1656 lines
187 KiB
Plaintext
1656 lines
187 KiB
Plaintext
{
|
||
"cells": [
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"<div style=\"\n",
|
||
" border: 2px solid #4CAF50; \n",
|
||
" padding: 15px; \n",
|
||
" background-color: #f4f4f4; \n",
|
||
" border-radius: 10px; \n",
|
||
" align-items: center;\">\n",
|
||
"\n",
|
||
"<h1 style=\"margin: 0; color: #4CAF50;\">Statistik im Data Science Bereich (Zentralmaße)</h1>\n",
|
||
"<h2 style=\"margin: 5px 0; color: #555;\">DSAI</h2>\n",
|
||
"<h3 style=\"margin: 5px 0; color: #555;\">Jakob Eggl</h3>\n",
|
||
"\n",
|
||
"<div style=\"flex-shrink: 0;\">\n",
|
||
" <img src=\"https://www.htl-grieskirchen.at/wp/wp-content/uploads/2022/11/logo_bildschirm-1024x503.png\" alt=\"Logo\" style=\"width: 250px; height: auto;\"/>\n",
|
||
"</div>\n",
|
||
"<p1> © 2024/25 Jakob Eggl. Nutzung oder Verbreitung nur mit ausdrücklicher Genehmigung des Autors.</p1>\n",
|
||
"</div>\n",
|
||
"<div style=\"flex: 1;\">\n",
|
||
"</div> "
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"# Statistik"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Warum Statisik(en) wichtig ist/sind:\n",
|
||
"* Geben Einblick in die (numerischen) Daten\n",
|
||
"* Mathematik lässt nur wenig Spielraum für subjektive Interpretationen bzw. (Mis)interpretationen\n",
|
||
"* Erlauben Vergleich zwischen verschiedenen Datensätzen\n",
|
||
"* Unterstützen bei der Identifikation von Ausreißern und Anomalien\n",
|
||
"* Helfen bei der Bestimmung von Trends und Mustern\n",
|
||
"* Ermöglichen fundierte Entscheidungen basierend auf Daten\n",
|
||
"* Unterstützen bei der Validierung von Hypothesen und Modellen"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"<b>Aber:</b>\n",
|
||
"Statistiken können auch <b>täuschen</b>, wie wir später sehen werden!"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Allgemein lassen sich die verschiedenen, für uns interessanten, Größen folgendermaßen gruppieren:\n",
|
||
"* <b>Lage- und Zentralmaße:</b> Mittelwert, Median, Modus, Geometrisches Mittel, Harmonisches Mittel, Quartile, Quantile\n",
|
||
"* <b>Streuungsmaße:</b> Varianz, Standardabweichung, Spannweite, Interquartilsabstand"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Wir arbeiten (vorerst) wieder mit unserem Titanic Dataset."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 1,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"import pandas as pd\n",
|
||
"import os\n",
|
||
"\n",
|
||
"path = os.path.join(\"..\", \"..\", \"_data\", \"titanic.csv\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"df = pd.read_csv(path, decimal=\".\", sep=\",\", header=0, index_col=False)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"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>pclass</th>\n",
|
||
" <th>survived</th>\n",
|
||
" <th>name</th>\n",
|
||
" <th>sex</th>\n",
|
||
" <th>age</th>\n",
|
||
" <th>sibsp</th>\n",
|
||
" <th>parch</th>\n",
|
||
" <th>ticket</th>\n",
|
||
" <th>fare</th>\n",
|
||
" <th>cabin</th>\n",
|
||
" <th>embarked</th>\n",
|
||
" <th>boat</th>\n",
|
||
" <th>body</th>\n",
|
||
" <th>home.dest</th>\n",
|
||
" </tr>\n",
|
||
" </thead>\n",
|
||
" <tbody>\n",
|
||
" <tr>\n",
|
||
" <th>0</th>\n",
|
||
" <td>1</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>Allen, Miss. Elisabeth Walton</td>\n",
|
||
" <td>female</td>\n",
|
||
" <td>29.0000</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>24160</td>\n",
|
||
" <td>211.3375</td>\n",
|
||
" <td>B5</td>\n",
|
||
" <td>S</td>\n",
|
||
" <td>2</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>St Louis, MO</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>1</th>\n",
|
||
" <td>1</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>Allison, Master. Hudson Trevor</td>\n",
|
||
" <td>male</td>\n",
|
||
" <td>0.9167</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>2</td>\n",
|
||
" <td>113781</td>\n",
|
||
" <td>151.5500</td>\n",
|
||
" <td>C22 C26</td>\n",
|
||
" <td>S</td>\n",
|
||
" <td>11</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>Montreal, PQ / Chesterville, ON</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>2</th>\n",
|
||
" <td>1</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>Allison, Miss. Helen Loraine</td>\n",
|
||
" <td>female</td>\n",
|
||
" <td>2.0000</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>2</td>\n",
|
||
" <td>113781</td>\n",
|
||
" <td>151.5500</td>\n",
|
||
" <td>C22 C26</td>\n",
