      <td>0.038157</td>\n",
       "      <td>47</td>\n",
       "      <td>0.046720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HUN</th>\n",
       "      <td>1079</td>\n",
       "      <td>0.034627</td>\n",
       "      <td>36</td>\n",
       "      <td>0.035785</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SWE</th>\n",
       "      <td>1044</td>\n",
       "      <td>0.033503</td>\n",
       "      <td>32</td>\n",
       "      <td>0.031809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NED</th>\n",
       "      <td>851</td>\n",
       "      <td>0.027310</td>\n",
       "      <td>30</td>\n",
       "      <td>0.029821</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GDR</th>\n",
       "      <td>825</td>\n",
       "      <td>0.026475</td>\n",
       "      <td>26</td>\n",
       "      <td>0.025845</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHN</th>\n",
       "      <td>807</td>\n",
       "      <td>0.025898</td>\n",
       "      <td>24</td>\n",
       "      <td>0.023857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>JPN</th>\n",
       "      <td>788</td>\n",
       "      <td>0.025288</td>\n",
       "      <td>32</td>\n",
       "      <td>0.031809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RUS</th>\n",
       "      <td>768</td>\n",
       "      <td>0.024646</td>\n",
       "      <td>21</td>\n",
       "      <td>0.020875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CAN</th>\n",
       "      <td>649</td>\n",
       "      <td>0.020827</td>\n",
       "      <td>17</td>\n",
       "      <td>0.016899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ROU</th>\n",
       "      <td>640</td>\n",
       "      <td>0.020538</td>\n",
       "      <td>17</td>\n",
       "      <td>0.016899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOR</th>\n",
       "      <td>554</td>\n",
       "      <td>0.017779</td>\n",
       "      <td>13</td>\n",
       "      <td>0.012922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KOR</th>\n",
       "      <td>529</td>\n",
       "      <td>0.016976</td>\n",
       "      <td>18</td>\n",
       "      <td>0.017893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>POL</th>\n",
       "      <td>511</td>\n",
       "      <td>0.016399</td>\n",
       "      <td>20</td>\n",
       "      <td>0.019881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DEN</th>\n",
       "      <td>507</td>\n",
       "      <td>0.016270</td>\n",
       "      <td>15</td>\n",
       "      <td>0.014911</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         count_total  proportion_total  count_sys_sample  \\\n",
       "Country                                                    \n",
       "USA             4585          0.147139               150   \n",
       "URS             2049          0.065755                47   \n",
       "GBR             1720          0.055197                75   \n",
       "FRA             1396          0.044800                32   \n",
       "GER             1305          0.041879                44   \n",
       "ITA             1296          0.041590                47   \n",
       "AUS             1189          0.038157                47   \n",
       "HUN             1079          0.034627                36   \n",
       "SWE             1044          0.033503                32   \n",
       "NED              851          0.027310                30   \n",
       "GDR              825          0.026475                26   \n",
       "CHN              807          0.025898                24   \n",
       "JPN              788          0.025288                32   \n",
       "RUS              768          0.024646                21   \n",
       "CAN              649          0.020827                17   \n",
       "ROU              640          0.020538                17   \n",
       "NOR              554          0.017779                13   \n",
       "KOR              529          0.016976                18   \n",
       "POL              511          0.016399                20   \n",
       "DEN              507          0.016270                15   \n",
       "\n",
       "         proportion_sys_sample  \n",
       "Country                         \n",
       "USA                   0.149105  \n",
       "URS                   0.046720  \n",
       "GBR                   0.074553  \n",
       "FRA                   0.031809  \n",
       "GER                   0.043738  \n",
       "ITA                   0.046720  \n",
       "AUS                   0.046720  \n",
       "HUN                   0.035785  \n",
       "SWE                   0.031809  \n",
       "NED                   0.029821  \n",
       "GDR                   0.025845  \n",
       "CHN                   0.023857  \n",
       "JPN                   0.031809  \n",
       "RUS                   0.020875  \n",
       "CAN                   0.016899  \n",
       "ROU                   0.016899  \n",
       "NOR                   0.012922  \n",
       "KOR                   0.017893  \n",
       "POL                   0.019881  \n",
       "DEN                   0.014911  "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "medal_count.merge(medal_count_sys_sample, left_on='Country', right_on='Country', \n",
    "                  suffixes=('_total', '_sys_sample')).head(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98f7847b",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "we can also see the simple sample, the systematic sample together \n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "acd19686",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.318709Z",
     "start_time": "2022-03-10T14:55:50.203878Z"
    }
   },
   "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>pop_proportion</th>\n",
       "      <th>simple_sample_proportion</th>\n",
       "      <th>sys_sample_proportion</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>USA</th>\n",
       "      <td>0.147139</td>\n",
       "      <td>0.135</td>\n",
       "      <td>0.149105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>URS</th>\n",
       "      <td>0.065755</td>\n",
       "      <td>0.075</td>\n",
       "      <td>0.046720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GBR</th>\n",
       "      <td>0.055197</td>\n",
       "      <td>0.057</td>\n",
       "      <td>0.074553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FRA</th>\n",
       "      <td>0.044800</td>\n",
       "      <td>0.052</td>\n",
       "      <td>0.031809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GER</th>\n",
       "      <td>0.041879</td>\n",
       "      <td>0.041</td>\n",
       "      <td>0.043738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ITA</th>\n",
       "      <td>0.041590</td>\n",
       "      <td>0.056</td>\n",
       "      <td>0.046720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AUS</th>\n",
       "      <td>0.038157</td>\n",
       "      <td>0.038</td>\n",
       "      <td>0.046720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HUN</th>\n",
       "      <td>0.034627</td>\n",
       "      <td>0.038</td>\n",
       "      <td>0.035785</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SWE</th>\n",
       "      <td>0.033503</td>\n",
       "      <td>0.030</td>\n",
       "      <td>0.031809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NED</th>\n",
       "      <td>0.027310</td>\n",
       "      <td>0.031</td>\n",
       "      <td>0.029821</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GDR</th>\n",
       "      <td>0.026475</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.025845</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHN</th>\n",
       "      <td>0.025898</td>\n",
       "      <td>0.023</td>\n",
       "      <td>0.023857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>JPN</th>\n",
       "      <td>0.025288</td>\n",
       "      <td>0.029</td>\n",
       "      <td>0.031809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RUS</th>\n",
       "      <td>0.024646</td>\n",
