05_dataset_analysis_cleaning.ipynb 696 KB
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{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fe2eed0f-4ff1-4587-aa6c-3589c0f41e07",
   "metadata": {},
   "source": [
    "# Data Preparation and Quality\n",
    "Lecture Data Engineering and Analytics<br>\n",
    "Eva Zangerle"
   ]
  },
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  {
   "cell_type": "code",
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   "execution_count": 2,
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   "id": "792af709-0621-4d64-8166-8c8cc28cc73c",
   "metadata": {},
   "outputs": [],
   "source": [
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    "# import required packages\n",
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    "import psycopg2\n",
    "import json\n",
    "import math\n",
    "import glob\n",
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    "import os\n",
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    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from scipy.stats import norm, kstest, median_abs_deviation\n",
    "import statsmodels.api as sm\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import MinMaxScaler, StandardScaler\n",
    "from sklearn.neighbors import KNeighborsRegressor\n",
    "\n",
    "# set seaborn style\n",
    "sns.set_style('darkgrid')"
   ]
  },
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  {
   "cell_type": "code",
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   "execution_count": 3,
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   "id": "82672d3c-d574-47f1-b2f1-9a42b414e278",
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   "metadata": {},
   "outputs": [],
   "source": [
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    "data_dir='../data'"
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   ]
  },
  {
   "cell_type": "markdown",
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   "id": "747aa842-23a2-4659-abdc-3131a07894e2",
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   "metadata": {},
   "source": [
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    "## Anomaly Detection"
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   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2bb2faf-e715-4232-9d0a-723729393f0a",
   "metadata": {},
   "source": [
    "### Missing Data: JSON\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1505590-6757-4f9a-ab78-7ee2bbe9086b",
   "metadata": {},
   "source": [
    "Example for JSON and dealing with sentinel values (adopted from CleanData)."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 12,
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   "id": "8da778a9-c262-42ce-9ff3-b2330101a394",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[nan, None, inf]"
      ]
     },
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     "execution_count": 12,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "json.loads('[NaN, null, Infinity]') "
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 13,
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   "id": "161f29a5-e0a6-478b-85f9-e5fe19fdfdb4",
   "metadata": {},
   "outputs": [],
   "source": [
    "json_data = '''\n",
    "{\"a\": {\"1\": NaN, \"2\": 1.23, \"4\": 3.45, \"5\": 6.78, \"6\": 9.01},\n",
    " \"b\": {\"1\": \"Not number\", \"2\": \"A number\", \"3\": \"A null\",\n",
    "       \"4\": \"Santiago\", \"5\": \"\"}\n",
    "}'''"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 14,
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   "id": "8b476b3a-d82d-48ba-9175-b0ba5f9e2a83",
   "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>a</th>\n",
       "      <th>b</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Not number</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.23</td>\n",
       "      <td>A number</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NaN</td>\n",
       "      <td>A null</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.45</td>\n",
       "      <td>Santiago</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6.78</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>9.01</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      a           b\n",
       "1   NaN  Not number\n",
       "2  1.23    A number\n",
       "3   NaN      A null\n",
       "4  3.45    Santiago\n",
       "5  6.78            \n",
       "6  9.01         NaN"
      ]
     },
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     "execution_count": 14,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.read_json(json_data).sort_index()"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 15,
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   "id": "e4c7eadb-fab7-4b52-8a67-cac1f910509c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Row 1, Col a: Not a Number\n",
      "Row 3, Col a: Missing\n",
      "Row 5, Col b: Empty value ''\n",
      "Row 6, Col b: Missing\n"
     ]
    }
   ],
   "source": [
    "data = json.loads(json_data)\n",
    "rows = {row for dct in data.values() \n",
    "            for row in dct.keys()}\n",
    "\n",
    "for row in sorted(rows):\n",
    "    for col in data.keys():\n",
    "        val = data[col].get(row)\n",
    "        if val is None:\n",
    "            print(f\"Row {row}, Col {col}: Missing\")\n",
    "        elif isinstance(val, float) and math.isnan(val):\n",
    "            print(f\"Row {row}, Col {col}: Not a Number\")\n",
    "        elif not val:\n",
    "            print(f\"Row {row}, Col {col}: Empty value {repr(val)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b00ee68e-a37e-442f-b494-1882101e99a1",
   "metadata": {},
   "source": [
    "### Missing Data: Textual Data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d320d948-16a2-46f9-a71f-573f85fc2d51",
   "metadata": {},
   "source": [
    "Real-World data from United States National Oceanic and Atmospheric Administration: weather station at Sorstokken, Norway (adopted from CleanData)."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 16,
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   "id": "43c7d634-fb1b-47ce-80e4-666d2e362400",
   "metadata": {},
   "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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       "        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>STATION</th>\n",
       "      <th>DATE</th>\n",