|
||
" <td>S</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>Montreal, PQ / Chesterville, ON</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>3</th>\n",
|
||
" <td>1</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>Allison, Mr. Hudson Joshua Creighton</td>\n",
|
||
" <td>male</td>\n",
|
||
" <td>30.0000</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>2</td>\n",
|
||
" <td>113781</td>\n",
|
||
" <td>151.5500</td>\n",
|
||
" <td>C22 C26</td>\n",
|
||
" <td>S</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>135.0</td>\n",
|
||
" <td>Montreal, PQ / Chesterville, ON</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>4</th>\n",
|
||
" <td>1</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>Allison, Mrs. Hudson J C (Bessie Waldo Daniels)</td>\n",
|
||
" <td>female</td>\n",
|
||
" <td>25.0000</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>2</td>\n",
|
||
" <td>113781</td>\n",
|
||
" <td>151.5500</td>\n",
|
||
" <td>C22 C26</td>\n",
|
||
" <td>S</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>Montreal, PQ / Chesterville, ON</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>...</th>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>1304</th>\n",
|
||
" <td>3</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>Zabour, Miss. Hileni</td>\n",
|
||
" <td>female</td>\n",
|
||
" <td>14.5000</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>2665</td>\n",
|
||
" <td>14.4542</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>C</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>328.0</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>1305</th>\n",
|
||
" <td>3</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>Zabour, Miss. Thamine</td>\n",
|
||
" <td>female</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>2665</td>\n",
|
||
" <td>14.4542</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>C</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>1306</th>\n",
|
||
" <td>3</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>Zakarian, Mr. Mapriededer</td>\n",
|
||
" <td>male</td>\n",
|
||
" <td>26.5000</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>2656</td>\n",
|
||
" <td>7.2250</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>C</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>304.0</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>1307</th>\n",
|
||
" <td>3</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>Zakarian, Mr. Ortin</td>\n",
|
||
" <td>male</td>\n",
|
||
" <td>27.0000</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>2670</td>\n",
|
||
" <td>7.2250</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>C</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>1308</th>\n",
|
||
" <td>3</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>Zimmerman, Mr. Leo</td>\n",
|
||
" <td>male</td>\n",
|
||
" <td>29.0000</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>315082</td>\n",
|
||
" <td>7.8750</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>S</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" </tr>\n",
|
||
" </tbody>\n",
|
||
"</table>\n",
|
||
"<p>1309 rows × 14 columns</p>\n",
|
||
"</div>"
|
||
],
|
||
"text/plain": [
|
||
" pclass survived name \\\n",
|
||
"0 1 1 Allen, Miss. Elisabeth Walton \n",
|
||
"1 1 1 Allison, Master. Hudson Trevor \n",
|
||
"2 1 0 Allison, Miss. Helen Loraine \n",
|
||
"3 1 0 Allison, Mr. Hudson Joshua Creighton \n",
|
||
"4 1 0 Allison, Mrs. Hudson J C (Bessie Waldo Daniels) \n",
|
||
"... ... ... ... \n",
|
||
"1304 3 0 Zabour, Miss. Hileni \n",
|
||
"1305 3 0 Zabour, Miss. Thamine \n",
|
||
"1306 3 0 Zakarian, Mr. Mapriededer \n",
|
||
"1307 3 0 Zakarian, Mr. Ortin \n",
|
||
"1308 3 0 Zimmerman, Mr. Leo \n",
|
||
"\n",
|
||
" sex age sibsp parch ticket fare cabin embarked boat \\\n",
|
||
"0 female 29.0000 0 0 24160 211.3375 B5 S 2 \n",
|
||
"1 male 0.9167 1 2 113781 151.5500 C22 C26 S 11 \n",
|
||
"2 female 2.0000 1 2 113781 151.5500 C22 C26 S NaN \n",
|
||
"3 male 30.0000 1 2 113781 151.5500 C22 C26 S NaN \n",
|
||
"4 female 25.0000 1 2 113781 151.5500 C22 C26 S NaN \n",
|
||
"... ... ... ... ... ... ... ... ... ... \n",
|
||
"1304 female 14.5000 1 0 2665 14.4542 NaN C NaN \n",
|
||
"1305 female NaN 1 0 2665 14.4542 NaN C NaN \n",
|
||
"1306 male 26.5000 0 0 2656 7.2250 NaN C NaN \n",
|
||
"1307 male 27.0000 0 0 2670 7.2250 NaN C NaN \n",
|
||