       "      <td>0.034</td>\n",
       "      <td>0.020875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CAN</th>\n",
       "      <td>0.020827</td>\n",
       "      <td>0.020</td>\n",
       "      <td>0.016899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ROU</th>\n",
       "      <td>0.020538</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.016899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOR</th>\n",
       "      <td>0.017779</td>\n",
       "      <td>0.017</td>\n",
       "      <td>0.012922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KOR</th>\n",
       "      <td>0.016976</td>\n",
       "      <td>0.018</td>\n",
       "      <td>0.017893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>POL</th>\n",
       "      <td>0.016399</td>\n",
       "      <td>0.012</td>\n",
       "      <td>0.019881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DEN</th>\n",
       "      <td>0.016270</td>\n",
       "      <td>0.017</td>\n",
       "      <td>0.014911</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     pop_proportion  simple_sample_proportion  sys_sample_proportion\n",
       "USA        0.147139                     0.135               0.149105\n",
       "URS        0.065755                     0.075               0.046720\n",
       "GBR        0.055197                     0.057               0.074553\n",
       "FRA        0.044800                     0.052               0.031809\n",
       "GER        0.041879                     0.041               0.043738\n",
       "ITA        0.041590                     0.056               0.046720\n",
       "AUS        0.038157                     0.038               0.046720\n",
       "HUN        0.034627                     0.038               0.035785\n",
       "SWE        0.033503                     0.030               0.031809\n",
       "NED        0.027310                     0.031               0.029821\n",
       "GDR        0.026475                     0.016               0.025845\n",
       "CHN        0.025898                     0.023               0.023857\n",
       "JPN        0.025288                     0.029               0.031809\n",
       "RUS        0.024646                     0.034               0.020875\n",
       "CAN        0.020827                     0.020               0.016899\n",
       "ROU        0.020538                     0.016               0.016899\n",
       "NOR        0.017779                     0.017               0.012922\n",
       "KOR        0.016976                     0.018               0.017893\n",
       "POL        0.016399                     0.012               0.019881\n",
       "DEN        0.016270                     0.017               0.014911"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = df[\"Country\"].value_counts(normalize=True).to_frame('pop_proportion')\n",
    "df2 = df_sample[\"Country\"].value_counts(normalize=True).to_frame('simple_sample_proportion')\n",
    "df3 = sys_sample [\"Country\"].value_counts(normalize=True).to_frame('sys_sample_proportion')\n",
    "\n",
    "pd.concat([df1, df2, df3],axis=1).head(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "4b7cfb98",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.812318Z",
     "start_time": "2022-03-10T14:55:50.321002Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axes = plt.subplots(1,3, figsize=(15,5))\n",
    "\n",
    "medal_count[\"proportion\"].hist(bins=np.arange(0,0.15,0.01),ax=axes[0])\n",
    "\n",
    "axes[0].spines['top'].set_visible(False)\n",
    "axes[0].spines['right'].set_visible(False)\n",
    "axes[0].set_title(\"fig 1. histogram plot: population \",fontsize=8)\n",
    "\n",
    "\n",
    "medal_count_sample[\"proportion\"].hist(bins=np.arange(0,0.15,0.01),ax=axes[1])\n",
    "axes[1].set_title(\"fig 2. histogram plot: simple random sample\",fontsize=8)\n",
    "\n",
    "axes[1].spines['top'].set_visible(False)\n",
    "axes[1].spines['right'].set_visible(False)\n",
    "\n",
    "medal_count_sys_sample[\"proportion\"].hist(bins=np.arange(0,0.15,0.01),ax=axes[2])\n",
    "axes[2].set_title(\"fig 3. histogram plot: Systematic random sample\",fontsize=8)\n",
    "\n",
    "axes[2].spines['top'].set_visible(False)\n",
    "axes[2].spines['right'].set_visible(False)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "214112c9",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "####  stratified sample and SMOTE (Synthetic Minority Oversampling Technique).\n",
    "\n",
    "$~$\n",
    "\n",
    "Continue with the sports theme data set and generate a stratified sample and a sample using SMOTE (Synthetic Minority Oversampling Technique):\n",
    "$~$\n",
    "___\n",
    "$~$\n",
    "\n",
    "#####  stratified sample\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b517eae5",
   "metadata": {},
   "source": [
    "\n",
    "$~$\n",
    "\n",
    "\n",
    "To make it easier to think about sampling subgroups, let's limit our analysis to these ten countries. \n",
    "\n",
    "\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "8c221c5a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.822846Z",
     "start_time": "2022-03-10T14:55:50.814669Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "USA    4585\n",
       "URS    2049\n",
       "GBR    1720\n",
       "FRA    1396\n",
       "GER    1305\n",
       "ITA    1296\n",
       "AUS    1189\n",
       "HUN    1079\n",
       "SWE    1044\n",
       "NED     851\n",
       "Name: Country, dtype: int64"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top_counts = df[\"Country\"].value_counts()\n",
    "top_counts.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "045e2fa1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.830563Z",
     "start_time": "2022-03-10T14:55:50.825072Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['USA', 'URS', 'GBR', 'FRA', 'GER', 'ITA', 'AUS', 'HUN', 'SWE', 'NED'], dtype='object')"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top_counts_countries = top_counts.head(10).index\n",
    "\n",
    "top_counts_countries\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71a182ec",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "We can use the dot-isin method to filter the population and only return the rows corresponding to these ten countries.\n",
    "\n",
    "$~$\n",
    "\n",
    "This filtered dataset is stored as countries_rating_top. \n",
    "\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "434a1d63",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.839904Z",
     "start_time": "2022-03-10T14:55:50.832721Z"
    }
   },
   "outputs": [],
   "source": [
    "top_counts_subset = df[\"Country\"].isin(top_counts_countries)\n",
    "\n",
    "countries_rating_top=df[top_counts_subset]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "8fa506d7",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.861914Z",
     "start_time": "2022-03-10T14:55:50.842891Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>City</th>\n",
       "      <th>Sport</th>\n",
       "      <th>Discipline</th>\n",
       "      <th>Athlete</th>\n",
       "      <th>Country</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1896</td>\n",
       "      <td>Athens</td>\n",
       "      <td>Aquatics</td>\n",
       "      <td>Swimming</td>\n",
       "      <td>HAJOS, Alfred</td>\n",
       "      <td>HUN</td>\n",
       "      <td>Men</td>\n",
       "      <td>100M Freestyle</td>\n",
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       "    <tr>\n",
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       "      <td>1896</td>\n",
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       "      <td>Aquatics</td>\n",
       "      <td>Swimming</td>\n",
       "      <td>HAJOS, Alfred</td>\n",
       "      <td>HUN</td>\n",
       "      <td>Men</td>\n",
       "      <td>1200M Freestyle</td>\n",
       "      <td>Gold</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1896</td>\n",
       "      <td>Athens</td>\n",
       "      <td>Athletics</td>\n",
       "      <td>Athletics</td>\n",
