06_dataset_analysis_exploratory.ipynb 1010 KB
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{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "975fa498-1cba-4a76-a3ce-f3e818cf9ac6",
   "metadata": {},
   "source": [
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    "# Explorative Data Analysis\n",
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    "\n",
    "Lecture Data Engineering and Analytics<br>\n",
    "Eva Zangerle"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 2,
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   "id": "01df2e3a-ba55-4e8b-9170-ae3e9ebf993b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
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    "\n",
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    "import matplotlib.pyplot as plt\n",
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    "import numpy as np\n",
    "import pandas as pd\n",
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    "import seaborn as sns\n",
    "import stemgraphic\n",
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    "from scipy.stats import probplot, shapiro, kstest"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 3,
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   "id": "068d0eb2-6ae3-42fb-8a73-1d05a347be72",
   "metadata": {},
   "outputs": [],
   "source": [
    "# set seaborn style\n",
    "sns.set_style(\"darkgrid\")"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 4,
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   "id": "2803cb89-5c14-4f24-9f22-016a61fdfafb",
   "metadata": {},
   "outputs": [],
   "source": [
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    "# set data directory\n",
    "data_dir = \"../data\""
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 5,
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   "id": "57e96ac3-8027-4daf-bc92-ed093ae13c8b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# set display options for pandas dataframes\n",
    "pd.set_option(\"display.max_rows\", 200)\n",
    "pd.set_option(\"display.max_columns\", 100)\n",
    "pd.set_option(\"display.max_colwidth\", 200)"
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   ]
  },
  {
   "cell_type": "markdown",
   "id": "052c3ebf-436f-449f-89a0-15d6669482d6",
   "metadata": {},
   "source": [
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    "The following examples make use of the hetrec2011-movielens-2k dataset (https://grouplens.org/datasets/hetrec-2011/). This dataset is based on the [MovieLens 10m dataset](https://grouplens.org/datasets/movielens/10m/) and extends it with further metadata from imdb on movies and movie reviews from rottentomatoe. Find the dataset's readme [here](https://files.grouplens.org/datasets/hetrec2011/hetrec2011-movielens-readme.txt)."
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 6,
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   "id": "63fa331a-c219-417f-bcb3-748a13bc3226",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 20809 entries, 1 to 65133\n",
      "Data columns (total 1 columns):\n",
      " #   Column  Non-Null Count  Dtype \n",
      "---  ------  --------------  ----- \n",
      " 0   genre   20809 non-null  object\n",
      "dtypes: object(1)\n",
      "memory usage: 1.4 MB\n"
     ]
    }
   ],
   "source": [
    "# read in genre data\n",
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    "genres = pd.read_csv(\n",
    "    os.path.join(data_dir, \"hetrec/movie_genres.dat\"),\n",
    "    delimiter=\"\\t\",\n",
    "    index_col=\"movieID\",\n",
    ")\n",
    "genres.info(memory_usage=\"deep\")"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 7,
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   "id": "9b9412b5-f3c4-4fe4-be5b-38ca26b80f01",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 855598 entries, 0 to 855597\n",
      "Data columns (total 9 columns):\n",
      " #   Column       Non-Null Count   Dtype  \n",
      "---  ------       --------------   -----  \n",
      " 0   userID       855598 non-null  int64  \n",
      " 1   movieID      855598 non-null  int64  \n",
      " 2   rating       855598 non-null  float64\n",
      " 3   date_day     855598 non-null  int64  \n",
      " 4   date_month   855598 non-null  int64  \n",
      " 5   date_year    855598 non-null  int64  \n",
      " 6   date_hour    855598 non-null  int64  \n",
      " 7   date_minute  855598 non-null  int64  \n",
      " 8   date_second  855598 non-null  int64  \n",
      "dtypes: float64(1), int64(8)\n",
      "memory usage: 58.7 MB\n"
     ]
    }
   ],
   "source": [
    "# read in rating data\n",
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    "ratings = pd.read_csv(\n",
    "    os.path.join(data_dir, \"hetrec/user_ratedmovies.dat\"), delimiter=\"\\t\"\n",
    ")\n",
    "ratings.info(memory_usage=\"deep\")"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 86,
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   "id": "b4595afa-a782-4059-a984-2054aa26e96d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 10197 entries, 0 to 10196\n",
      "Data columns (total 21 columns):\n",
      " #   Column                  Non-Null Count  Dtype  \n",
      "---  ------                  --------------  -----  \n",
      " 0   id                      10197 non-null  int64  \n",