       "      <th>TEMP</th>\n",
       "      <th>VISIB</th>\n",
       "      <th>GUST</th>\n",
       "      <th>DEWP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1001499999</td>\n",
       "      <td>2019-01-01</td>\n",
       "      <td>39.7</td>\n",
       "      <td>6.2</td>\n",
       "      <td>52.1</td>\n",
       "      <td>30.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1001499999</td>\n",
       "      <td>2019-01-02</td>\n",
       "      <td>36.4</td>\n",
       "      <td>6.2</td>\n",
       "      <td>999.9</td>\n",
       "      <td>29.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1001499999</td>\n",
       "      <td>2019-01-03</td>\n",
       "      <td>36.5</td>\n",
       "      <td>3.3</td>\n",
       "      <td>999.9</td>\n",
       "      <td>35.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1001499999</td>\n",
       "      <td>UNKNOWN</td>\n",
       "      <td>45.6</td>\n",
       "      <td>2.2</td>\n",
       "      <td>22.0</td>\n",
       "      <td>44.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1001499999</td>\n",
       "      <td>2019-01-06</td>\n",
       "      <td>42.5</td>\n",
       "      <td>1.9</td>\n",
       "      <td>999.9</td>\n",
       "      <td>42.5</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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>294</th>\n",
       "      <td>1001499999</td>\n",
       "      <td>2019-12-16</td>\n",
       "      <td>39.1</td>\n",
       "      <td>6.2</td>\n",
       "      <td>999.9</td>\n",
       "      <td>36.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>295</th>\n",
       "      <td>1001499999</td>\n",
       "      <td>2019-12-17</td>\n",
       "      <td>40.5</td>\n",
       "      <td>6.2</td>\n",
       "      <td>999.9</td>\n",
       "      <td>39.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>296</th>\n",
       "      <td>1001499999</td>\n",
       "      <td>2019-12-18</td>\n",
       "      <td>38.8</td>\n",
       "      <td>6.2</td>\n",
       "      <td>999.9</td>\n",
       "      <td>38.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>297</th>\n",
       "      <td>1001499999</td>\n",
       "      <td>2019-12-19</td>\n",
       "      <td>45.5</td>\n",
       "      <td>6.1</td>\n",
       "      <td>999.9</td>\n",
       "      <td>42.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>298</th>\n",
       "      <td>1001499999</td>\n",
       "      <td>2019-12-20</td>\n",
       "      <td>51.8</td>\n",
       "      <td>6.2</td>\n",
       "      <td>35.0</td>\n",
       "      <td>41.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>299 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        STATION        DATE  TEMP  VISIB   GUST  DEWP\n",
       "0    1001499999  2019-01-01  39.7    6.2   52.1  30.4\n",
       "1    1001499999  2019-01-02  36.4    6.2  999.9  29.8\n",
       "2    1001499999  2019-01-03  36.5    3.3  999.9  35.6\n",
       "3    1001499999     UNKNOWN  45.6    2.2   22.0  44.8\n",
       "4    1001499999  2019-01-06  42.5    1.9  999.9  42.5\n",
       "..          ...         ...   ...    ...    ...   ...\n",
       "294  1001499999  2019-12-16  39.1    6.2  999.9  36.8\n",
       "295  1001499999  2019-12-17  40.5    6.2  999.9  39.2\n",
       "296  1001499999  2019-12-18  38.8    6.2  999.9  38.2\n",
       "297  1001499999  2019-12-19  45.5    6.1  999.9  42.7\n",
       "298  1001499999  2019-12-20  51.8    6.2   35.0  41.2\n",
       "\n",
       "[299 rows x 6 columns]"
      ]
     },
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     "execution_count": 16,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
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    "sorstokken = pd.read_csv(os.path.join(data_dir, 'sorstokken-no.csv.gz'))\n",
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    "sorstokken"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 17,
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   "id": "97b89d82-42a9-4711-836d-f396c92f3998",
   "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>STATION</th>\n",
       "      <th>DATE</th>\n",
       "      <th>TEMP</th>\n",
       "      <th>VISIB</th>\n",
       "      <th>GUST</th>\n",
       "      <th>DEWP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1001499999</td>\n",
       "      <td>2019-01-01</td>\n",
       "      <td>27.2</td>\n",
       "      <td>1.2</td>\n",
       "      <td>17.1</td>\n",
       "      <td>16.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1001499999</td>\n",
       "      <td>UNKNOWN</td>\n",
       "      <td>88.1</td>\n",
       "      <td>999.9</td>\n",
       "      <td>999.9</td>\n",
       "      <td>63.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      STATION        DATE  TEMP  VISIB   GUST  DEWP\n",
       "0  1001499999  2019-01-01  27.2    1.2   17.1  16.5\n",
       "1  1001499999     UNKNOWN  88.1  999.9  999.9  63.5"
      ]
     },
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     "execution_count": 17,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame([sorstokken.min(), sorstokken.max()])"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 18,
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   "id": "19b41f7f-7e52-4078-9c30-c1e03fe0d7a0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Normal max:\n",
      "VISIB 6.8 ...standard deviation w/ & w/o sentinel: 254.4 / 0.7\n",
      "GUST 62.2 ...standard deviation w/ & w/o sentinel: 452.4 / 8.1\n"
     ]
    }
   ],
   "source": [
    "print(\"Normal max:\")\n",
    "for col in ['VISIB', 'GUST']:\n",
    "        s = sorstokken[col]\n",
    "        print(col, s[s < 999.9].max(), \n",
    "              \"...standard deviation w/ & w/o sentinel:\",\n",
    "              f\"{s.std():.1f} / {s[s < 999.9].std():.1f}\")"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 19,
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   "id": "7279b418-c3a3-4066-a71c-e729b54764d9",
   "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>STATION</th>\n",
       "      <th>DATE</th>\n",
       "      <th>TEMP</th>\n",
       "      <th>VISIB</th>\n",
       "      <th>GUST</th>\n",
       "      <th>DEWP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1001499999</td>\n",
       "      <td>2019-01-01</td>\n",
       "      <td>39.7</td>\n",
       "      <td>6.2</td>\n",
       "      <td>52.1</td>\n",