       "      <td>LANE, Francis</td>\n",
       "      <td>USA</td>\n",
       "      <td>Men</td>\n",
       "      <td>100M</td>\n",
       "      <td>Bronze</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1896</td>\n",
       "      <td>Athens</td>\n",
       "      <td>Athletics</td>\n",
       "      <td>Athletics</td>\n",
       "      <td>SZOKOLYI, Alajos</td>\n",
       "      <td>HUN</td>\n",
       "      <td>Men</td>\n",
       "      <td>100M</td>\n",
       "      <td>Bronze</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1896</td>\n",
       "      <td>Athens</td>\n",
       "      <td>Athletics</td>\n",
       "      <td>Athletics</td>\n",
       "      <td>BURKE, Thomas</td>\n",
       "      <td>USA</td>\n",
       "      <td>Men</td>\n",
       "      <td>100M</td>\n",
       "      <td>Gold</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16509</th>\n",
       "      <td>2012</td>\n",
       "      <td>London</td>\n",
       "      <td>Wrestling</td>\n",
       "      <td>Wrestling Freestyle</td>\n",
       "      <td>EUREN, Johan</td>\n",
       "      <td>SWE</td>\n",
       "      <td>Men</td>\n",
       "      <td>Wg 120 KG</td>\n",
       "      <td>Bronze</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16510</th>\n",
       "      <td>2012</td>\n",
       "      <td>London</td>\n",
       "      <td>Wrestling</td>\n",
       "      <td>Wrestling Freestyle</td>\n",
       "      <td>MODOS, Peter</td>\n",
       "      <td>HUN</td>\n",
       "      <td>Men</td>\n",
       "      <td>Wg 55 KG</td>\n",
       "      <td>Bronze</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16511</th>\n",
       "      <td>2012</td>\n",
       "      <td>London</td>\n",
       "      <td>Wrestling</td>\n",
       "      <td>Wrestling Freestyle</td>\n",
       "      <td>LORINCZ, Tamas</td>\n",
       "      <td>HUN</td>\n",
       "      <td>Men</td>\n",
       "      <td>Wg 66 KG</td>\n",
       "      <td>Silver</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16512</th>\n",
       "      <td>2012</td>\n",
       "      <td>London</td>\n",
       "      <td>Wrestling</td>\n",
       "      <td>Wrestling Freestyle</td>\n",
       "      <td>GUENOT, Steeve</td>\n",
       "      <td>FRA</td>\n",
       "      <td>Men</td>\n",
       "      <td>Wg 66 KG</td>\n",
       "      <td>Bronze</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16513</th>\n",
       "      <td>2012</td>\n",
       "      <td>London</td>\n",
       "      <td>Wrestling</td>\n",
       "      <td>Wrestling Freestyle</td>\n",
       "      <td>LIDBERG, Jimmy</td>\n",
       "      <td>SWE</td>\n",
       "      <td>Men</td>\n",
       "      <td>Wg 96 KG</td>\n",
       "      <td>Bronze</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>16514 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Year    City      Sport           Discipline           Athlete Country  \\\n",
       "0      1896  Athens   Aquatics             Swimming     HAJOS, Alfred     HUN   \n",
       "1      1896  Athens   Aquatics             Swimming     HAJOS, Alfred     HUN   \n",
       "2      1896  Athens  Athletics            Athletics     LANE, Francis     USA   \n",
       "3      1896  Athens  Athletics            Athletics  SZOKOLYI, Alajos     HUN   \n",
       "4      1896  Athens  Athletics            Athletics     BURKE, Thomas     USA   \n",
       "...     ...     ...        ...                  ...               ...     ...   \n",
       "16509  2012  London  Wrestling  Wrestling Freestyle      EUREN, Johan     SWE   \n",
       "16510  2012  London  Wrestling  Wrestling Freestyle      MODOS, Peter     HUN   \n",
       "16511  2012  London  Wrestling  Wrestling Freestyle    LORINCZ, Tamas     HUN   \n",
       "16512  2012  London  Wrestling  Wrestling Freestyle    GUENOT, Steeve     FRA   \n",
       "16513  2012  London  Wrestling  Wrestling Freestyle    LIDBERG, Jimmy     SWE   \n",
       "\n",
       "      Gender            Event   Medal  \n",
       "0        Men   100M Freestyle    Gold  \n",
       "1        Men  1200M Freestyle    Gold  \n",
       "2        Men             100M  Bronze  \n",
       "3        Men             100M  Bronze  \n",
       "4        Men             100M    Gold  \n",
       "...      ...              ...     ...  \n",
       "16509    Men        Wg 120 KG  Bronze  \n",
       "16510    Men         Wg 55 KG  Bronze  \n",
       "16511    Men         Wg 66 KG  Silver  \n",
       "16512    Men         Wg 66 KG  Bronze  \n",
       "16513    Men         Wg 96 KG  Bronze  \n",
       "\n",
       "[16514 rows x 9 columns]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "countries_rating_top.reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe7bbb34",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "Let's see how many medals each country has:\n",
    "\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "0e08acc1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.875794Z",
     "start_time": "2022-03-10T14:55:50.864779Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "USA    0.277643\n",
       "URS    0.124077\n",
       "GBR    0.104154\n",
       "FRA    0.084534\n",
       "GER    0.079024\n",
       "ITA    0.078479\n",
       "AUS    0.072000\n",
       "HUN    0.065339\n",
       "SWE    0.063219\n",
       "NED    0.051532\n",
       "Name: Country, dtype: float64"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "countries_rating_top[\"Country\"].value_counts(normalize=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70b32d0f",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "Let's take a ten percent simple random sample of the dataset using dot-sample with frac set to zero-point-one. We also set the random_state argument to ensure reproducibility. \n",
    "\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "aff0fd83",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.896067Z",
     "start_time": "2022-03-10T14:55:50.878430Z"
    }
   },
   "outputs": [],
   "source": [
    "country_rating_samp = countries_rating_top.groupby(\"Country\")\\\n",
    "                                            .sample(frac=0.1,random_state=2021)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eee29803",
   "metadata": {},
   "source": [
    "\n",
    "$~$\n",
    "\n",
    "By grouping (by country) then sampling, the size of each group in the sample is representative of the size of the sample in the population.\n",
    "\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "577a0b48",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.915152Z",
     "start_time": "2022-03-10T14:55:50.898379Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "    }\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>City</th>\n",
       "      <th>Sport</th>\n",
       "      <th>Discipline</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1996</td>\n",
       "      <td>Atlanta</td>\n",
       "      <td>Softball</td>\n",
       "      <td>Softball</td>\n",
       "      <td>BROWN, Joanne</td>\n",
       "      <td>AUS</td>\n",
       "      <td>Women</td>\n",
       "      <td>Softball</td>\n",
       "      <td>Bronze</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1988</td>\n",
       "      <td>Seoul</td>\n",
       "      <td>Cycling</td>\n",
       "      <td>Cycling Track</td>\n",
       "      <td>MCCARNEY, Wayne</td>\n",
       "      <td>AUS</td>\n",
       "      <td>Men</td>\n",
       "      <td>Team Pursuit (4000M)</td>\n",
       "      <td>Bronze</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2000</td>\n",
       "      <td>Sydney</td>\n",
       "      <td>Aquatics</td>\n",
       "      <td>Swimming</td>\n",
       "      <td>THORPE, Ian</td>\n",
       "      <td>AUS</td>\n",
       "      <td>Men</td>\n",
       "      <td>4X100M Freestyle Relay</td>\n",
       "      <td>Gold</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1996</td>\n",
       "      <td>Atlanta</td>\n",
       "      <td>Aquatics</td>\n",
       "      <td>Swimming</td>\n",