"1308 male 29.0000 0 0 315082 7.8750 NaN S NaN \n",
|
||
"\n",
|
||
" body home.dest \n",
|
||
"0 NaN St Louis, MO \n",
|
||
"1 NaN Montreal, PQ / Chesterville, ON \n",
|
||
"2 NaN Montreal, PQ / Chesterville, ON \n",
|
||
"3 135.0 Montreal, PQ / Chesterville, ON \n",
|
||
"4 NaN Montreal, PQ / Chesterville, ON \n",
|
||
"... ... ... \n",
|
||
"1304 328.0 NaN \n",
|
||
"1305 NaN NaN \n",
|
||
"1306 304.0 NaN \n",
|
||
"1307 NaN NaN \n",
|
||
"1308 NaN NaN \n",
|
||
"\n",
|
||
"[1309 rows x 14 columns]"
|
||
]
|
||
},
|
||
"execution_count": 3,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"df"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"---"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Minimum/Maximum\n",
|
||
"Der kleinste bzw. größte vorkommende Wert in einer Liste/Serie von Daten. \n",
|
||
"\n",
|
||
"In der Statistik und Datenanalyse ist es oft wichtig, die Extrema in einer Datenmenge zu identifizieren. Diese Werte werden als Minimum oder Maximum bezeichnet. Sie sind hilfreich, um Ausreißer (Outlier), i.e. besonders hohe oder besonders niedrige Werte, zu identifizieren.\n",
|
||
"\n",
|
||
"Eigenschaften:\n",
|
||
"* Empfindlich gegenüber Ausreißern (--> Quartile bzw. Quantile) (Bsp. Overflow bei Integern)\n",
|
||
"* Einfache und leicht verständliche Maßzahlen.\n",
|
||
"* In Kombination mit anderen statistischen Kennzahlen wie dem Mittelwert kann das Minimum bzw. Maximum helfen, die Verteilung der Daten besser zu verstehen."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"pclass 1.0000\n",
|
||
"survived 0.0000\n",
|
||
"age 0.1667\n",
|
||
"sibsp 0.0000\n",
|
||
"parch 0.0000\n",
|
||
"fare 0.0000\n",
|
||
"body 1.0000\n",
|
||
"dtype: float64\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"# Minima des Dataframes berechnen\n",
|
||
"minima = df.min(numeric_only=True)\n",
|
||
"\n",
|
||
"print(minima)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Wir können auch das Minimum/Maximum über Zeilen berechnen, indem wir die <em>axis</em> angeben."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"min_of_columns = df.min(axis=0, skipna=True, numeric_only=True)\n",
|
||
"min_of_rows = df.min(axis=1, skipna=True, numeric_only=True)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"pclass 1.0000\n",
|
||
"survived 0.0000\n",
|
||
"age 0.1667\n",
|
||
"sibsp 0.0000\n",
|
||
"parch 0.0000\n",
|
||
"fare 0.0000\n",
|
||
"body 1.0000\n",
|
||
"dtype: float64"
|
||
]
|
||
},
|
||
"execution_count": 6,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"min_of_columns"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0 0.0000\n",
|
||
"1 0.9167\n",
|
||
"2 0.0000\n",
|
||
"3 0.0000\n",
|
||
"4 0.0000\n",
|
||
" ... \n",
|
||
"1304 0.0000\n",
|
||
"1305 0.0000\n",
|
||
"1306 0.0000\n",
|
||
"1307 0.0000\n",
|
||
"1308 0.0000\n",
|
||
"Length: 1309, dtype: float64"
|
||
]
|
||
},
|
||
"execution_count": 7,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"min_of_rows"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"---"
|
||
]
|
||
},
|
||
{
|
||
"attachments": {
|
||
"image.png": {
|
||
"image/png": "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"
|
||
}
|
||
},
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Mittelwert (arithmetisches Mittel)\n",
|
||
"\n",
|
||
"Der Mittelwert, auch Durchschnitt genannt, ist eine zentrale Tendenz, die den Durchschnittswert einer Datenmenge beschreibt. Er ist die häufigste verwendete statistische Kennzahl. Berechnet wird er, indem man die Summe aller Werte durch die Anzahl der Werte teilt.\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"(from https://datatab.de/tutorial/mittelwert-median-modus)\n",
|
||
"\n",
|
||
"### Berechnung des Mittelwerts\n",
|
||
"\n",
|
||
"Für eine gegebene Datenmenge $x_1, x_2, \\ldots, x_n$ wird der Mittelwert $\\bar{x}$ wie folgt berechnet:\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\bar{x} = \\frac{1}{n} \\sum_{i=1}^{n} x_i.\n",
|
||
"$$\n",
|
||
"\n",
|
||
"Dabei ist:\n",
|
||
"- $\\bar{x}$ der Mittelwert\n",
|
||
"- $n$ die Anzahl der Datenpunkte\n",
|
||
"- $x_i$ der $ i$-te Datenpunkt\n",
|
||
"\n",
|
||
"### Beispiel1\n",
|
||
"\n",
|
||
"Angenommen, wir haben die folgenden Datenpunkte: $$2, 4, 6, 8, 10.$$ Der Mittelwert wird wie folgt berechnet:\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\bar{x} = \\frac{1}{5} (2 + 4 + 6 + 8 + 10) = \\frac{30}{5} = 6\n",
|
||
"$$\n",
|
||
"\n",
|
||
"Der Mittelwert dieser Datenpunkte ist 6.\n",