      " 1   title                   10197 non-null  object \n",
      " 2   imdbID                  10197 non-null  int64  \n",
      " 3   spanishTitle            10197 non-null  object \n",
      " 4   imdbPictureURL          10016 non-null  object \n",
      " 5   year                    10197 non-null  int64  \n",
      " 6   rtID                    9886 non-null   object \n",
      " 7   rtAllCriticsRating      9967 non-null   float64\n",
      " 8   rtAllCriticsNumReviews  9967 non-null   float64\n",
      " 9   rtAllCriticsNumFresh    9967 non-null   float64\n",
      " 10  rtAllCriticsNumRotten   9967 non-null   float64\n",
      " 11  rtAllCriticsScore       9967 non-null   float64\n",
      " 12  rtTopCriticsRating      9967 non-null   float64\n",
      " 13  rtTopCriticsNumReviews  9967 non-null   float64\n",
      " 14  rtTopCriticsNumFresh    9967 non-null   float64\n",
      " 15  rtTopCriticsNumRotten   9967 non-null   float64\n",
      " 16  rtTopCriticsScore       9967 non-null   float64\n",
      " 17  rtAudienceRating        9967 non-null   float64\n",
      " 18  rtAudienceNumRatings    9967 non-null   float64\n",
      " 19  rtAudienceScore         9967 non-null   float64\n",
      " 20  rtPictureURL            9967 non-null   object \n",
      "dtypes: float64(13), int64(3), object(5)\n",
      "memory usage: 6.2 MB\n"
     ]
    }
   ],
   "source": [
    "# read in movie data, prefix rt = rottenTomatoes\n",
    "# only works when specifying encoding correctly (fails due to ~n)\n",
    "movies = pd.read_csv(\n",
    "    os.path.join(data_dir, \"hetrec/movies.dat\"),\n",
    "    delimiter=\"\\t\",\n",
    "    na_values=[\"\\\\N\"],\n",
    "    encoding=\"latin1\",\n",
    ")\n",
    "movies.info(memory_usage=\"deep\")"
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   ]
  },
  {
   "cell_type": "markdown",
   "id": "df11f9a4-dab6-456c-93d7-6eab4600500d",
   "metadata": {},
   "source": [
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    "## Univariate Non-Graphical EDA"
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   ]
  },
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  {
   "cell_type": "markdown",
   "id": "c85638d9-0714-454f-8804-e00cbc9b374a",
   "metadata": {},
   "source": [
    "In the following, we will perform non-graphical exploratory data analysis as a first step towards getting a deeper understanding of the characteristics of the dataset. Particularly, we will start with the genre data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d021c42-4c63-44a7-a337-2dbcd4f3b06b",
   "metadata": {},
   "source": [
    "### Basics"
   ]
  },
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  {
   "cell_type": "code",
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   "execution_count": 9,
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   "id": "9f8c82dc-7300-49c0-b467-9ed94e5182f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>genre</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>movieID</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Adventure</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Animation</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Children</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Comedy</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Fantasy</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             genre\n",
       "movieID           \n",
       "1        Adventure\n",
       "1        Animation\n",
       "1         Children\n",
       "1           Comedy\n",
       "1          Fantasy"
      ]
     },
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     "execution_count": 9,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "20809"
      ]
     },
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     "execution_count": 9,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# simple exploration\n",
    "genres.head()\n",
    "len(genres)"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 10,
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   "id": "9f85dc2e-572d-416c-a1f6-1f3127bf8cb9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Adventure', 'Animation', 'Children', 'Comedy', 'Fantasy',\n",
       "       'Romance', 'Drama', 'Action', 'Crime', 'Thriller', 'Horror',\n",
       "       'Mystery', 'Sci-Fi', 'IMAX', 'Documentary', 'War', 'Musical',\n",
       "       'Film-Noir', 'Western', 'Short'], dtype=object)"
      ]
     },
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     "execution_count": 10,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# which genres are contained?\n",
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    "genres[\"genre\"].unique()"
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   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad0bab35-d8c3-49d8-91b9-acfbd5589b4e",
   "metadata": {},
   "source": [
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    "### Tabulation for Categorical Data"
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   ]
  },
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  {
   "cell_type": "markdown",
   "id": "73879162-ec37-43b4-b23b-7f1969501620",
   "metadata": {},
   "source": [
    "In a first step, we will use tabulation to investigate the distribution of genres across movies."