       "      <td>30.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1001499999</td>\n",
       "      <td>2019-01-02</td>\n",
       "      <td>36.4</td>\n",
       "      <td>6.2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>29.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1001499999</td>\n",
       "      <td>2019-01-03</td>\n",
       "      <td>36.5</td>\n",
       "      <td>3.3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>35.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1001499999</td>\n",
       "      <td>NaT</td>\n",
       "      <td>45.6</td>\n",
       "      <td>2.2</td>\n",
       "      <td>22.0</td>\n",
       "      <td>44.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1001499999</td>\n",
       "      <td>2019-01-06</td>\n",
       "      <td>42.5</td>\n",
       "      <td>1.9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>42.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      STATION       DATE  TEMP  VISIB  GUST  DEWP\n",
       "0  1001499999 2019-01-01  39.7    6.2  52.1  30.4\n",
       "1  1001499999 2019-01-02  36.4    6.2   NaN  29.8\n",
       "2  1001499999 2019-01-03  36.5    3.3   NaN  35.6\n",
       "3  1001499999        NaT  45.6    2.2  22.0  44.8\n",
       "4  1001499999 2019-01-06  42.5    1.9   NaN  42.5"
      ]
     },
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     "execution_count": 19,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
608
    "sorstokken = pd.read_csv(os.path.join(data_dir,'../data/sorstokken-no.csv.gz'), \n",
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    "                         na_values={'DATE': 'UNKNOWN', \n",
    "                                    'VISIB': '999.9',\n",
    "                                    'GUST': '999.9'},\n",
    "                         parse_dates=['DATE'])\n",
    "sorstokken.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "171f078b-8e0f-42e6-bae7-538eda9758c1",
   "metadata": {},
   "source": [
    "### Sentinel Values\n",
    "\n",
    "Example for sentinel value in Python (adopted from CleanData)"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 20,
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   "id": "6cc05d4a-9a2c-417d-91f7-4fa556b927e1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n=7:\n",
      "  method1: 1.109\n",
      "  method2: 1.109\n",
      "n=8:\n",
      "  method1: 1.229\n",
      "  method2: 1.229\n",
      "n=9:\n",
      "  method1: nan\n",
      "  method2: 1.510\n"
     ]
    }
   ],
   "source": [
    "for n in range(7, 10):\n",
    "    exp1 = 2**n\n",
    "    a = (22/7) ** exp1 \n",
652
    "    b = math.pi ** exp1\n",
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    "    # Compute answer in two \"equivalent\" ways\n",
    "    res1 = (a * a) / (b * b)\n",
    "    res2 = (a / b) * (a / b)\n",
    "    print(f\"n={n}:\\n  \"\n",
    "          f\"method1: {res1:.3f}\\n  \"\n",
    "          f\"method2: {res2:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ba3ee54-458c-49d7-84ae-aa6beb4bdcea",
   "metadata": {},
   "source": [
    "### Miscoded Data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3594e67-0140-43ac-b99a-93d9eff810ff",
   "metadata": {},
   "source": [
    "#### Ordinals"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70a7f971-ff24-4edb-9f94-3cb82b214d5f",
   "metadata": {},
   "source": [
    "Miscoded data: for ordinals, we need to check minimum, maximum and whether data type is integer; adopted from CleanData."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 6,
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   "id": "7b89a886-33ab-480c-bdf6-d2ac032991b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1)\n",
    "\n",
    "# Histopathological Attributes: (values 0, 1, 2, 3)\n",
    "# Clinical Attributes: (values 0, 1, 2, 3, unless indicated)\n",
    "features = [\n",
    "    \"erythema\",\n",
    "    \"scaling\",\n",
    "    \"definite borders\",\n",
    "    \"itching\",\n",
    "    \"koebner phenomenon\",\n",
    "    \"polygonal papules\",\n",
    "    \"follicular papules\",\n",
    "    \"oral mucosal involvement\",\n",
    "    \"knee and elbow involvement\",\n",
    "    \"scalp involvement\",\n",
    "    \"family history\",  # 0 or 1\n",
    "    \"melanin incontinence\",\n",
    "    \"eosinophils in the infiltrate\",\n",
    "    \"PNL infiltrate\",\n",
    "    \"fibrosis of the papillary dermis\",\n",
    "    \"exocytosis\",\n",
    "    \"acanthosis\",\n",
    "    \"hyperkeratosis\",\n",
    "    \"parakeratosis\",\n",
    "    \"clubbing of the rete ridges\",\n",
    "    \"elongation of the rete ridges\",\n",
    "    \"thinning of the suprapapillary epidermis\",\n",
    "    \"spongiform pustule\",\n",
    "    \"munro microabcess\",\n",
    "    \"focal hypergranulosis\",\n",
    "    \"disappearance of the granular layer\",\n",
    "    \"vacuolisation and damage of basal layer\",\n",
    "    \"spongiosis\",\n",
    "    \"saw-tooth appearance of retes\",\n",
    "    \"follicular horn plug\",\n",
    "    \"perifollicular parakeratosis\",\n",
    "    \"inflammatory monoluclear inflitrate\",\n",
    "    \"band-like infiltrate\",\n",
    "    \"Age\",  # linear; missing marked '?'\n",
    "    \"TARGET\"  # See mapping\n",
    "]\n",
    "\n",
    "targets = {\n",
    "    1:\"psoriasis\",                 # 112 instances\n",
    "    2:\"seboreic dermatitis\",       # 61\n",
    "    3:\"lichen planus\",             # 72\n",
    "    4:\"pityriasis rosea\",          # 49\n",
    "    5:\"cronic dermatitis\",         # 52\n",
    "    6:\"pityriasis rubra pilaris\",  # 20\n",
    "}\n",
    "\n",
    "\n",
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    "data = os.path.join(data_dir, 'dermatology.data')\n",
    "metadata = os.path.join(data_dir, 'dermatology.names')\n",
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    "df = pd.read_csv(data, header=None, names=features)\n",
    "df['TARGET'] = df.TARGET.map(targets)\n",
    "\n",
    "derm = df.copy()\n",
    "derm.loc[derm.Age == '?', 'Age'] = None\n",
    "derm['Age'] = derm.Age.astype(float)"
   ]
  },
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  {
   "cell_type": "markdown",
   "id": "45f6a92b-4b9c-4a81-bcb3-1fbac980f682",
   "metadata": {},
   "source": [
    "**Todo for all:** have a look at dermatology.names and dermatology.data for further information on the data, its provenance and structure."