|
||
"\n",
|
||
"### Beispiel2\n",
|
||
"\n",
|
||
"Angenommen, wir haben die Werte:\n",
|
||
"\n",
|
||
"$$1, 2, a, 3a, 4, 5, -a, 1, 0, 9$$\n",
|
||
"\n",
|
||
"und haben einen Mittelwert von 4. Welchen Wert muss a annehmen?\n",
|
||
"\n",
|
||
"Lösung?\n",
|
||
"\n",
|
||
"### Beispiel3\n",
|
||
"\n",
|
||
"Nach einem Test in DSAI ist die Notenverteilung wie folgt:\n",
|
||
"\n",
|
||
"1|2|3|4|5\n",
|
||
":--- | ---: | ---: | ---: | ---:\n",
|
||
"6|3|6|3|3\n",
|
||
"\n",
|
||
"Berechne den Mittelwert!\n",
|
||
"\n",
|
||
"Lösung?\n",
|
||
"\n",
|
||
"Gibt es eine weitere Möglichkeit?\n",
|
||
"\n",
|
||
"\n",
|
||
"### Eigenschaften des Mittelwerts\n",
|
||
"\n",
|
||
"- Der Mittelwert ist empfindlich gegenüber Ausreißern, d.h., extrem hohe oder niedrige Werte können den Mittelwert stark beeinflussen.\n",
|
||
"- Der Mittelwert ist eine gute Maßzahl für symmetrische Verteilungen ohne Ausreißer.\n",
|
||
"\n",
|
||
"Der Mittelwert ist ein grundlegendes Konzept in der Statistik und wird häufig verwendet, um zentrale Tendenzen in Datensätzen zu beschreiben."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Mittelwerte des Dataframes berechnen\n",
|
||
"\n",
|
||
"mean_of_df = df.mean(skipna=True, numeric_only=True) # (Fast) gleiche Syntax"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"pclass 2.294882\n",
|
||
"survived 0.381971\n",
|
||
"age 29.881135\n",
|
||
"sibsp 0.498854\n",
|
||
"parch 0.385027\n",
|
||
"fare 33.295479\n",
|
||
"body 160.809917\n",
|
||
"dtype: float64"
|
||
]
|
||
},
|
||
"execution_count": 9,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"mean_of_df"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 10,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Auch hier kann der Mittelwert über die Zeilen genommen werden\n",
|
||
"mean_of_rows = df.mean(axis=1, skipna=True, numeric_only=True)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 11,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0 40.389583\n",
|
||
"1 26.244450\n",
|
||
"2 26.258333\n",
|
||
"3 45.792857\n",
|
||
"4 30.091667\n",
|
||
" ... \n",
|
||
"1304 51.564886\n",
|
||
"1305 3.690840\n",
|
||
"1306 48.675000\n",
|
||
"1307 6.204167\n",
|
||
"1308 6.645833\n",
|
||
"Length: 1309, dtype: float64"
|
||
]
|
||
},
|
||
"execution_count": 11,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"mean_of_rows"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"---"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Geometrisches und Harmonisches Mittel"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Geometrisches Mittel\n",
|
||
"\n",
|
||
"Das geometrische Mittel ist eine Maßzahl der zentralen Tendenz, die insbesondere bei proportionalen Daten oder Wachstumsraten verwendet wird. Es wird berechnet, indem man das Produkt aller Werte nimmt und daraus die $n$-te Wurzel zieht, wobei $n$ die Anzahl der Werte ist.\n",
|
||
"\n",
|
||
"#### Berechnung des geometrischen Mittels\n",
|
||
"\n",
|
||
"Für eine gegebene Datenmenge $x_1, x_2, \\ldots, x_n$ wird das geometrische Mittel $\\bar{x}_{geom}$ wie folgt berechnet:\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\bar{x}_{\\text{geom}} = \\left( \\prod_{i=1}^{n} x_i \\right)^{\\frac{1}{n}}.\n",
|
||
"$$\n",
|
||
"\n",
|
||
"#### Beispiel 1\n",
|
||
"\n",
|
||
"Angenommen, wir haben die folgenden Datenpunkte: \\(2, 8\\). Das geometrische Mittel wird wie folgt berechnet:\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\bar{x}_{geom} = \\sqrt{2 \\times 8} = \\sqrt{16} = 4\n",
|
||
"$$\n",
|
||
"\n",
|
||
"Das geometrische Mittel dieser Datenpunkte ist 4.\n",
|
||
"\n",
|
||
"#### Beispiel 2\n",
|
||
"\n",
|
||
"Angenommen, die Wertentwicklung (in Prozent) für eine Aktie pro Monat ist wie folgt:\n",
|
||
"$$+3\\%, -8\\%, -10\\%, -2\\%, -15\\%, +5\\%, +1\\%, \\pm 0\\%, -5\\%, +2\\%, +1\\%, -3\\%.$$\n",
|
||
"Berechne den durchschnittlichen Anstieg bzw. die durchschnittliche Reduzierung der Aktie in diesem Jahr.\n",
|
||
"\n",
|
||
"Lösung? \n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Harmonisches Mittel\n",
|
||
"\n",
|
||
"Das harmonische Mittel ist eine weitere Maßzahl der zentralen Tendenz, die insbesondere bei Verhältniszahlen oder Raten verwendet wird. Es wird berechnet, indem man die Anzahl der Werte durch die Summe der Kehrwerte der Werte teilt.\n",
|
||
"\n",
|
||
"#### Berechnung des harmonischen Mittels\n",
|
||
"\n",
|
||