       "      <td>KOWALSKI, Daniel</td>\n",
       "      <td>AUS</td>\n",
       "      <td>Men</td>\n",
       "      <td>1500M Freestyle</td>\n",
       "      <td>Silver</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1960</td>\n",
       "      <td>Rome</td>\n",
       "      <td>Boxing</td>\n",
       "      <td>Boxing</td>\n",
       "      <td>TAYLOR, Oliver</td>\n",
       "      <td>AUS</td>\n",
       "      <td>Men</td>\n",
       "      <td>51 - 54KG (Bantamweight)</td>\n",
       "      <td>Bronze</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1646</th>\n",
       "      <td>1988</td>\n",
       "      <td>Seoul</td>\n",
       "      <td>Sailing</td>\n",
       "      <td>Sailing</td>\n",
       "      <td>JEWELL, Lynne M.</td>\n",
       "      <td>USA</td>\n",
       "      <td>Women</td>\n",
       "      <td>470 - Two Person Dinghy</td>\n",
       "      <td>Gold</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1647</th>\n",
       "      <td>1920</td>\n",
       "      <td>Antwerp</td>\n",
       "      <td>Aquatics</td>\n",
       "      <td>Swimming</td>\n",
       "      <td>KAHANAMOKU, Duke Paoa</td>\n",
       "      <td>USA</td>\n",
       "      <td>Men</td>\n",
       "      <td>4X200M Freestyle Relay</td>\n",
       "      <td>Gold</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1648</th>\n",
       "      <td>2004</td>\n",
       "      <td>Athens</td>\n",
       "      <td>Aquatics</td>\n",
       "      <td>Swimming</td>\n",
       "      <td>KIRK, Tara</td>\n",
       "      <td>USA</td>\n",
       "      <td>Women</td>\n",
       "      <td>4X100M Medley Relay</td>\n",
       "      <td>Silver</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1649</th>\n",
       "      <td>1988</td>\n",
       "      <td>Seoul</td>\n",
       "      <td>Aquatics</td>\n",
       "      <td>Swimming</td>\n",
       "      <td>BIONDI, Matthew</td>\n",
       "      <td>USA</td>\n",
       "      <td>Men</td>\n",
       "      <td>4X100M Medley Relay</td>\n",
       "      <td>Gold</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1650</th>\n",
       "      <td>1996</td>\n",
       "      <td>Atlanta</td>\n",
       "      <td>Aquatics</td>\n",
       "      <td>Swimming</td>\n",
       "      <td>OLSEN, Jon</td>\n",
       "      <td>USA</td>\n",
       "      <td>Men</td>\n",
       "      <td>4X100M Freestyle Relay</td>\n",
       "      <td>Gold</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1651 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Year     City     Sport     Discipline                Athlete Country  \\\n",
       "0     1996  Atlanta  Softball       Softball          BROWN, Joanne     AUS   \n",
       "1     1988    Seoul   Cycling  Cycling Track        MCCARNEY, Wayne     AUS   \n",
       "2     2000   Sydney  Aquatics       Swimming            THORPE, Ian     AUS   \n",
       "3     1996  Atlanta  Aquatics       Swimming       KOWALSKI, Daniel     AUS   \n",
       "4     1960     Rome    Boxing         Boxing         TAYLOR, Oliver     AUS   \n",
       "...    ...      ...       ...            ...                    ...     ...   \n",
       "1646  1988    Seoul   Sailing        Sailing       JEWELL, Lynne M.     USA   \n",
       "1647  1920  Antwerp  Aquatics       Swimming  KAHANAMOKU, Duke Paoa     USA   \n",
       "1648  2004   Athens  Aquatics       Swimming             KIRK, Tara     USA   \n",
       "1649  1988    Seoul  Aquatics       Swimming        BIONDI, Matthew     USA   \n",
       "1650  1996  Atlanta  Aquatics       Swimming             OLSEN, Jon     USA   \n",
       "\n",
       "     Gender                     Event   Medal  \n",
       "0     Women                  Softball  Bronze  \n",
       "1       Men      Team Pursuit (4000M)  Bronze  \n",
       "2       Men    4X100M Freestyle Relay    Gold  \n",
       "3       Men           1500M Freestyle  Silver  \n",
       "4       Men  51 - 54KG (Bantamweight)  Bronze  \n",
       "...     ...                       ...     ...  \n",
       "1646  Women   470 - Two Person Dinghy    Gold  \n",
       "1647    Men    4X200M Freestyle Relay    Gold  \n",
       "1648  Women       4X100M Medley Relay  Silver  \n",
       "1649    Men       4X100M Medley Relay    Gold  \n",
       "1650    Men    4X100M Freestyle Relay    Gold  \n",
       "\n",
       "[1651 rows x 9 columns]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "country_rating_samp.reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fcb5832",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "To make comparisons easier, as we do before, we set normalize to True to convert the counts into a proportion, which shows what proportion of medals in the sample came from each country. \n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "95bd01f6",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.926799Z",
     "start_time": "2022-03-10T14:55:50.917543Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "USA    0.277408\n",
       "URS    0.124167\n",
       "GBR    0.104179\n",
       "FRA    0.084797\n",
       "GER    0.078740\n",
       "ITA    0.078740\n",
       "AUS    0.072078\n",
       "HUN    0.065415\n",
       "SWE    0.062992\n",
       "NED    0.051484\n",
       "Name: Country, dtype: float64"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "country_rating_samp[\"Country\"].value_counts(normalize=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09480b54",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T13:34:57.681916Z",
     "start_time": "2022-03-10T13:34:57.677897Z"
    }
   },
   "source": [
    "$~$\n",
    "\n",
    "now we can compare our population with the stratified sample\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "a5a6962a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.944212Z",
     "start_time": "2022-03-10T14:55:50.930829Z"
    }
   },
   "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>pop_proportion</th>\n",
       "      <th>stat_proportion</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>USA</th>\n",
       "      <td>0.277643</td>\n",
       "      <td>0.277408</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>URS</th>\n",
       "      <td>0.124077</td>\n",
       "      <td>0.124167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GBR</th>\n",
       "      <td>0.104154</td>\n",
       "      <td>0.104179</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FRA</th>\n",
       "      <td>0.084534</td>\n",
       "      <td>0.084797</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GER</th>\n",
       "      <td>0.079024</td>\n",
       "      <td>0.078740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ITA</th>\n",
       "      <td>0.078479</td>\n",
       "      <td>0.078740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AUS</th>\n",
       "      <td>0.072000</td>\n",
       "      <td>0.072078</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HUN</th>\n",
       "      <td>0.065339</td>\n",
       "      <td>0.065415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SWE</th>\n",
       "      <td>0.063219</td>\n",
       "      <td>0.062992</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NED</th>\n",
       "      <td>0.051532</td>\n",
       "      <td>0.051484</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     pop_proportion  stat_proportion\n",
       "USA        0.277643         0.277408\n",
       "URS        0.124077         0.124167\n",
       "GBR        0.104154         0.104179\n",
       "FRA        0.084534         0.084797\n",
       "GER        0.079024         0.078740\n",
       "ITA        0.078479         0.078740\n",
       "AUS        0.072000         0.072078\n",
       "HUN        0.065339         0.065415\n",
       "SWE        0.063219         0.062992\n",
       "NED        0.051532         0.051484"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = countries_rating_top[\"Country\"].value_counts(normalize=True).to_frame('pop_proportion')\n",
    "df2 = country_rating_samp[\"Country\"].value_counts(normalize=True).to_frame('stat_proportion')\n",