   ]
  },
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  {
   "cell_type": "code",
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   "execution_count": 7,
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   "id": "0348f05a-931a-43b1-8361-eb95e6a0118d",
   "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>min</th>\n",
       "      <th>max</th>\n",
       "      <th>dtype</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>erythema</th>\n",
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       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>int64</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>scaling</th>\n",
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       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>int64</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>definite borders</th>\n",
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       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>int64</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>itching</th>\n",
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       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>int64</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>koebner phenomenon</th>\n",
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       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>int64</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>perifollicular parakeratosis</th>\n",
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       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>int64</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>inflammatory monoluclear inflitrate</th>\n",
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       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>int64</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>band-like infiltrate</th>\n",
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       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>int64</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>Age</th>\n",
       "      <td>0.0</td>\n",
       "      <td>75.0</td>\n",
       "      <td>float64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TARGET</th>\n",
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       "      <td>cronic dermatitis</td>\n",
       "      <td>seboreic dermatitis</td>\n",
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       "      <td>object</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>35 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
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       "                                                   min                  max  \\\n",
       "erythema                                             0                    3   \n",
       "scaling                                              0                    3   \n",
       "definite borders                                     0                    3   \n",
       "itching                                              0                    3   \n",
       "koebner phenomenon                                   0                    3   \n",
       "...                                                ...                  ...   \n",
       "perifollicular parakeratosis                         0                    3   \n",
       "inflammatory monoluclear inflitrate                  0                    3   \n",
       "band-like infiltrate                                 0                    3   \n",
       "Age                                                0.0                 75.0   \n",
       "TARGET                               cronic dermatitis  seboreic dermatitis   \n",
       "\n",
       "                                       dtype  \n",
       "erythema                               int64  \n",
       "scaling                                int64  \n",
       "definite borders                       int64  \n",
       "itching                                int64  \n",
       "koebner phenomenon                     int64  \n",
       "...                                      ...  \n",
       "perifollicular parakeratosis           int64  \n",
       "inflammatory monoluclear inflitrate    int64  \n",
       "band-like infiltrate                   int64  \n",
       "Age                                  float64  \n",
       "TARGET                                object  \n",
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       "\n",
       "[35 rows x 3 columns]"
      ]
     },
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     "execution_count": 7,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(pd.DataFrame(\n",
    "    [derm.min(), derm.max(), derm.dtypes])\n",
    "     .T\n",
    "     .rename(columns={0:'min', 1:'max', 2:'dtype'})\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2510cb5c-6bed-4fe5-8492-b07f1a3d12c2",
   "metadata": {},
   "source": [
    "#### Categorical Data"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 23,
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   "id": "5286816f-dbef-4a9f-8f86-b04c6f7f0696",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\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>Height</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Hair_Length</th>\n",
       "      <th>Favorite</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>21492</th>\n",
       "      <td>176.958650</td>\n",
       "      <td>72.604585</td>\n",
       "      <td>14.0</td>\n",
       "      <td>red</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9488</th>\n",
       "      <td>169.000221</td>\n",
       "      <td>79.559843</td>\n",
       "      <td>0.0</td>\n",
       "      <td>blue</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16933</th>\n",
       "      <td>171.104306</td>\n",
       "      <td>71.125528</td>\n",
       "      <td>5.5</td>\n",
       "      <td>red</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12604</th>\n",
       "      <td>174.481084</td>\n",
       "      <td>79.496237</td>\n",
       "      <td>8.1</td>\n",
       "      <td>blue</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8222</th>\n",
       "      <td>171.275578</td>\n",
       "      <td>77.094118</td>\n",
       "      <td>14.6</td>\n",
       "      <td>green</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Height     Weight  Hair_Length Favorite\n",
       "21492  176.958650  72.604585         14.0      red\n",
       "9488   169.000221  79.559843          0.0     blue\n",
       "16933  171.104306  71.125528          5.5      red\n",
       "12604  174.481084  79.496237          8.1     blue\n",
       "8222   171.275578  77.094118         14.6    green"
      ]
     },
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     "execution_count": 23,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
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    "humans = pd.read_csv(os.path.join(data_dir, 'humans-err.csv'))\n",
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    "# random_stae for deterministic sample\n",
    "humans.sample(5, random_state=1)"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 24,
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   "id": "1cb4ad60-1d4b-4f87-bd51-340c5012a218",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['red', 'green', 'blue', 'Red', ' red', 'grееn', 'blüe',\n",