"Für eine gegebene Datenmenge $x_1, x_2, \\ldots, x_n$ wird das harmonische Mittel $\\bar{x}_{harm}$ wie folgt berechnet:\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\bar{x}_{harm} = \\frac{n}{\\sum_{i=1}^{n} \\frac{1}{x_i}}\n",
|
||
"$$\n",
|
||
"\n",
|
||
"#### Beispiel 1\n",
|
||
"\n",
|
||
"Angenommen, wir haben die folgenden Datenpunkte: \\(2, 8\\). Das harmonische Mittel wird wie folgt berechnet:\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\bar{x}_{harm} = \\frac{2}{\\frac{1}{2} + \\frac{1}{8}} = \\frac{2}{0.5 + 0.125} = \\frac{2}{0.625} = 3.2\n",
|
||
"$$\n",
|
||
"\n",
|
||
"Das harmonische Mittel dieser Datenpunkte ist $3.2$.\n",
|
||
"\n",
|
||
"#### Beispiel 2\n",
|
||
"\n",
|
||
"Angenommen, bei einer Autofahrt beträgt die Fahrgeschwindigkeit in der ersten Stunde $50 \\frac{\\text{km}}{\\text{h}}$ und in der zweiten Stunde $100 \\frac{\\text{km}}{\\text{h}}$. Wie groß ist die Durchschnittsgeschwindigkeit?\n",
|
||
"\n",
|
||
"Dieses Beispiel ist sehr einfach und benötigt nur den arithmetischen Mittelwert. Bezieht man sich aber nun nicht auf die Zeit, sondern auf die zurückgelegte Strecke, so ändert sich das Ergebnis drastisch.\n",
|
||
"\n",
|
||
"Zum Beispiel: Die ersten $100 \\textrm{km}$ werden mit $100 \\frac{\\text{km}}{\\text{h}}$ gefahren, die zweiten $100 \\textrm{km}$ mit $50 \\frac{\\text{km}}{\\text{h}}$. Wie groß ist nun die Durchschnittsgeschwindigkeit?\n",
|
||
"\n",
|
||
"*Hinweis:* Klarerweise gilt $v=\\frac{s}{t}$.\n",
|
||
"\n",
|
||
"Lösung?\n",
|
||
"\n",
|
||
"### Eigenschaften\n",
|
||
"\n",
|
||
"- Das geometrische Mittel ist besonders nützlich bei Daten, die multiplikative Effekte aufweisen, wie z.B. Wachstumsraten.\n",
|
||
"- Das harmonische Mittel ist besonders nützlich bei Daten, die Verhältnisse oder Raten darstellen, wie z.B. Geschwindigkeiten.\n",
|
||
"- Beide Mittelwerte sind weniger empfindlich gegenüber Ausreißern im Vergleich zum arithmetischen Mittel."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 12,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/home/tikaiz/miniconda3/envs/dsai/lib/python3.9/site-packages/numpy/_core/_methods.py:56: RuntimeWarning: overflow encountered in reduce\n",
|
||
" return umr_prod(a, axis, dtype, out, keepdims, initial, where)\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"# Berechnen des geometrischen Mittels\n",
|
||
"\n",
|
||
"geometric_mean = df.prod(axis=0, skipna=True, numeric_only=True) ** (1 / len(df)) # macht jedoch für die gegebenen Daten wenig Sinn"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 13,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"pclass 0.000000\n",
|
||
"survived 0.000000\n",
|
||
"age inf\n",
|
||
"sibsp 0.000000\n",
|
||
"parch 0.000000\n",
|
||
"fare 0.000000\n",
|
||
"body 1.551917\n",
|
||
"dtype: float64"
|
||
]
|
||
},
|
||
"execution_count": 13,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"geometric_mean"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Berechnen des harmonischen Mittels\n",
|
||
"\n",
|
||
"from scipy.stats import hmean\n",
|
||
"\n",
|
||
"harmonic_mean = df.select_dtypes(include='number').apply(lambda x: hmean(x)) # erneut: wenig Sinn für die gegebenen Daten"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 15,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"pclass 1.875806\n",
|
||
"survived 0.000000\n",
|
||
"age NaN\n",
|
||
"sibsp 0.000000\n",
|
||
"parch 0.000000\n",
|
||
"fare NaN\n",
|
||
"body NaN\n",
|
||
"dtype: float64"
|
||
]
|
||
},
|
||
"execution_count": 15,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"harmonic_mean"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"---"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Median"
|
||
]
|
||
},
|
||
{
|
||
"attachments": {
|
||
"image.png": {
|
||
"image/png": "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"
|
||
}
|
||
},
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Der Median ist ein Maß der zentralen Tendenz, das den mittleren Wert einer geordneten Datenmenge beschreibt. Im Gegensatz zum Mittelwert ist der Median weniger empfindlich gegenüber Ausreißern und bietet daher eine robustere Darstellung des Zentrums einer Verteilung.\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"(from https://datatab.de/tutorial/mittelwert-median-modus)\n",
|
||
"\n",
|
||
"### Berechnung des Medians\n",
|
||
"\n",
|
||
"Für eine gegebene Datenmenge $x_1, x_2, \\ldots, x_n$, die der Größe nach geordnet ist, wird der Median $\\tilde{x}$ wie folgt berechnet:\n",