   ]
  },
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  {
   "cell_type": "code",
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   "execution_count": 11,
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   "id": "e03f89b3-fca8-404f-9136-7b92de976715",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>share</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Drama</th>\n",
       "      <td>5076</td>\n",
       "      <td>0.243933</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Comedy</th>\n",
       "      <td>3566</td>\n",
       "      <td>0.171368</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Thriller</th>\n",
       "      <td>1664</td>\n",
       "      <td>0.079965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Romance</th>\n",
       "      <td>1644</td>\n",
       "      <td>0.079004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Action</th>\n",
       "      <td>1445</td>\n",
       "      <td>0.069441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Crime</th>\n",
       "      <td>1086</td>\n",
       "      <td>0.052189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Adventure</th>\n",
       "      <td>1003</td>\n",
       "      <td>0.048200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Horror</th>\n",
       "      <td>978</td>\n",
       "      <td>0.046999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sci-Fi</th>\n",
       "      <td>740</td>\n",
       "      <td>0.035562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fantasy</th>\n",
       "      <td>535</td>\n",
       "      <td>0.025710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Children</th>\n",
       "      <td>519</td>\n",
       "      <td>0.024941</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mystery</th>\n",
       "      <td>497</td>\n",
       "      <td>0.023884</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>War</th>\n",
       "      <td>494</td>\n",
       "      <td>0.023740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Documentary</th>\n",
       "      <td>430</td>\n",
       "      <td>0.020664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Musical</th>\n",
       "      <td>421</td>\n",
       "      <td>0.020232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Animation</th>\n",
       "      <td>279</td>\n",
       "      <td>0.013408</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Western</th>\n",
       "      <td>261</td>\n",
       "      <td>0.012543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Film-Noir</th>\n",
       "      <td>145</td>\n",
       "      <td>0.006968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IMAX</th>\n",
       "      <td>25</td>\n",
       "      <td>0.001201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Short</th>\n",
       "      <td>1</td>\n",
       "      <td>0.000048</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             count     share\n",
       "Drama         5076  0.243933\n",
       "Comedy        3566  0.171368\n",
       "Thriller      1664  0.079965\n",
       "Romance       1644  0.079004\n",
       "Action        1445  0.069441\n",
       "Crime         1086  0.052189\n",
       "Adventure     1003  0.048200\n",
       "Horror         978  0.046999\n",
       "Sci-Fi         740  0.035562\n",
       "Fantasy        535  0.025710\n",
       "Children       519  0.024941\n",
       "Mystery        497  0.023884\n",
       "War            494  0.023740\n",
       "Documentary    430  0.020664\n",
       "Musical        421  0.020232\n",
       "Animation      279  0.013408\n",
       "Western        261  0.012543\n",
       "Film-Noir      145  0.006968\n",
       "IMAX            25  0.001201\n",
       "Short            1  0.000048"
      ]
     },
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     "execution_count": 11,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# combine counts and relative frequency in a dataframe to prettify output\n",
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    "pd.DataFrame(\n",
    "    {\n",
    "        \"count\": genres[\"genre\"].value_counts(),\n",
    "        \"share\": genres[\"genre\"].value_counts(normalize=True),\n",
    "    }\n",
    ")"
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   ]
  },
  {
   "cell_type": "markdown",
   "id": "f43e3750-d441-4144-9a98-8c01cbbb2002",
   "metadata": {},
   "source": [
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    "### Location"
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   ]
  },
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  {
   "cell_type": "markdown",
   "id": "78c558fc-d9c8-458e-9451-fd80d6b91f4a",
   "metadata": {},
   "source": [
    "In a next step, we will also include the ratings data in our evaluation and investigate the rating behavior of users for movies."