       "       'chartreuse'], dtype=object)"
      ]
     },
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     "execution_count": 24,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# observe unique values\n",
    "humans.Favorite.unique()"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 25,
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   "id": "aeb97307-c7cd-4aca-ac0e-ca43325ac5ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "red           9576\n",
       "blue          7961\n",
       "green         7458\n",
       "Red              1\n",
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       " red             1\n",
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       "grееn            1\n",
       "blüe             1\n",
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       "chartreuse       1\n",
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       "Name: Favorite, dtype: int64"
      ]
     },
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     "execution_count": 25,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# how rare are such variations?\n",
    "humans.Favorite.value_counts()"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 26,
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   "id": "e0d9609a-1a45-4727-b2a0-f5153a83e3e0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       red [32, 114, 101, 100]\n",
      "       Red [82, 101, 100]\n",
      "      blue [98, 108, 117, 101]\n",
      "      blüe [98, 108, 252, 101]\n",
      "chartreuse [99, 104, 97, 114, 116, 114, 101, 117, 115, 101]\n",
      "     green [103, 114, 101, 101, 110]\n",
      "     grееn [103, 114, 1077, 1077, 110]\n",
      "       red [114, 101, 100]\n"
     ]
    }
   ],
   "source": [
    "# look at labels more closely\n",
    "for color in sorted(humans.Favorite.unique()):\n",
    "    print(f\"{color:>10s}\", [ord(c) for c in color])"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 27,
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   "id": "5e76c750-1925-45f1-8909-73853079737a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "red      9578\n",
       "blue     7962\n",
       "green    7459\n",
       "Name: Favorite, dtype: int64"
      ]
     },
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     "execution_count": 27,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# transform troublesome values\n",
    "humans.loc[humans.Favorite.isin(['Red', ' red']), 'Favorite'] = 'red'\n",
    "humans.loc[humans.Favorite == 'chartreuse', 'Favorite'] = None\n",
    "humans.loc[humans.Favorite == 'blüe', 'Favorite'] = 'blue'\n",
    "humans.loc[humans.Favorite == 'grееn', 'Favorite'] = 'green'\n",
    "humans.Favorite.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d09918c6-2e4b-4e19-88b8-cf26f639a057",
   "metadata": {},
   "source": [
    "### Fixed Bounds"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d023b7dd-59b2-4fd4-a115-45da44647d1c",
   "metadata": {},
   "source": [
    "Continues previous example of humans, adapted from CleanData."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 28,
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   "id": "420205a3-2266-4441-a8de-4d86d5ad9605",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
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     "execution_count": 28,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# any humans exceeding the given bounds?\n",
    "((humans.Height < 92) | (humans.Height > 213)).any()"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 29,
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   "id": "8aea02dd-a13a-4753-9d12-c8834de31c1e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Height</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Hair_Length</th>\n",
       "      <th>Favorite</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1984</th>\n",
       "      <td>165.634695</td>\n",
       "      <td>62.979993</td>\n",
       "      <td>127.0</td>\n",
       "      <td>red</td>\n",
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       "    <tr>\n",
       "      <th>8929</th>\n",
       "      <td>175.186061</td>\n",
       "      <td>73.899992</td>\n",
       "      <td>120.6</td>\n",
       "      <td>blue</td>\n",
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       "    <tr>\n",
       "      <th>14673</th>\n",
       "      <td>174.948037</td>\n",
       "      <td>77.644434</td>\n",
       "      <td>130.1</td>\n",
       "      <td>blue</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14735</th>\n",
       "      <td>176.385525</td>\n",
       "      <td>68.735397</td>\n",
       "      <td>121.7</td>\n",
       "      <td>green</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16672</th>\n",
       "      <td>173.172298</td>\n",
       "      <td>71.814699</td>\n",
       "      <td>121.4</td>\n",
       "      <td>red</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17093</th>\n",
       "      <td>169.771111</td>\n",
       "      <td>77.958278</td>\n",
       "      <td>133.2</td>\n",
       "      <td>blue</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Height     Weight  Hair_Length Favorite\n",
       "1984   165.634695  62.979993        127.0      red\n",
       "8929   175.186061  73.899992        120.6     blue\n",
       "14673  174.948037  77.644434        130.1     blue\n",
       "14735  176.385525  68.735397        121.7    green\n",
       "16672  173.172298  71.814699        121.4      red\n",
       "17093  169.771111  77.958278        133.2     blue"
      ]
     },
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     "execution_count": 29,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "humans.query('Hair_Length > 120')"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 30,
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   "id": "a78e7b9f-20f3-4dba-bb1d-0f775a1c530f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>Height</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Hair_Length</th>\n",
       "      <th>Favorite</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1984</th>\n",
       "      <td>165.634695</td>\n",
       "      <td>62.979993</td>\n",
       "      <td>120.0</td>\n",
       "      <td>red</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4146</th>\n",
       "      <td>173.930107</td>\n",
       "      <td>72.701456</td>\n",
       "      <td>119.6</td>\n",
       "      <td>red</td>\n",
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       "    <tr>\n",
       "      <th>8929</th>\n",
       "      <td>175.186061</td>\n",
       "      <td>73.899992</td>\n",
       "      <td>120.0</td>\n",
       "      <td>blue</td>\n",
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       "    <tr>\n",
       "      <th>9259</th>\n",
       "      <td>179.215974</td>\n",
       "      <td>82.538890</td>\n",
       "      <td>119.4</td>\n",
       "      <td>green</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14673</th>\n",
       "      <td>174.948037</td>\n",
       "      <td>77.644434</td>\n",
       "      <td>120.0</td>\n",
       "      <td>blue</td>\n",
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       "    <tr>\n",
       "      <th>14735</th>\n",
       "      <td>176.385525</td>\n",
       "      <td>68.735397</td>\n",
       "      <td>120.0</td>\n",