    "\n",
    "pd.concat([df1, df2],axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ac06476",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "**we see that the sample proportion is more similar to the population proportion**\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcf43d89",
   "metadata": {},
   "source": [
    "___\n",
    "$~$\n",
    "\n",
    "#####  second method of stratified sample\n",
    "\n",
    "$~$\n",
    "\n",
    "now we are going to use a second method to obtain stratified samples. Here we will use the library: \"sklearn.model_selection.train_test_split\"\n",
    "which will allow us to do what we did before, but much faster.\n",
    "\n",
    "$~$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "93281c67",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.967418Z",
     "start_time": "2022-03-10T14:55:50.946407Z"
    }
   },
   "outputs": [],
   "source": [
    "Xtrain, Xtest = train_test_split(countries_rating_top, test_size=0.10, stratify=countries_rating_top['Country'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "1036353e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.984338Z",
     "start_time": "2022-03-10T14:55:50.970188Z"
    }
   },
   "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>Year</th>\n",
       "      <th>City</th>\n",
       "      <th>Sport</th>\n",
       "      <th>Discipline</th>\n",
       "      <th>Athlete</th>\n",
       "      <th>Country</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Event</th>\n",
       "      <th>Medal</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>16950</th>\n",
       "      <td>1984</td>\n",
       "      <td>Los Angeles</td>\n",
       "      <td>Athletics</td>\n",
       "      <td>Athletics</td>\n",
       "      <td>CONLEY, Mike</td>\n",
       "      <td>USA</td>\n",
       "      <td>Men</td>\n",
       "      <td>Triple Jump</td>\n",
       "      <td>Silver</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>195</th>\n",
       "      <td>1900</td>\n",
       "      <td>Paris</td>\n",
       "      <td>Aquatics</td>\n",
       "      <td>Water polo</td>\n",
       "      <td>PESLOY</td>\n",
       "      <td>FRA</td>\n",
       "      <td>Men</td>\n",
       "      <td>Water Polo</td>\n",
       "      <td>Bronze</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8599</th>\n",
       "      <td>1952</td>\n",
       "      <td>Helsinki</td>\n",
       "      <td>Gymnastics</td>\n",
       "      <td>Artistic G.</td>\n",
       "      <td>KALINCHUK, Ekaterina</td>\n",
       "      <td>URS</td>\n",
       "      <td>Women</td>\n",
       "      <td>Team Competition</td>\n",
       "      <td>Gold</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6435</th>\n",
       "      <td>1936</td>\n",
       "      <td>Berlin</td>\n",
       "      <td>Athletics</td>\n",
       "      <td>Athletics</td>\n",
       "      <td>BECCALI, Luigi</td>\n",
       "      <td>ITA</td>\n",
       "      <td>Men</td>\n",
       "      <td>1500M</td>\n",
       "      <td>Bronze</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3923</th>\n",
       "      <td>1920</td>\n",
       "      <td>Antwerp</td>\n",
       "      <td>Shooting</td>\n",
       "      <td>Shooting</td>\n",
       "      <td>BRACKEN, Raymond</td>\n",
       "      <td>USA</td>\n",
       "      <td>Men</td>\n",
       "      <td>50M Army Pistol, Team</td>\n",
       "      <td>Gold</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Year         City       Sport   Discipline               Athlete  \\\n",
       "16950  1984  Los Angeles   Athletics    Athletics          CONLEY, Mike   \n",
       "195    1900        Paris    Aquatics   Water polo                PESLOY   \n",
       "8599   1952     Helsinki  Gymnastics  Artistic G.  KALINCHUK, Ekaterina   \n",
       "6435   1936       Berlin   Athletics    Athletics        BECCALI, Luigi   \n",
       "3923   1920      Antwerp    Shooting     Shooting      BRACKEN, Raymond   \n",
       "\n",
       "      Country Gender                  Event   Medal  \n",
       "16950     USA    Men            Triple Jump  Silver  \n",
       "195       FRA    Men             Water Polo  Bronze  \n",
       "8599      URS  Women       Team Competition    Gold  \n",
       "6435      ITA    Men                  1500M  Bronze  \n",
       "3923      USA    Men  50M Army Pistol, Team    Gold  "
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stratified_df = pd.DataFrame(Xtest)\n",
    "stratified_df.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "904a0f89",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:50.993055Z",
     "start_time": "2022-03-10T14:55:50.986637Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1652, 9)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stratified_df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "308e5863",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:51.000814Z",
     "start_time": "2022-03-10T14:55:50.996181Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(16514, 9)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "countries_rating_top.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "f9148e2b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:51.012298Z",
     "start_time": "2022-03-10T14:55:51.003777Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "USA    0.277845\n",
       "URS    0.124092\n",
       "GBR    0.104116\n",
       "FRA    0.084746\n",
       "ITA    0.078692\n",
       "GER    0.078692\n",
       "AUS    0.072034\n",
       "HUN    0.065375\n",
       "SWE    0.062954\n",
       "NED    0.051453\n",
       "Name: Country, dtype: float64"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stratified_df[\"Country\"].value_counts(normalize=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54003135",
   "metadata": {},
   "source": [
    "\n",
    "$~$\n",
    "\n",
    "now we can compare the two methods with our population\n",
    "\n",
    "\n",
    "$~$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "cd43fd70",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:55:51.031006Z",
     "start_time": "2022-03-10T14:55:51.014998Z"
    },
    "scrolled": true
   },
   "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>pop_proportion</th>\n",
       "      <th>stat_proportion</th>\n",
       "      <th>train_stat_proportion</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>USA</th>\n",
       "      <td>0.277643</td>\n",
       "      <td>0.277408</td>\n",
       "      <td>0.277845</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>URS</th>\n",
       "      <td>0.124077</td>\n",
       "      <td>0.124167</td>\n",
       "      <td>0.124092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GBR</th>\n",
       "      <td>0.104154</td>\n",
       "      <td>0.104179</td>\n",
       "      <td>0.104116</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FRA</th>\n",
       "      <td>0.084534</td>\n",
       "      <td>0.084797</td>\n",
       "      <td>0.084746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GER</th>\n",
       "      <td>0.079024</td>\n",
       "      <td>0.078740</td>\n",
       "      <td>0.078692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ITA</th>\n",
       "      <td>0.078479</td>\n",
       "      <td>0.078740</td>\n",
       "      <td>0.078692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AUS</th>\n",
       "      <td>0.072000</td>\n",
       "      <td>0.072078</td>\n",
       "      <td>0.072034</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HUN</th>\n",
       "      <td>0.065339</td>\n",
       "      <td>0.065415</td>\n",
       "      <td>0.065375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SWE</th>\n",
       "      <td>0.063219</td>\n",
       "      <td>0.062992</td>\n",
       "      <td>0.062954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NED</th>\n",
       "      <td>0.051532</td>\n",
       "      <td>0.051484</td>\n",
       "      <td>0.051453</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     pop_proportion  stat_proportion  train_stat_proportion\n",