   ]
  },
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  {
   "cell_type": "code",
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   "execution_count": 12,
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   "id": "f0e61052-ddd0-49bc-a709-c89fba59908f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1.0\n",
       "1    4.5\n",
       "2    4.0\n",
       "3    2.0\n",
       "4    4.0\n",
       "Name: rating, dtype: float64"
      ]
     },
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     "execution_count": 12,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "855593    4.0\n",
       "855594    4.0\n",
       "855595    4.5\n",
       "855596    5.0\n",
       "855597    4.5\n",
       "Name: rating, dtype: float64"
      ]
     },
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     "execution_count": 12,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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>userID</th>\n",
       "      <th>movieID</th>\n",
       "      <th>rating</th>\n",
       "      <th>date_day</th>\n",
       "      <th>date_month</th>\n",
       "      <th>date_year</th>\n",
       "      <th>date_hour</th>\n",
       "      <th>date_minute</th>\n",
       "      <th>date_second</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>618259</th>\n",
       "      <td>50670</td>\n",
       "      <td>517</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>2001</td>\n",
       "      <td>21</td>\n",
       "      <td>49</td>\n",
       "      <td>46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>122393</th>\n",
       "      <td>10132</td>\n",
       "      <td>60753</td>\n",
       "      <td>4.0</td>\n",
       "      <td>23</td>\n",
       "      <td>8</td>\n",
       "      <td>2008</td>\n",
       "      <td>17</td>\n",
       "      <td>5</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>653376</th>\n",
       "      <td>52834</td>\n",
       "      <td>147</td>\n",
       "      <td>3.0</td>\n",
       "      <td>13</td>\n",
       "      <td>12</td>\n",
       "      <td>1999</td>\n",
       "      <td>17</td>\n",
       "      <td>40</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147297</th>\n",
       "      <td>12296</td>\n",
       "      <td>1094</td>\n",
       "      <td>4.0</td>\n",
       "      <td>27</td>\n",
       "      <td>5</td>\n",
       "      <td>1998</td>\n",
       "      <td>15</td>\n",
       "      <td>19</td>\n",
       "      <td>49</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>156557</th>\n",
       "      <td>13029</td>\n",
       "      <td>6281</td>\n",
       "      <td>5.0</td>\n",
       "      <td>27</td>\n",
       "      <td>1</td>\n",
       "      <td>2006</td>\n",
       "      <td>23</td>\n",
       "      <td>37</td>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3949</th>\n",
       "      <td>533</td>\n",
       "      <td>3196</td>\n",
       "      <td>4.5</td>\n",
       "      <td>22</td>\n",
       "      <td>6</td>\n",
       "      <td>2003</td>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24877</th>\n",
       "      <td>2471</td>\n",
       "      <td>1704</td>\n",
       "      <td>3.0</td>\n",
       "      <td>15</td>\n",
       "      <td>7</td>\n",
       "      <td>2008</td>\n",
       "      <td>9</td>\n",
       "      <td>40</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25245</th>\n",
       "      <td>2513</td>\n",
       "      <td>1653</td>\n",
       "      <td>4.5</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>2007</td>\n",
       "      <td>21</td>\n",
       "      <td>46</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>638844</th>\n",
       "      <td>51901</td>\n",
       "      <td>4571</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1</td>\n",
       "      <td>11</td>\n",
       "      <td>2005</td>\n",
       "      <td>11</td>\n",
       "      <td>45</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>209532</th>\n",
       "      <td>17999</td>\n",
       "      <td>249</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>2004</td>\n",
       "      <td>19</td>\n",
       "      <td>44</td>\n",
       "      <td>48</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        userID  movieID  rating  date_day  date_month  date_year  date_hour  \\\n",
       "618259   50670      517     4.0         1           6       2001         21   \n",
       "122393   10132    60753     4.0        23           8       2008         17   \n",
       "653376   52834      147     3.0        13          12       1999         17   \n",
       "147297   12296     1094     4.0        27           5       1998         15   \n",
       "156557   13029     6281     5.0        27           1       2006         23   \n",
       "3949       533     3196     4.5        22           6       2003          8   \n",
       "24877     2471     1704     3.0        15           7       2008          9   \n",
       "25245     2513     1653     4.5         8           7       2007         21   \n",
       "638844   51901     4571     3.5         1          11       2005         11   \n",
       "209532   17999      249     3.0         3           6       2004         19   \n",
       "\n",
       "        date_minute  date_second  \n",
       "618259           49           46  \n",
       "122393            5           45  \n",
       "653376           40           45  \n",
       "147297           19           49  \n",
       "156557           37           41  \n",
       "3949             10           16  \n",
       "24877            40           36  \n",
       "25245            46            6  \n",
       "638844           45            7  \n",
       "209532           44           48  "
      ]
     },
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     "execution_count": 12,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
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    "# look at raw data\n",
    "ratings[\"rating\"].head()\n",
    "ratings[\"rating\"].tail()\n",
    "ratings.sample(n=10, random_state=3)"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 13,
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   "id": "d809ecd1-c278-426c-b512-2f75c6a0871c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
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    "#  rating distribution across all movies\n",
    "plt.hist(ratings[\"rating\"], bins=10)\n",
    "plt.xlabel(\"Rating\")\n",
    "plt.ylabel(\"Frequency\");"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 14,
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   "id": "d36d867a-263c-4741-8bfc-ddb4a6a7a4bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.437945156487042"
      ]
     },
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     "execution_count": 14,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "3.5"
      ]
     },
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     "execution_count": 14,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0    4.0\n",
       "dtype: float64"
      ]
     },
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     "execution_count": 14,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
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    "# inspect location\n",
    "# mean\n",
    "ratings[\"rating\"].mean()\n",
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    "# median\n",
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    "ratings[\"rating\"].median()\n",
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    "# mode\n",
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    "ratings[\"rating\"].mode()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4327620f-4705-45b1-8846-d73ceecb9008",
   "metadata": {},
   "source": [
    "The following examples showcase the role of location for a normal, hence, symmetric distribution and a highly skewed distribution."