       "      <td>green</td>\n",
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       "    <tr>\n",
       "      <th>16672</th>\n",
       "      <td>173.172298</td>\n",
       "      <td>71.814699</td>\n",
       "      <td>120.0</td>\n",
       "      <td>red</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17093</th>\n",
       "      <td>169.771111</td>\n",
       "      <td>77.958278</td>\n",
       "      <td>120.0</td>\n",
       "      <td>blue</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Height     Weight  Hair_Length Favorite\n",
       "1984   165.634695  62.979993        120.0      red\n",
       "4146   173.930107  72.701456        119.6      red\n",
       "8929   175.186061  73.899992        120.0     blue\n",
       "9259   179.215974  82.538890        119.4    green\n",
       "14673  174.948037  77.644434        120.0     blue\n",
       "14735  176.385525  68.735397        120.0    green\n",
       "16672  173.172298  71.814699        120.0      red\n",
       "17093  169.771111  77.958278        120.0     blue"
      ]
     },
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     "execution_count": 30,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "humans2 = humans.copy()  # Retain prior versions of data set\n",
    "humans2['Hair_Length'] = humans2.Hair_Length.clip(upper=120)\n",
    "humans2[humans2.Hair_Length > 119]"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 31,
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   "id": "122cdada-e0b8-422a-a97d-3b7cc4d5d964",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\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>Height</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Hair_Length</th>\n",
       "      <th>Favorite</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>177.297182</td>\n",
       "      <td>81.153493</td>\n",
       "      <td>0.0</td>\n",
       "      <td>blue</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>217</th>\n",
       "      <td>171.893967</td>\n",
       "      <td>68.553526</td>\n",
       "      <td>0.0</td>\n",
       "      <td>blue</td>\n",
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       "    <tr>\n",
       "      <th>240</th>\n",
       "      <td>161.862237</td>\n",
       "      <td>76.914599</td>\n",
       "      <td>0.0</td>\n",
       "      <td>blue</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>354</th>\n",
       "      <td>172.972247</td>\n",
       "      <td>73.175032</td>\n",
       "      <td>0.0</td>\n",
       "      <td>red</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>371</th>\n",
       "      <td>179.866011</td>\n",
       "      <td>80.418554</td>\n",
       "      <td>0.0</td>\n",
       "      <td>red</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24818</th>\n",
       "      <td>171.537554</td>\n",
       "      <td>72.619095</td>\n",
       "      <td>0.0</td>\n",
       "      <td>green</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24834</th>\n",
       "      <td>170.991301</td>\n",
       "      <td>67.652660</td>\n",
       "      <td>0.0</td>\n",
       "      <td>green</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24892</th>\n",
       "      <td>177.002643</td>\n",
       "      <td>77.286141</td>\n",
       "      <td>0.0</td>\n",
       "      <td>green</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24919</th>\n",
       "      <td>169.012286</td>\n",
       "      <td>74.593809</td>\n",
       "      <td>0.0</td>\n",
       "      <td>blue</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24967</th>\n",
       "      <td>169.061308</td>\n",
       "      <td>65.985481</td>\n",
       "      <td>0.0</td>\n",
       "      <td>green</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>517 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           Height     Weight  Hair_Length Favorite\n",
       "6      177.297182  81.153493          0.0     blue\n",
       "217    171.893967  68.553526          0.0     blue\n",
       "240    161.862237  76.914599          0.0     blue\n",
       "354    172.972247  73.175032          0.0      red\n",
       "371    179.866011  80.418554          0.0      red\n",
       "...           ...        ...          ...      ...\n",
       "24818  171.537554  72.619095          0.0    green\n",
       "24834  170.991301  67.652660          0.0    green\n",
       "24892  177.002643  77.286141          0.0    green\n",
       "24919  169.012286  74.593809          0.0     blue\n",
       "24967  169.061308  65.985481          0.0    green\n",
       "\n",
       "[517 rows x 4 columns]"
      ]
     },
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     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "humans2[humans2.Hair_Length == 0]"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 32,
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   "id": "02eda6a2-6702-4c97-b7d1-89d54609f4be",
   "metadata": {},
   "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",
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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>Height</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Hair_Length</th>\n",
       "      <th>Favorite</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>493</th>\n",
       "      <td>167.703398</td>\n",
       "      <td>72.567763</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>blue</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>528</th>\n",
       "      <td>167.355393</td>\n",
       "      <td>60.276190</td>\n",
       "      <td>-20.7</td>\n",
       "      <td>green</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>562</th>\n",
       "      <td>172.416114</td>\n",
       "      <td>60.867457</td>\n",
       "      <td>-68.1</td>\n",
       "      <td>green</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>569</th>\n",
       "      <td>177.644146</td>\n",
       "      <td>74.027147</td>\n",
       "      <td>-5.9</td>\n",
       "      <td>green</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>738</th>\n",
       "      <td>178.094818</td>\n",
       "      <td>76.963924</td>\n",
       "      <td>-57.2</td>\n",
       "      <td>blue</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>24042</th>\n",
       "      <td>174.608922</td>\n",
       "      <td>64.846422</td>\n",
       "      <td>-22.7</td>\n",
       "      <td>green</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24055</th>\n",
       "      <td>172.831608</td>\n",
       "      <td>74.096660</td>\n",
       "      <td>-13.3</td>\n",
       "      <td>red</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24063</th>\n",
       "      <td>172.687488</td>\n",
       "      <td>69.466838</td>\n",
       "      <td>-14.2</td>\n",
       "      <td>green</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24386</th>\n",
       "      <td>176.668430</td>\n",
       "      <td>62.984811</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>green</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24944</th>\n",
       "      <td>172.300925</td>\n",
       "      <td>72.067862</td>\n",
       "      <td>-24.4</td>\n",
       "      <td>red</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>118 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           Height     Weight  Hair_Length Favorite\n",