|
||
"\n",
|
||
"- Wenn $n$ ungerade ist, ist der Median der mittlere Wert:\n",
|
||
"$$\n",
|
||
"\\tilde{x} = x_{\\frac{n+1}{2}}\n",
|
||
"$$\n",
|
||
"\n",
|
||
"- Wenn $n$ gerade ist, ist der Median der Durchschnitt der beiden mittleren Werte:\n",
|
||
"$$\n",
|
||
"\\tilde{x} = \\frac{1}{2} (x_{\\frac{n}{2}} + x_{\\frac{n}{2} + 1})\n",
|
||
"$$\n",
|
||
"\n",
|
||
"### Beispiel 1\n",
|
||
"\n",
|
||
"Angenommen, wir haben die folgenden Datenpunkte: $$9,1,3,5,7.$$ Da die Anzahl der Datenpunkte ungerade ist, ist der Median der mittlere Wert:\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\tilde{x} = 5\n",
|
||
"$$\n",
|
||
"\n",
|
||
"Der Median dieser Datenpunkte ist 5.\n",
|
||
"\n",
|
||
"### Beispiel 2\n",
|
||
"\n",
|
||
"Angenommen, wir haben die Werte: $$1, 6, 5, 4, 2, 3.$$ Da die Anzahl der Datenpunkte gerade ist, ist der Median der Durchschnitt der beiden mittleren Werte:\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\tilde{x} = \\frac{1}{2} (3 + 4) = 3.5\n",
|
||
"$$\n",
|
||
"\n",
|
||
"Der Median dieser Datenpunkte ist 3.5.\n",
|
||
"\n",
|
||
"### Beispiel 3\n",
|
||
"\n",
|
||
"Folgende Daten sind gegeben: $$16,5,9,-4,1,a,7,0,16,5.$$\n",
|
||
"\n",
|
||
"\n",
|
||
"* Für welche(n) Wert(e) $a\\in\\mathbb{R}$ ist $a$ der Median?\n",
|
||
"* Was wäre, wenn wir den Wert $7$ entfernen?\n",
|
||
"* Was wäre, wenn wir den Wert $0$ entfernen?\n",
|
||
"\n",
|
||
"### Beispiel 4\n",
|
||
"\n",
|
||
"Nach einem Test in DSAI ist die Notenverteilung wie folgt:\n",
|
||
"\n",
|
||
"1|2|3|4|5\n",
|
||
":--- | ---: | ---: | ---: | ---:\n",
|
||
"6|3|6|3|3\n",
|
||
"\n",
|
||
"Berechne den Median!\n",
|
||
"\n",
|
||
"Lösung?\n",
|
||
"\n",
|
||
"### Eigenschaften des Medians\n",
|
||
"\n",
|
||
"- Der Median ist weniger empfindlich gegenüber Ausreißern im Vergleich zum Mittelwert.\n",
|
||
"- Der Median muss nicht immer ein Wert der Daten sein.\n",
|
||
"- Der Median teilt die Datenmenge in zwei Hälften, wobei 50% der Werte kleiner und 50% der Werte größer als der Median sind.\n",
|
||
"- Der Median ist eine gute Maßzahl für asymmetrische Verteilungen oder Verteilungen mit Ausreißern.\n",
|
||
"- Der Median kann aber auch sehr instabil sein: Bestehen die Daten nur aus Ausreißern (hohe Varianz), dann ist der Median sehr instabil. Beispiel: Daten sind gleich oft $-1000$ und $1000$ (und keine anderen Werte). Dann ist der Median $0$, fügt man aber einen Wert $x\\notin[-1000,1000]$ hinzu, so ist der Median $\\pm 1000$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": []
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 16,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Berechnen von Median (Erneut (fast) identische Syntax)\n",
|
||
"median_of_df = df.median(skipna=True, numeric_only=True)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 17,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"pclass 3.0000\n",
|
||
"survived 0.0000\n",
|
||
"age 28.0000\n",
|
||
"sibsp 0.0000\n",
|
||
"parch 0.0000\n",
|
||
"fare 14.4542\n",
|
||
"body 155.0000\n",
|
||
"dtype: float64"
|
||
]
|
||
},
|
||
"execution_count": 17,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"median_of_df"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"---"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Modus/Modalwert"
|
||
]
|
||
},
|
||
{
|
||
"attachments": {
|
||
"image.png": {
|
||
"image/png": "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"
|
||
}
|
||
},
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Der **Modus** oder **Modalwert** ist ein Maß der zentralen Tendenz, das den häufigsten Wert in einer Datenmenge beschreibt. Im Gegensatz zum Mittelwert und Median, die auf die Ordnung oder Durchschnittlichkeit der Werte abzielen, gibt der Modus denjenigen Wert an, der am häufigsten auftritt. Der Modus ist besonders nützlich für **kategoriale** bzw. **nominale** Daten oder diskrete Verteilungen, kann aber auch auf stetige Daten angewendet werden.\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"(from https://datatab.de/tutorial/mittelwert-median-modus)\n",
|
||
"\n",
|
||
"### Berechnung des Modus\n",
|
||
"\n",
|
||
"Für eine gegebene Datenmenge $x_1, x_2, \\ldots, x_n$, wird der Modus $\\hat{x}$ bestimmt, indem man den Wert sucht, der am häufigsten vorkommt:\n",
|
||
"\n",
|
||
"### Beispiel 1\n",
|
||
"\n",
|
||