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 15,
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   "id": "ac5bea93-9af4-4205-bd6c-dbc00405cbe6",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
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    "# create a symmetricly distributed dataset\n",
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    "normal_distribution = pd.Series(np.random.randn(20000) + 100)\n",
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    "plt.hist(normal_distribution, bins=50)\n",
    "plt.xlabel(\"Value\")\n",
    "plt.ylabel(\"Occurrences\");"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 16,
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   "id": "669e4fc1-3270-4912-8c53-22ef4bfe6427",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "100.0036948049208"
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      ]
     },
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     "execution_count": 16,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
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       "100.00700767844339"
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      ]
     },
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     "execution_count": 16,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
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    "# location\n",
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    "normal_distribution.mean()\n",
    "normal_distribution.median()"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 17,
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   "id": "358e93e2-1060-4575-bcf3-92c8d51fc366",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "movieID\n",
       "5405       1\n",
       "795        1\n",
       "7322       1\n",
       "7295       1\n",
       "7291       1\n",
       "        ... \n",
       "5952    1528\n",
       "296     1537\n",
       "356     1568\n",
       "4993    1576\n",
       "2571    1670\n",
       "Name: rating, Length: 10109, dtype: int64"
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      ]
     },
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     "execution_count": 17,
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     "metadata": {},
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     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "movieID\n",
       "67       1\n",
       "134      1\n",
       "139      1\n",
       "143      1\n",
       "226      1\n",
       "        ..\n",
       "65006    1\n",
       "65011    1\n",
       "65088    1\n",
       "65091    1\n",
       "65130    1\n",
       "Name: rating, Length: 602, dtype: int64"
      ]
     },
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     "execution_count": 17,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
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   "source": [
    "# asymmetric, skewed distribution\n",
    "# number of ratings per movie\n",
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    "rating_counts = ratings.groupby(\"movieID\")[\"rating\"].agg(\"count\")\n",
    "rating_counts.sort_values()\n",
    "rating_counts[rating_counts == 1]"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 18,
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   "id": "de4ea66e-1743-45d6-886a-54e06b397c6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot number of movies with given number of ratings\n",
    "plt.plot(rating_counts.value_counts())\n",
    "plt.xlabel(\"Number of Ratings\")\n",
    "plt.ylabel(\"Number of Movies\");"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 19,
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   "id": "54488e96-63ce-4bab-aeba-f063e437a4e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# histogram of number of movies with given number of ratings\n",
    "# (binned value counts)\n",
    "fig, axes = plt.subplots(1, 2, figsize=(15, 5))\n",
    "axes[0].hist(rating_counts, bins=100)\n",
    "axes[0].set_ylabel(\"Number of Movies\")\n",
    "axes[0].set_xlabel(\"Number of Ratings\")\n",
    "axes[1].hist(rating_counts, log=True, bins=100)\n",
    "axes[1].set_ylabel(\"Number of Movies (log)\")\n",
    "axes[1].set_xlabel(\"Number of Ratings\");"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 20,
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   "id": "e68666c9-0fa6-493e-9f6c-b190315811b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "84.63725393213967"
      ]
     },
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     "execution_count": 20,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "21.0"
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      ]
     },
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     "execution_count": 20,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
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       "count    10109.000000\n",
       "mean        84.637254\n",
       "std        172.115584\n",
       "min          1.000000\n",
       "25%          6.000000\n",
       "50%         21.000000\n",
       "75%         75.000000\n",
       "max       1670.000000\n",
       "Name: rating, dtype: float64"
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      ]
     },
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     "execution_count": 20,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
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    "# mean and median number of ratings\n",
    "rating_counts.mean()\n",
    "rating_counts.median()\n",
    "rating_counts.describe()"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 21,
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   "id": "d7374509-6104-40fb-9463-f1ee6768c3ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# slightly different way of getting overview of ratings per movie\n",
    "# plot distribution of binned count values\n",
    "count_histogram = rating_counts.value_counts()\n",
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    "fig, axes = plt.subplots(1, 2, figsize=(15, 5))\n",
    "axes[0].scatter(count_histogram.index, count_histogram)\n",
    "axes[0].set_xlabel(\"Number of Ratings\")\n",
    "axes[0].set_ylabel(\"Number of Movies\")\n",
    "axes[1].scatter(count_histogram.index, count_histogram)\n",
    "axes[1].set_xlabel(\"Number of Ratings (log)\")\n",
    "axes[1].set_ylabel(\"Number of Movies (log)\")\n",
    "axes[1].set_xscale(\"log\")\n",
    "axes[1].set_yscale(\"log\");"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 22,