       "493    167.703398  72.567763         -1.0     blue\n",
       "528    167.355393  60.276190        -20.7    green\n",
       "562    172.416114  60.867457        -68.1    green\n",
       "569    177.644146  74.027147         -5.9    green\n",
       "738    178.094818  76.963924        -57.2     blue\n",
       "...           ...        ...          ...      ...\n",
       "24042  174.608922  64.846422        -22.7    green\n",
       "24055  172.831608  74.096660        -13.3      red\n",
       "24063  172.687488  69.466838        -14.2    green\n",
       "24386  176.668430  62.984811         -1.0    green\n",
       "24944  172.300925  72.067862        -24.4      red\n",
       "\n",
       "[118 rows x 4 columns]"
      ]
     },
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     "execution_count": 32,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "neg_hair = humans2[humans2.Hair_Length < 0]\n",
    "neg_hair"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 33,
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   "id": "c29e21b4-1bec-4ab7-9328-bf7122a14278",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    118.000000\n",
       "mean     -24.348305\n",
       "std       22.484691\n",
       "min      -95.700000\n",
       "25%      -38.075000\n",
       "50%      -20.650000\n",
       "75%       -5.600000\n",
       "max       -0.700000\n",
       "Name: Hair_Length, dtype: float64"
      ]
     },
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     "execution_count": 33,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "neg_hair.Hair_Length.describe()"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 34,
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   "id": "0fec5b37-cfd8-456f-b97d-fd16785bc86e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    24365.000000\n",
       "mean        26.675485\n",
       "std         21.206516\n",
       "min          0.100000\n",
       "25%          9.900000\n",
       "50%         21.700000\n",
       "75%         38.400000\n",
       "max        120.000000\n",
       "Name: Hair_Length, dtype: float64"
      ]
     },
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     "execution_count": 34,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pos_hair = humans2[humans2.Hair_Length > 0]\n",
    "pos_hair.Hair_Length.describe()"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 35,
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   "id": "77d46cf5-721f-487f-a834-2bb52a27ce9c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 2.,  0.,  0.,  0.,  0.,  2.,  0.,  0.,  2.,  3.,  0.,  1.,  5.,\n",
       "         1.,  4.,  1.,  3.,  5.,  4.,  3.,  6.,  3.,  8.,  7.,  2.,  4.,\n",
       "         9.,  8., 12., 23.]),\n",
       " array([-95.7       , -92.53333333, -89.36666667, -86.2       ,\n",
       "        -83.03333333, -79.86666667, -76.7       , -73.53333333,\n",
       "        -70.36666667, -67.2       , -64.03333333, -60.86666667,\n",
       "        -57.7       , -54.53333333, -51.36666667, -48.2       ,\n",
       "        -45.03333333, -41.86666667, -38.7       , -35.53333333,\n",
       "        -32.36666667, -29.2       , -26.03333333, -22.86666667,\n",
       "        -19.7       , -16.53333333, -13.36666667, -10.2       ,\n",
       "         -7.03333333,  -3.86666667,  -0.7       ]),\n",
       " <BarContainer object of 30 artists>)"
      ]
     },
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Distribution of invalid negative hair length')"
      ]
     },
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     "execution_count": 35,
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    {
     "data": {
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      "text/plain": [
       "Text(0.5, 0, 'Hair length')"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Number of humans')"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "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": [
    "sns.set_style('darkgrid')\n",
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    "plt.hist(neg_hair.Hair_Length, bins=30)\n",
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    "plt.title(\"Distribution of invalid negative hair length\")\n",
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    "plt.xlabel('Hair length')\n",
    "plt.ylabel('Number of humans')"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 36,
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   "id": "e2ed85e9-4aa8-4621-959f-89a0c61222d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([2455., 2545., 2315., 2181., 1934., 1786., 1625., 1484., 1269.,\n",
       "        1132.,  971.,  814.,  718.,  571.,  487.,  444.,  354.,  309.,\n",
       "         241.,  170.,  137.,  105.,   77.,   77.,   44.,   43.,   27.,\n",
       "          15.,   13.,   22.]),\n",
       " array([1.00000000e-01, 4.09666667e+00, 8.09333333e+00, 1.20900000e+01,\n",
       "        1.60866667e+01, 2.00833333e+01, 2.40800000e+01, 2.80766667e+01,\n",
       "        3.20733333e+01, 3.60700000e+01, 4.00666667e+01, 4.40633333e+01,\n",
       "        4.80600000e+01, 5.20566667e+01, 5.60533333e+01, 6.00500000e+01,\n",
       "        6.40466667e+01, 6.80433333e+01, 7.20400000e+01, 7.60366667e+01,\n",
       "        8.00333333e+01, 8.40300000e+01, 8.80266667e+01, 9.20233333e+01,\n",
       "        9.60200000e+01, 1.00016667e+02, 1.04013333e+02, 1.08010000e+02,\n",
       "        1.12006667e+02, 1.16003333e+02, 1.20000000e+02]),\n",
       " <BarContainer object of 30 artists>)"
      ]
     },
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     "execution_count": 36,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Distribution of positive hair length')"
      ]
     },
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     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Hair length')"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Number of humans')"
      ]
     },
     "execution_count": 36,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.hist(pos_hair.Hair_Length, bins=30,)\n",
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    "plt.title('Distribution of positive hair length')\n",
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    "plt.xlabel('Hair length')\n",
    "plt.ylabel('Number of humans')"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 37,
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   "id": "a50e0d11-b2e4-4630-8fb0-83e0a0afca5a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.0     19\n",
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       "-41.6     2\n",
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       "-10.9     2\n",
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       "-6.8      2\n",
       "-8.5      2\n",
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       "         ..\n",
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       "-19.4     1\n",
       "-25.1     1\n",
       "-13.5     1\n",
       "-42.2     1\n",
       "-24.4     1\n",
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       "Name: Hair_Length, Length: 93, dtype: int64"
      ]
     },
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     "execution_count": 37,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "neg_hair.Hair_Length.value_counts()"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 38,