"Angenommen, wir haben die folgenden Datenpunkte: 99, **86**, 87, 88, 111, **86**, 103, 87, 94, 78, 77, 85, **86**\n",
|
||
"\n",
|
||
"Der Wert 86 tritt dreimal auf, häufiger als jeder andere Wert. Daher ist der Modus:\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\hat{x} = 86.\n",
|
||
"$$\n",
|
||
"\n",
|
||
"Der Modus dieser Datenpunkte ist 86.\n",
|
||
"\n",
|
||
"### Beispiel 2\n",
|
||
"\n",
|
||
"Angenommen, wir haben folgende Daten: **7**, 8, 10, **12**, **7**, **12**.\n",
|
||
"\n",
|
||
"In diesem Fall gibt es zwei Werte, die jeweils zweimal auftreten (7 und 12). Diese Datenmenge ist **bimodal**, und die beiden Modi sind:\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\hat{x}_1 = 7 \\quad \\text{und} \\quad \\hat{x}_2 = 12\n",
|
||
"$$\n",
|
||
"\n",
|
||
"### Beispiel 4\n",
|
||
"\n",
|
||
"Nach einer Umfrage zur Lieblingsfrucht der Schülerinnen und Schüler ist die Häufigkeitsverteilung wie folgt:\n",
|
||
"\n",
|
||
"Frucht | Apfel | Banane | Orange\n",
|
||
":--- | ---: | ---: | ---: \n",
|
||
"Häufigkeit | 11 | 8 | 3 \n",
|
||
"\n",
|
||
"Der Modus ist:\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\hat{x} = \\text{Apfel}.\n",
|
||
"$$\n",
|
||
"\n",
|
||
"### Eigenschaften des Modus\n",
|
||
"\n",
|
||
"- Der Modus ist besonders nützlich bei kategorialen Daten.\n",
|
||
"- Eine Datenmenge kann **einen** Modus (unimodal), **zwei** Modi (bimodal) oder **mehrere** Modi (multimodal) haben.\n",
|
||
"- Der Modus kann auch für stetige Verteilungen geschätzt werden, zum Beispiel durch Histogramme oder modale Klassen.\n",
|
||
"- Im Gegensatz zu Median und Mittelwert kann der Modus stark von der Verteilung abhängen und ist nicht immer eindeutig.\n",
|
||
"- Der Modus ist empfindlich gegenüber kleinen Veränderungen in den Daten, insbesondere wenn die Häufigkeiten der Werte nahe beieinanderliegen.\n",
|
||
"- Der Modus ist stabil gegenüber Ausreißern, solange diese die Häufigkeitsverteilung nicht stark beeinflussen."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 18,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Der Modus kann wie folgt berechnet werden\n",
|
||
"mode_of_df = df.mode(numeric_only=True).iloc[0]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 19,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"pclass 3.00\n",
|
||
"survived 0.00\n",
|
||
"age 24.00\n",
|
||
"sibsp 0.00\n",
|
||
"parch 0.00\n",
|
||
"fare 8.05\n",
|
||
"body 1.00\n",
|
||
"Name: 0, dtype: float64"
|
||
]
|
||
},
|
||
"execution_count": 19,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"mode_of_df"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"---"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Quartile und Quantile"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Quartile und Quantile sind zentrale Konzepte in der Statistik, die dabei helfen, eine Datenmenge in Abschnitte zu unterteilen, um deren Verteilung zu beschreiben."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"#### Quartile\n",
|
||
"\n",
|
||
"Quartile unterteilen eine geordnete Datenreihe in vier gleich große Teile und ermöglichen so eine anschauliche Darstellung der Datenverteilung. Es gibt drei Schlüsselwerte:\n",
|
||
"\n",
|
||
"- **Erstes Quartil (Q1)**: Der Wert, unter dem 25 % der Daten liegen, auch bekannt als unteres Quartil.\n",
|
||
"- **Zweites Quartil (Q2)**: Der Median, der die Daten in zwei Hälften teilt, unter dem 50 % der Werte liegen.\n",
|
||
"- **Drittes Quartil (Q3)**: Der Wert, unter dem 75 % der Daten liegen, auch als oberes Quartil bezeichnet.\n",
|
||
"\n",
|
||
"Diese Quartile bieten eine nützliche Übersicht darüber, wie die Daten gestreut sind und helfen, ungewöhnliche Werte (Ausreißer) zu erkennen."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"#### Quantile\n",
|
||
"\n",
|
||
"Quantile erweitern das Konzept der Quartile und erlauben eine flexiblere Aufteilung der Daten in beliebig viele Abschnitte. Ein p-Quantil bezeichnet den Wert, unter dem ein bestimmter Prozentsatz \\(p\\) der Daten liegt. Beispiele hierfür sind:\n",
|
||
"\n",
|
||
"- **0.25-Quantil**: Entspricht dem ersten Quartil (Q1).\n",
|
||
"- **0.50-Quantil**: Entspricht dem Median (Q2).\n",
|
||
"- **0.75-Quantil**: Entspricht dem dritten Quartil (Q3).\n",
|
||
"\n",
|
||
"Das Besondere an Quantilen ist, dass \\(p\\) jede beliebige Zahl zwischen 0 und 1 sein kann. So gibt es beispielsweise auch ein \\(0.90\\)-Quantil, das den Punkt markiert, unter dem 90 % der Daten liegen."