       "USA        0.277643         0.277408               0.277845\n",
       "URS        0.124077         0.124167               0.124092\n",
       "GBR        0.104154         0.104179               0.104116\n",
       "FRA        0.084534         0.084797               0.084746\n",
       "GER        0.079024         0.078740               0.078692\n",
       "ITA        0.078479         0.078740               0.078692\n",
       "AUS        0.072000         0.072078               0.072034\n",
       "HUN        0.065339         0.065415               0.065375\n",
       "SWE        0.063219         0.062992               0.062954\n",
       "NED        0.051532         0.051484               0.051453"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = countries_rating_top[\"Country\"].value_counts(normalize=True).to_frame('pop_proportion')\n",
    "df2 = country_rating_samp[\"Country\"].value_counts(normalize=True).to_frame('stat_proportion')\n",
    "df3 = stratified_df[\"Country\"].value_counts(normalize=True).to_frame('train_stat_proportion')\n",
    "\n",
    "pd.concat([df1, df2, df3],axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60a86fb0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T11:42:19.113171Z",
     "start_time": "2022-03-10T11:42:19.096709Z"
    }
   },
   "source": [
    "$~$\n",
    "\n",
    "**We see that with the two methods we obtain very similar results.**\n",
    "\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22071c22",
   "metadata": {},
   "source": [
    "___\n",
    "$~$\n",
    "\n",
    "#####  SMOTE\n",
    "\n",
    "$~$\n",
    "\n",
    "+ The first thing we must do before applying the SMOTE method is to transform our variables.\n",
    "+ we are going to transform the variable \"Country\" . Let's change the country name to a number. We will do the same with the variable \"Medal\"\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c513146",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "###### label encode\n",
    "\n",
    "$~$\n",
    "\n",
    "for this, we will use the [label Encode function](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.LabelEncoder.html)\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "8585cc3f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:57:52.942143Z",
     "start_time": "2022-03-10T14:57:52.935324Z"
    }
   },
   "outputs": [],
   "source": [
    "labelencoder1 = LabelEncoder()\n",
    "countries_rating_top[\"Country_label\"] = labelencoder1.fit_transform(countries_rating_top[\"Country\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "eeccde58",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:58:03.703316Z",
     "start_time": "2022-03-10T14:58:03.695548Z"
    }
   },
   "outputs": [],
   "source": [
    "labelencoder2 = LabelEncoder()\n",
    "countries_rating_top[\"medal_label\"] = labelencoder2.fit_transform(countries_rating_top[\"Medal\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "7f38edeb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:58:04.729876Z",
     "start_time": "2022-03-10T14:58:04.723009Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9    0.277643\n",
       "8    0.124077\n",
       "2    0.104154\n",
       "1    0.084534\n",
       "3    0.079024\n",
       "5    0.078479\n",
       "0    0.072000\n",
       "4    0.065339\n",
       "7    0.063219\n",
       "6    0.051532\n",
       "Name: Country_label, dtype: float64"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "countries_rating_top[\"Country_label\"].value_counts(normalize=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1418a930",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "as you can see above, we have changed the names of countries by numbers in the column \"Country_Label\"\n",
    "\n",
    "$~$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "2a239d68",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:58:06.553740Z",
     "start_time": "2022-03-10T14:58:06.545372Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "USA    0.277643\n",
       "URS    0.124077\n",
       "GBR    0.104154\n",
       "FRA    0.084534\n",
       "GER    0.079024\n",
       "ITA    0.078479\n",
       "AUS    0.072000\n",
       "HUN    0.065339\n",
       "SWE    0.063219\n",
       "NED    0.051532\n",
       "Name: Country, dtype: float64"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "countries_rating_top[\"Country\"].value_counts(normalize=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01b11b7b",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "Having done all of the above,  now we can do SMOTE sampling\n",
    "\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "f3b56d4c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:58:07.753297Z",
     "start_time": "2022-03-10T14:58:07.668816Z"
    }
   },
   "outputs": [],
   "source": [
    "smote = SMOTE(sampling_strategy=\"not minority\", random_state=6858)\n",
    "\n",
    "X,y = smote.fit_resample(countries_rating_top[[\"Country_label\",\"medal_label\"]],countries_rating_top[\"Country_label\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "5fc36ec7",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:58:08.168544Z",
     "start_time": "2022-03-10T14:58:08.160813Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4    0.108866\n",
       "9    0.108866\n",
       "3    0.108866\n",
       "2    0.108866\n",
       "1    0.108866\n",
       "0    0.108866\n",
       "7    0.108866\n",
       "5    0.108866\n",
       "8    0.108866\n",
       "6    0.020206\n",
       "Name: Country_label, dtype: float64"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.value_counts(normalize=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "9463a617",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:58:08.860463Z",
     "start_time": "2022-03-10T14:58:08.855819Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(42116, 2)\n",
      "(16514, 11)\n"
     ]
    }
   ],
   "source": [
    "print(X.shape)\n",
    "print(countries_rating_top.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82c8a2b8",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "as a result we have that now the proportion of medals is balanced and we also have a larger dataset (check the X.shape)\n",
    "\n",
    "$~$\n",
    "___\n",
    "to be able to make comparisons, we are going to put the country labels back\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "da317909",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:58:10.177873Z",
     "start_time": "2022-03-10T14:58:10.170892Z"
    }
   },
   "outputs": [],
   "source": [
    "X[\"Country\"] = labelencoder1.inverse_transform(X[\"Country_label\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffb6689b",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "Next, let's see the results of the proportions of the different sampling methods\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "175f68ff",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:58:11.403475Z",
     "start_time": "2022-03-10T14:58:11.357059Z"
    }
   },
   "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>pop_proportion</th>\n",
       "      <th>stat_proportion</th>\n",
       "      <th>train_stat_proportion</th>\n",
       "      <th>smote_proportion</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>USA</th>\n",
       "      <td>0.277643</td>\n",
       "      <td>0.277408</td>\n",
       "      <td>0.277845</td>\n",
       "      <td>0.108866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>URS</th>\n",
       "      <td>0.124077</td>\n",
       "      <td>0.124167</td>\n",
       "      <td>0.124092</td>\n",
       "      <td>0.108866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GBR</th>\n",
       "      <td>0.104154</td>\n",
       "      <td>0.104179</td>\n",
       "      <td>0.104116</td>\n",
       "      <td>0.108866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FRA</th>\n",
       "      <td>0.084534</td>\n",
       "      <td>0.084797</td>\n",