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   "id": "a829de93-fba0-4669-a533-28cf61a0196e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([2919., 2559., 2324., 2198., 1959., 1776., 1646., 1496., 1278.,\n",
       "        1143.,  979.,  802.,  733.,  579.,  496.,  441.,  361.,  311.,\n",
       "         243.,  171.,  141.,  105.,   75.,   80.,   44.,   45.,   26.,\n",
       "          16.,   13.,   22.]),\n",
       " array([  0.,   4.,   8.,  12.,  16.,  20.,  24.,  28.,  32.,  36.,  40.,\n",
       "         44.,  48.,  52.,  56.,  60.,  64.,  68.,  72.,  76.,  80.,  84.,\n",
       "         88.,  92.,  96., 100., 104., 108., 112., 116., 120.]),\n",
       " <BarContainer object of 30 artists>)"
      ]
     },
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     "execution_count": 38,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Distribution of corrected hair lengths')"
      ]
     },
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     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Hair length')"
      ]
     },
     "execution_count": 38,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "Text(0, 0.5, 'Number of humans')"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "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": [
    "humans3 = humans2.copy()     # Versioned changes to data\n",
    "\n",
    "# The \"sentinel\" negative value means missing\n",
    "humans3.loc[humans3.Hair_Length == -1, 'Hair_Length'] = None\n",
    "\n",
    "# All other values simply become non-negative\n",
    "humans3['Hair_Length'] = humans3.Hair_Length.abs()\n",
    "\n",
    "plt.hist(humans3.Hair_Length, bins=30)\n",
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    "plt.title('Distribution of corrected hair lengths')\n",
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    "plt.xlabel('Hair length')\n",
    "plt.ylabel('Number of humans')"
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   ]
  },
  {
   "cell_type": "markdown",
   "id": "e31b017b-036a-4ba0-8216-c2a3ceb0555e",
   "metadata": {},
   "source": [
    "### Outlier Detection"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62b43554-02b5-495f-858f-a21de1e91549",
   "metadata": {},
   "source": [
    "#### Z-Score"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5d85e2b-8f25-4859-96c2-2a5d1e9799a3",
   "metadata": {},
   "source": [
    "Tests for normal distribution"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 39,
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   "id": "f0787b5f-1c1e-4d23-a561-e8d6160a80b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
2012
      "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": [
    "def plot_distribution(data):\n",
    "    # fit normal distribution -> compute mean and std\n",
    "    mean, std = norm.fit(data)\n",
    "    \n",
    "    plt.hist(data, bins=50)\n",
    "    \n",
    "    # compute probability density function for given distribution\n",
    "    xmin, xmax = plt.xlim()\n",
    "    x = np.linspace(xmin, xmax, 100)\n",
    "    p = norm.pdf(x, mean, std)\n",
    "    plt.plot(x, p, 'k')\n",
    "    \n",
    "    title = \"Fit Values: {:.2f} and {:.2f}\".format(mean, std)\n",
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    "    plt.xlabel(\"Height\")\n",
    "    plt.ylabel(\"Number of humans\")\n",
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    "    plt.title(title)\n",
    "    plt.show()\n",
    "\n",
    "plot_distribution(humans.Height)"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 40,
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   "id": "e2a8f65e-1d9d-468a-a614-65ffd512e492",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
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     "execution_count": 40,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# test for normal distribution\n",
    "# plot boxplot (in this case, via pandas)\n",
    "humans.Height.plot(kind = 'box')"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 41,
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   "id": "4dfb45f0-8114-4c8f-b4c5-1cc1924740c5",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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      "/home/eva/.local/share/virtualenvs/data-engineering-analytics-notebooks-Qx0adyYX/lib64/python3.9/site-packages/statsmodels/graphics/gofplots.py:993: UserWarning: marker is redundantly defined by the 'marker' keyword argument and the fmt string \"bo\" (-> marker='o'). The keyword argument will take precedence.\n",
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      "  ax.plot(x, y, fmt, **plot_style)\n"
     ]
    },
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
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     "execution_count": 41,
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     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "## QQ plot\n",
    "sm.qqplot(humans.Height, line='45',fit=True)"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 42,
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   "id": "c388b2eb-5dcb-4556-8eae-9fb309355765",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0 0.0\n"
     ]
    }
   ],
   "source": [
    "# Kolmogorov-Smirnov test\n",
    "ks_statistic, p_value = kstest(humans.Height, 'norm')\n",
    "print(ks_statistic, p_value)"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 43,
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   "id": "204e833c-0f26-49c3-ae4e-1fe6f82b6fbc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Height', 'Weight', 'Hair_Length', 'Favorite', 'zscore_Height',\n",
       "       'zscore_Weight', 'zscore_Hair_Length'],\n",
       "      dtype='object')"
      ]
     },
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     "execution_count": 43,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute z-scores\n",
    "\n",
    "humans4 = humans3.copy()\n",
    "\n",
    "for var in ('Height', 'Weight', 'Hair_Length'):\n",
    "    zscore = (humans4[var] - humans4[var].mean()) / humans4[var].std()\n",
    "    humans4[f\"zscore_{var}\"] = zscore\n",
    "\n",
    "humans4.columns"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 44,
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2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
2340
2341
2342
2343
2344
2345
2346
2347
2348
2349
   "id": "f439a5f5-9710-4cd7-989f-9907dfac9bca",
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   "outputs": [
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       "      <th>Height</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Hair_Length</th>\n",
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       "      <th>zscore_Weight</th>\n",
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       "      <th>138</th>\n",
       "      <td>187.708718</td>\n",
       "      <td>86.829633</td>\n",
       "      <td>19.3</td>\n",
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       "      <td>2.084216</td>\n",
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       "    <tr>\n",
       "      <th>174</th>\n",
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       "      <th>412</th>\n",
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       "      <td>-1.542673</td>\n",
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       "    <tr>\n",
       "      <th>1162</th>\n",