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   "id": "eb52beb5-4f94-4cce-81e2-6e95c166de3c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    855598.000000\n",
       "mean          3.437945\n",
       "std           1.002561\n",
       "min           0.500000\n",
       "25%           3.000000\n",
       "50%           3.500000\n",
       "75%           4.000000\n",
       "max           5.000000\n",
       "Name: rating, dtype: float64"
      ]
     },
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     "execution_count": 22,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
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    "# use describe function for summary of ratings generally\n",
    "ratings[\"rating\"].describe()"
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   ]
  },
  {
   "cell_type": "markdown",
   "id": "15364d28-75aa-4f9b-90a6-382c904b2705",
   "metadata": {},
   "source": [
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    "### Spread"
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   ]
  },
  {
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   "cell_type": "markdown",
   "id": "cd0c9b60-cc3e-4a8f-9214-78cd4f1ce7d2",
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   "metadata": {},
   "source": [
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    "The following examples show measure of spread for our ratings example."
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 23,
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   "id": "1d4f957e-30ed-4995-9ecb-0228ed41ddab",
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   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "1.002560872161038"
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      ]
     },
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     "execution_count": 23,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
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       "1.005128302388301"
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      ]
     },
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     "execution_count": 23,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
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    "ratings[\"rating\"].std()\n",
    "ratings[\"rating\"].var()"
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   ]
  },
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  {
   "cell_type": "code",
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   "execution_count": 24,
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   "id": "8776f04a-6a0f-475c-aee3-c920d59a90f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
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     "execution_count": 24,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "count    855598.000000\n",
       "mean          3.437945\n",
       "std           1.002561\n",
       "min           0.500000\n",
       "25%           3.000000\n",
       "50%           3.500000\n",
       "75%           4.000000\n",
       "max           5.000000\n",
       "Name: rating, dtype: float64"
      ]
     },
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     "execution_count": 24,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# IQR\n",
    "ratings[\"rating\"].quantile(0.75) - ratings[\"rating\"].quantile(0.25)\n",
    "ratings[\"rating\"].describe()"
   ]
  },
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  {
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   "cell_type": "markdown",
   "id": "d6db406d-d3cf-471a-a78f-bec544e99cce",
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   "metadata": {},
   "source": [
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    "Short detour: how does sample size impact how representative the sample is for the full population."
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 25,
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   "id": "2846ff54-b36a-4042-b553-188414fcc6a4",
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   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "1.0142448879302735"
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      ]
     },
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     "execution_count": 25,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
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       "1.028692692692693"
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     },
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     "execution_count": 25,
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     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
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    "# sampling effect (for n=10 vs. n=1000, for instance)\n",
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    "sample_ratings = ratings.sample(n=1000, random_state=5)\n",
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    "sample_ratings[\"rating\"].std()\n",
    "sample_ratings[\"rating\"].var()"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 26,
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   "id": "529f94c2-a440-4a5a-b639-dd8200a39e90",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>userID</th>\n",
       "      <th>movieID</th>\n",
       "      <th>rating</th>\n",
       "      <th>date_day</th>\n",
       "      <th>date_month</th>\n",
       "      <th>date_year</th>\n",
       "      <th>date_hour</th>\n",
       "      <th>date_minute</th>\n",
       "      <th>date_second</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
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       "      <th>97121</th>\n",
       "      <td>8127</td>\n",
       "      <td>7254</td>\n",
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       "      <td>3.0</td>\n",
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       "      <td>4</td>\n",
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       "      <td>12</td>\n",
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       "      <td>2006</td>\n",
       "      <td>13</td>\n",
       "      <td>57</td>\n",
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       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
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       "      <th>854304</th>\n",
       "      <td>71509</td>\n",
       "      <td>3060</td>\n",
       "      <td>3.5</td>\n",
       "      <td>30</td>\n",
       "      <td>8</td>\n",
       "      <td>2004</td>\n",
       "      <td>16</td>\n",