       "      <td>0.084746</td>\n",
       "      <td>0.108866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GER</th>\n",
       "      <td>0.079024</td>\n",
       "      <td>0.078740</td>\n",
       "      <td>0.078692</td>\n",
       "      <td>0.108866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ITA</th>\n",
       "      <td>0.078479</td>\n",
       "      <td>0.078740</td>\n",
       "      <td>0.078692</td>\n",
       "      <td>0.108866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AUS</th>\n",
       "      <td>0.072000</td>\n",
       "      <td>0.072078</td>\n",
       "      <td>0.072034</td>\n",
       "      <td>0.108866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HUN</th>\n",
       "      <td>0.065339</td>\n",
       "      <td>0.065415</td>\n",
       "      <td>0.065375</td>\n",
       "      <td>0.108866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SWE</th>\n",
       "      <td>0.063219</td>\n",
       "      <td>0.062992</td>\n",
       "      <td>0.062954</td>\n",
       "      <td>0.108866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NED</th>\n",
       "      <td>0.051532</td>\n",
       "      <td>0.051484</td>\n",
       "      <td>0.051453</td>\n",
       "      <td>0.020206</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     pop_proportion  stat_proportion  train_stat_proportion  smote_proportion\n",
       "USA        0.277643         0.277408               0.277845          0.108866\n",
       "URS        0.124077         0.124167               0.124092          0.108866\n",
       "GBR        0.104154         0.104179               0.104116          0.108866\n",
       "FRA        0.084534         0.084797               0.084746          0.108866\n",
       "GER        0.079024         0.078740               0.078692          0.108866\n",
       "ITA        0.078479         0.078740               0.078692          0.108866\n",
       "AUS        0.072000         0.072078               0.072034          0.108866\n",
       "HUN        0.065339         0.065415               0.065375          0.108866\n",
       "SWE        0.063219         0.062992               0.062954          0.108866\n",
       "NED        0.051532         0.051484               0.051453          0.020206"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = countries_rating_top[\"Country\"].value_counts(normalize=True).to_frame('pop_proportion')\n",
    "df2 = country_rating_samp[\"Country\"].value_counts(normalize=True).to_frame('stat_proportion')\n",
    "df3 = stratified_df[\"Country\"].value_counts(normalize=True).to_frame('train_stat_proportion')\n",
    "df4= X[\"Country\"].value_counts(normalize=True).to_frame(\"smote_proportion\")\n",
    "\n",
    "pd.concat([df1, df2, df3,df4],axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12b27828",
   "metadata": {},
   "source": [
    "___\n",
    "$~$\n",
    "\n",
    "####   Reservoir sampling method\n",
    "\n",
    "$~$\n",
    "Continue with the sports theme dataset and generate a sample using the Reservoir sampling method.\n",
    "\n",
    "$~$\n",
    "\n",
    "+ here we will follow this [tutorial](https://towardsdatascience.com/the-5-sampling-algorithms-every-data-scientist-need-to-know-43c7bc11d17c):\n",
    "\n",
    "$~$\n",
    "___"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "3ca650d5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:58:12.791700Z",
     "start_time": "2022-03-10T14:58:12.773803Z"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "def generator(max):\n",
    "    number = 1\n",
    "    while number < max:\n",
    "        number += 1\n",
    "        yield number\n",
    "\n",
    "stream = generator(len(countries_rating_top))\n",
    "k=384\n",
    "reservoir = []\n",
    "\n",
    "for i, element in enumerate(stream):\n",
    "    if i+1<= k:\n",
    "        reservoir.append(element)\n",
    "    else:\n",
    "        probability = k/(i+1)\n",
    "        if random.random() < probability:\n",
    "             reservoir[random.choice(range(0,k))] = element"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "c7171803",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:58:13.733801Z",
     "start_time": "2022-03-10T14:58:13.720247Z"
    }
   },
   "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>Year</th>\n",
       "      <th>City</th>\n",
       "      <th>Sport</th>\n",
       "      <th>Discipline</th>\n",
       "      <th>Athlete</th>\n",
       "      <th>Country</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Event</th>\n",
       "      <th>Medal</th>\n",
       "      <th>Country_label</th>\n",
       "      <th>medal_label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1113</th>\n",
       "      <td>1904</td>\n",
       "      <td>St Louis</td>\n",
       "      <td>Wrestling</td>\n",
       "      <td>Wrestling Free.</td>\n",
       "      <td>CURRY, Robert</td>\n",
       "      <td>USA</td>\n",
       "      <td>Men</td>\n",
       "      <td>- 47.6KG (Light-Flyweight)</td>\n",
       "      <td>Gold</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10267</th>\n",
       "      <td>1960</td>\n",
       "      <td>Rome</td>\n",
       "      <td>Fencing</td>\n",
       "      <td>Fencing</td>\n",
       "      <td>CURLETTO, Mario</td>\n",
       "      <td>ITA</td>\n",
       "      <td>Men</td>\n",
       "      <td>Foil Team</td>\n",
       "      <td>Silver</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19807</th>\n",
       "      <td>1992</td>\n",
       "      <td>Barcelona</td>\n",
       "      <td>Aquatics</td>\n",
       "      <td>Water polo</td>\n",
       "      <td>GANDOLFI, Ferdinando</td>\n",
       "      <td>ITA</td>\n",
       "      <td>Men</td>\n",
       "      <td>Water Polo</td>\n",
       "      <td>Gold</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14143</th>\n",
       "      <td>1976</td>\n",
       "      <td>Montreal</td>\n",
       "      <td>Athletics</td>\n",
       "      <td>Athletics</td>\n",
       "      <td>AKSENOVA, Lyudmila</td>\n",
       "      <td>URS</td>\n",
       "      <td>Women</td>\n",
       "      <td>4X400M Relay</td>\n",
       "      <td>Bronze</td>\n",
       "      <td>8</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29377</th>\n",
       "      <td>2012</td>\n",
       "      <td>London</td>\n",
       "      <td>Aquatics</td>\n",
       "      <td>Swimming</td>\n",
       "      <td>DORSOGNA, Tommaso</td>\n",
       "      <td>AUS</td>\n",
       "      <td>Men</td>\n",
       "      <td>4X100M Medley</td>\n",
       "      <td>Bronze</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Year       City      Sport       Discipline               Athlete  \\\n",
       "1113   1904   St Louis  Wrestling  Wrestling Free.         CURRY, Robert   \n",
       "10267  1960       Rome    Fencing          Fencing       CURLETTO, Mario   \n",
       "19807  1992  Barcelona   Aquatics       Water polo  GANDOLFI, Ferdinando   \n",
       "14143  1976   Montreal  Athletics        Athletics    AKSENOVA, Lyudmila   \n",
       "29377  2012     London   Aquatics         Swimming     DORSOGNA, Tommaso   \n",
       "\n",
       "      Country Gender                       Event   Medal  Country_label  \\\n",
       "1113      USA    Men  - 47.6KG (Light-Flyweight)    Gold              9   \n",
       "10267     ITA    Men                   Foil Team  Silver              5   \n",
       "19807     ITA    Men                  Water Polo    Gold              5   \n",
       "14143     URS  Women                4X400M Relay  Bronze              8   \n",
       "29377     AUS    Men               4X100M Medley  Bronze              0   \n",
       "\n",
       "       medal_label  \n",
       "1113             1  \n",
       "10267            2  \n",
       "19807            1  \n",
       "14143            0  \n",
       "29377            0  "
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reservoir_sample = countries_rating_top.iloc[reservoir]\n",