       "      <td>50</td>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>320729</th>\n",
       "      <td>26116</td>\n",
       "      <td>8933</td>\n",
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       "      <td>4.0</td>\n",
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       "      <td>12</td>\n",
       "      <td>10</td>\n",
       "      <td>2004</td>\n",
       "      <td>1</td>\n",
       "      <td>14</td>\n",
       "      <td>41</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
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       "      <th>75021</th>\n",
       "      <td>6757</td>\n",
       "      <td>2692</td>\n",
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       "      <td>3.0</td>\n",
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       "      <td>5</td>\n",
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       "      <td>7</td>\n",
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       "      <td>2002</td>\n",
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       "      <td>9</td>\n",
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       "      <td>26</td>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>772382</th>\n",
       "      <td>64621</td>\n",
       "      <td>3654</td>\n",
       "      <td>4.0</td>\n",
       "      <td>20</td>\n",
       "      <td>10</td>\n",
       "      <td>2001</td>\n",
       "      <td>5</td>\n",
       "      <td>39</td>\n",
       "      <td>11</td>\n",
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       "    </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",
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       "      <th>469043</th>\n",
       "      <td>37419</td>\n",
       "      <td>588</td>\n",
       "      <td>4.0</td>\n",
       "      <td>11</td>\n",
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       "      <td>8</td>\n",
       "      <td>2007</td>\n",
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       "      <td>9</td>\n",
       "      <td>11</td>\n",
       "      <td>8</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
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       "      <th>541266</th>\n",
       "      <td>43527</td>\n",
       "      <td>8873</td>\n",
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       "      <td>4.0</td>\n",
       "      <td>2</td>\n",
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       "      <td>9</td>\n",
       "      <td>2006</td>\n",
       "      <td>17</td>\n",
       "      <td>33</td>\n",
       "      <td>58</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
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       "      <th>768444</th>\n",
       "      <td>64472</td>\n",
       "      <td>1438</td>\n",
       "      <td>2.5</td>\n",
       "      <td>27</td>\n",
       "      <td>5</td>\n",
       "      <td>2003</td>\n",
       "      <td>22</td>\n",
       "      <td>46</td>\n",
       "      <td>53</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>519540</th>\n",
       "      <td>41201</td>\n",
       "      <td>101</td>\n",
       "      <td>3.5</td>\n",
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       "      <td>1</td>\n",
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       "      <td>11</td>\n",
       "      <td>2008</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>806968</th>\n",
       "      <td>67635</td>\n",
       "      <td>1544</td>\n",
       "      <td>3.0</td>\n",
       "      <td>8</td>\n",
       "      <td>4</td>\n",
       "      <td>2004</td>\n",
       "      <td>14</td>\n",
       "      <td>26</td>\n",
       "      <td>24</td>\n",
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       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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       "<p>698 rows × 9 columns</p>\n",
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       "</div>"
      ],
      "text/plain": [
       "        userID  movieID  rating  date_day  date_month  date_year  date_hour  \\\n",
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       "97121     8127     7254     3.0         4          12       2006         13   \n",
       "854304   71509     3060     3.5        30           8       2004         16   \n",
       "320729   26116     8933     4.0        12          10       2004          1   \n",
       "75021     6757     2692     3.0         5           7       2002          9   \n",
       "772382   64621     3654     4.0        20          10       2001          5   \n",
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       "...        ...      ...     ...       ...         ...        ...        ...   \n",
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       "469043   37419      588     4.0        11           8       2007          9   \n",
       "541266   43527     8873     4.0         2           9       2006         17   \n",
       "768444   64472     1438     2.5        27           5       2003         22   \n",
       "519540   41201      101     3.5         1          11       2008          0   \n",
       "806968   67635     1544     3.0         8           4       2004         14   \n",
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       "\n",
       "        date_minute  date_second  \n",
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       "97121            57           17  \n",
       "854304           50           29  \n",
       "320729           14           41  \n",
       "75021            26           34  \n",
       "772382           39           11  \n",
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       "...             ...          ...  \n",
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       "469043           11            8  \n",
       "541266           33           58  \n",
       "768444           46           53  \n",
       "519540            0           17  \n",
       "806968           26           24  \n",
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       "\n",
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       "[698 rows x 9 columns]"
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      ]
     },
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     "execution_count": 26,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
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    "# look at all samples that have a rating within mean +/- 1 std\n",
    "sample_ratings = ratings.sample(n=1000, random_state=5)\n",