    "reservoir_sample.head()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b12bd4d3",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "to see how good this method is, let's see the proportion of medals by country:\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "777e3112",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:58:15.266707Z",
     "start_time": "2022-03-10T14:58:15.259961Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "USA    0.257812\n",
       "URS    0.106771\n",
       "GBR    0.104167\n",
       "GER    0.093750\n",
       "FRA    0.091146\n",
       "AUS    0.080729\n",
       "SWE    0.080729\n",
       "ITA    0.070312\n",
       "NED    0.065104\n",
       "HUN    0.049479\n",
       "Name: Country, dtype: float64"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reservoir_sample[\"Country\"].value_counts(normalize=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26d6daa3",
   "metadata": {},
   "source": [
    "$~$\n",
    "\n",
    "to get a better perspective, let's look at 3  methods together:\n",
    "\n",
    "$~$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "3d34a2a1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-10T14:58:16.719255Z",
     "start_time": "2022-03-10T14:58:16.696662Z"
    }
   },
   "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>pop_proportion</th>\n",
       "      <th>stat_proportion</th>\n",
       "      <th>train_stat_proportion</th>\n",
       "      <th>smote_proportion</th>\n",
       "      <th>reservoir_sample</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>USA</th>\n",
       "      <td>0.277643</td>\n",
       "      <td>0.277408</td>\n",
       "      <td>0.277845</td>\n",
       "      <td>0.108866</td>\n",
       "      <td>0.257812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>URS</th>\n",
       "      <td>0.124077</td>\n",
       "      <td>0.124167</td>\n",
       "      <td>0.124092</td>\n",
       "      <td>0.108866</td>\n",
       "      <td>0.106771</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GBR</th>\n",
       "      <td>0.104154</td>\n",
       "      <td>0.104179</td>\n",
       "      <td>0.104116</td>\n",
       "      <td>0.108866</td>\n",
       "      <td>0.104167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FRA</th>\n",
       "      <td>0.084534</td>\n",
       "      <td>0.084797</td>\n",
       "      <td>0.084746</td>\n",
       "      <td>0.108866</td>\n",
       "      <td>0.091146</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GER</th>\n",
       "      <td>0.079024</td>\n",
       "      <td>0.078740</td>\n",
       "      <td>0.078692</td>\n",
       "      <td>0.108866</td>\n",
       "      <td>0.093750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ITA</th>\n",
       "      <td>0.078479</td>\n",
       "      <td>0.078740</td>\n",
       "      <td>0.078692</td>\n",
       "      <td>0.108866</td>\n",
       "      <td>0.070312</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AUS</th>\n",
       "      <td>0.072000</td>\n",
       "      <td>0.072078</td>\n",
       "      <td>0.072034</td>\n",
       "      <td>0.108866</td>\n",
       "      <td>0.080729</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HUN</th>\n",
       "      <td>0.065339</td>\n",
       "      <td>0.065415</td>\n",
       "      <td>0.065375</td>\n",
       "      <td>0.108866</td>\n",
       "      <td>0.049479</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SWE</th>\n",
       "      <td>0.063219</td>\n",
       "      <td>0.062992</td>\n",
       "      <td>0.062954</td>\n",
       "      <td>0.108866</td>\n",
       "      <td>0.080729</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NED</th>\n",
       "      <td>0.051532</td>\n",
       "      <td>0.051484</td>\n",
       "      <td>0.051453</td>\n",
       "      <td>0.020206</td>\n",
       "      <td>0.065104</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     pop_proportion  stat_proportion  train_stat_proportion  smote_proportion  \\\n",
       "USA        0.277643         0.277408               0.277845          0.108866   \n",
       "URS        0.124077         0.124167               0.124092          0.108866   \n",
       "GBR        0.104154         0.104179               0.104116          0.108866   \n",
       "FRA        0.084534         0.084797               0.084746          0.108866   \n",
       "GER        0.079024         0.078740               0.078692          0.108866   \n",
       "ITA        0.078479         0.078740               0.078692          0.108866   \n",
       "AUS        0.072000         0.072078               0.072034          0.108866   \n",
       "HUN        0.065339         0.065415               0.065375          0.108866   \n",
       "SWE        0.063219         0.062992               0.062954          0.108866   \n",
       "NED        0.051532         0.051484               0.051453          0.020206   \n",
       "\n",
       "     reservoir_sample  \n",
       "USA          0.257812  \n",
       "URS          0.106771  \n",
       "GBR          0.104167  \n",
       "FRA          0.091146  \n",
       "GER          0.093750  \n",
       "ITA          0.070312  \n",
       "AUS          0.080729  \n",
       "HUN          0.049479  \n",
       "SWE          0.080729  \n",
       "NED          0.065104  "
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = countries_rating_top[\"Country\"].value_counts(normalize=True).to_frame('pop_proportion')\n",
    "df2 = country_rating_samp[\"Country\"].value_counts(normalize=True).to_frame('stat_proportion')\n",
    "df3 = stratified_df[\"Country\"].value_counts(normalize=True).to_frame('train_stat_proportion')\n",
    "df4= X[\"Country\"].value_counts(normalize=True).to_frame(\"smote_proportion\")\n",
    "df5= reservoir_sample[\"Country\"].value_counts(normalize=True).to_frame(\"reservoir_sample\")\n",
    "pd.concat([df1, df2, df3,df4,df5],axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff19e1db",
   "metadata": {},
   "source": [
    "_____\n",
    "$~$\n",
    "\n",
    "###  conclusions\n",
    "\n",
    "$~$\n",
    "\n",
    "+ simple random sampling can be useful, but must be taken into account if the data is subgrouped.\n",
    "+ both simple random sampling and random sampling how systematic sampling negatively affects subgroups with low proportions\n",
    "+ Stratified sampling can be obtained by two different methods. In both cases the results obtained are similar.\n",
    "+ to apply the SMOTE method it is necessary to transform the categorical variables to numeric ones. And this can be done using the label encoder\n",
    "+ the reservoir sample method can be interesting, however, in the case of having data with subgroups, the samples obtained tend to be unbalanced"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0eedf5c",
   "metadata": {},
   "source": [
    "----------------\n",
    "$~$\n",
    "\n",
    "### *references*:\n",
    "\n",
    "+ [\n",
    "How to Download Kaggle Datasets using Jupyter Notebook\n",
    "](https://www.analyticsvidhya.com/blog/2021/04/how-to-download-kaggle-datasets-using-jupyter-notebook/)\n",
    "+ [Combining Pandas DataFrames: The easy way](https://towardsdatascience.com/combining-pandas-dataframes-the-easy-way-41eb0f2c1ebf)\n",
    "+ [How to Display Two Pandas Dataframes side by side in Jupyter Notebook ](https://softhints.com/display-two-pandas-dataframes-side-by-side-jupyter-notebook/#solution3displaytwodataframebypandasmergewithoutindex)\n",
    "+ [The 5 Sampling Algorithms every Data Scientist need to know](https://towardsdatascience.com/the-5-sampling-algorithms-every-data-scientist-need-to-know-43c7bc11d17c)\n",
    "+ [LabelEncoder](https://interactivechaos.com/es/python/function/labelencoder)\n",
    "+ [Label Encoding in Python Explained](https://www.mygreatlearning.com/blog/label-encoding-in-python/#labelencodingusingpython)\n",
    "\n",
    "\n",
    "\n",
    "-------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "62037148",
   "metadata": {},
   "outputs": [],
   "source": []
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