    "sample_ratings[\n",
    "    (\n",
    "        sample_ratings[\"rating\"]\n",
    "        > (sample_ratings[\"rating\"].mean() - sample_ratings[\"rating\"].std())\n",
    "    )\n",
    "    & (\n",
    "        sample_ratings[\"rating\"]\n",
    "        < (sample_ratings[\"rating\"].mean() + sample_ratings[\"rating\"].std())\n",
    "    )\n",
    "]"
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   ]
  },
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  {
   "cell_type": "code",
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   "execution_count": 27,
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   "id": "07fa94c3-8a62-44e4-b52e-48d962972c9c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "855598"
      ]
     },
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     "execution_count": 27,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(ratings)"
   ]
  },
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  {
   "cell_type": "markdown",
   "id": "dfc7d9a3-4b1b-41c0-88cb-390e3b2b9240",
   "metadata": {},
   "source": [
    "Side note - for normal distributions:  \n",
    "68% of all observations fall within +/- 1 standard deviation  \n",
    "95% of all observations fall within +/- 2 standard deviations  \n",
    "99.7% of all observations fall within +/- 3 standard deviations"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 28,
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   "id": "adf25d75-1f21-4e37-9911-a82110647781",
   "metadata": {},
   "outputs": [
    {
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     "data": {
      "text/plain": [
       "(0.931491494178772, 5.4851319809639435e-21)"
      ]
     },
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     "execution_count": 28,
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     "metadata": {},
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    }
   ],
   "source": [
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    "# use shapiro-wilk test to test for normal distribution (usually quite suited\n",
    "# for smaller samples)\n",
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    "# here, non-normal distribution is already clear from the histogram\n",
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    "# output of shapiro-wilk: test statistics, p-value\n",
    "# null hypothesis: distribution was drawn from normally distributed data\n",
    "statistics, p = shapiro(sample_ratings[\"rating\"])\n",
    "statistics, p"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 29,
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   "id": "f3c51f11-48a6-48c1-bf8d-32ee288d5a3f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9092498680518208, 0.0)"
      ]
     },
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     "execution_count": 29,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Kolmogorov-Smirnov test\n",
    "ks_statistic, p_value = kstest(sample_ratings[\"rating\"], \"norm\")\n",
    "ks_statistic, p_value"
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   ]
  },
  {
   "cell_type": "markdown",
   "id": "eaddb47c-7b83-4c78-abab-139b08e07235",
   "metadata": {},
   "source": [
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    "### Shape"
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  },
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  {
   "cell_type": "markdown",
   "id": "8bcfc241-02f1-4437-b550-487a04add2d6",
   "metadata": {},
   "source": [
    "The following examples showcase shape measures for the given dataset."
   ]
  },
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  {
   "cell_type": "code",
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   "execution_count": 30,
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   "id": "9470ef42-f954-461b-94ba-792a5e467d9b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.7009990282814003"
      ]
     },
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     "execution_count": 30,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.33623508094406773"
      ]
     },
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     "execution_count": 30,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
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    "# skewness and kurtosis of ratings\n",
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    "ratings[\"rating\"].skew()\n",
    "ratings[\"rating\"].kurtosis()"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 31,
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   "id": "69654f99-9ce3-4a14-a660-46b29207eae0",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": "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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
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    "plt.hist(ratings[\"rating\"])\n",
    "plt.xlabel(\"Rating\")\n",
    "plt.ylabel(\"Frequency\");"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 32,
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   "id": "467d6cd0-05b7-45c4-906e-05b9a03effa4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.981817617200359"
      ]
     },
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     "execution_count": 32,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "19.488816492218888"
      ]
     },
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     "execution_count": 32,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#skewness and kurtosis of rating counts\n",
    "rating_counts.skew()\n",
    "rating_counts.kurtosis()"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 33,
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   "id": "5184b3e2-5b5a-42ae-b26f-d12c3948ee52",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(rating_counts);\n",
    "plt.xlabel(\"Ratings\")\n",
    "plt.ylabel(\"Movies\");"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 34,
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   "id": "e27b0c37-6758-4492-9302-8e12e925a848",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "-0.025304929630210707"
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      ]
     },
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     "execution_count": 34,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
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       "0.019646099647941728"
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      ]
     },
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     "execution_count": 34,