|
||
]
|
||
},
|
||
{
|
||
"attachments": {
|
||
"image.png": {
|
||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAqcAAAGLCAYAAAD6YzvUAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAM2bSURBVHhe7J0FoBzV1cf/Y7v7LO4eLAkWIyFCcHd39wKlpYUWKG2pIIXylVJoi7ZQSilSXIOFhAABAkESSAIhxD1PV8a+c87dSV6QFkmyT85v37y5O3NnduTeOf97rowVE1AURVEURVGUJoBdnCuKoiiKoihKyVFxqiiKoiiKojQZVJwqiqIoiqIoTQYVp4qiKIqiKEqTQcWpoiiKoiiK0mRQcaooiqIoiqI0GVScKoqiKIqiKE0GFaeKoiiKoihKk0HFqaIoiqIoitJkUHGqKIqiKIqiNBlUnCqKoiiKoihNBhWniqIoiqIoSpNBxamiKIqiKIrSZFBxqiiKoiiKojQZVJwqiqIoLZ445on+SdjMoyiSifn8OkVRSodFGVFzoqIoitIqYItnWcUvnyOmj0UfRVFKi3pOFUVRlBYPi1L2xbAwDcNQwnPmzMXCRUskHIWRCFP11yhK6VFxqiiKorR4jOaMZR4EIYlUC/fd9xBeePFlCUdBJJ7TYkRFUUqIilNFURSlxdO4st5xbPGQDhq4Jfr06Sthy7FYmmqlvqI0AbTNqaIoitLiEUtnsWdUKu/lY8EGd4eyiv9FmVIU9qQqilI6VJwqiqIorQMRqDwzHZ+i2LQzZTGaLCtGURSlhGi1vqIoitLiSTynPBcRSgHbso0wpbARpjRXf42ilBwVp4qiKEqrINGdZmzTGPM+W4TFS1ZIOI7MSpWmilJ6VJwqiqIoLR9RnUZ6mt76Nh544GG8NIF769sIaZmgnlNFKTkqThVFUZSWjzQkTVqTcvV+jO7du6Jjhw4SXoN2hlKUkqMdohRFUZRWAAtS7vxk2p0ySa98MYMUtGg9t0uVL4qilAwVp4qiKEorYV3hmZg/HTpKUZoWKk4VRVGUFs+6pi4G94niwfgZeXWpBI1IVbGqKKVF25wqiqIorQAjTlmkilCladnSlVi1skbWrBWvjUWsoiilQMWpoiiK0kowHlHf9+G4Dh588D94+eWJ4kHlZWb8U/WaKkqpUXGqKIqitAJYdMZSZc+D77OntEBCNJAOUjEc20VMYa3RV5TSo+JUURRFafFwT3wWoSxOkymiKWR/afE7e03XVu8rilIqVJwqiqIoLR7jFV1XfKZTHlKuW/zGHaG0M5SiNAW0t76iKIrS4vkyU5fL52HbNlKeV1xiaCxQv46JTERvSxC261sSfL5A8Hn4kvHq5nDt1ue1aQlpZUOi4lRRFEVRviFsOhOB0TjcYmGlsOYUE9nwv885uTafv0Yxt//9Gts3N1rqeW1sVJwqiqIoLR5j6lg0GJNnxJLNASMoGgmndUTUl5hIXsYeV15lwi3Tc5qcE895iqJIztu2neL6SOZMFIVyZW2Kn6xnku0Tkv04HKfR5WoO167xeTQmWc6iNKJrwl9txzbXi87ry86tJaSVDYmKU0VRFKXFw0LKvL7UhHkQ/ob6nIitTFkKjsNigSc2iV8uHBJh5bouFixahHfe/gB777krCREjwHhfzR0+PyMo+Rrx+cZIpVhsrj23fCFfFF0k0Om7x9fOWitIC4WC7MNxHBJrJGxpHzxcF18jWkTw8oAuKO2Dr5nIkC+/5k2VRDrx9UqwLRKjTkrCBT+PlJeWcBiGMv9f6UMF61qaf05SFEVRlK9BYvsDEguu6+A/Dz6EiS9PlHAQsIBgUWY8XcnUmESYLlmyDC+9OAlDhmwlwlRoIcIiOWfxKhOplIdlK6rx0KPP4o67/o13p32IdIpFVyjXw6PrUVOXxSOPP4fb77xX1qdSLNBY2NJ1JjXqea5cX9734qWr8fT4CVi2cpUI2zgsVoQXr3fjqbHvLAl/Mc4X11FIlq+dm3UMx/2yfZm4vE7WNFq+Fj7fZH8CfeH0wBNtgpwf4Mc//Q1uuvlOOe9XXnkDb099Z5398G+wYGfMb6w9DmUtKk4VRVGUlg+JThYQrAtICohIqG6oR10+J2EWB2a+VsAkE7NGmC5ejuefm4Dddt0ZPXt0p/XGc8bSgqM27cmIr8bnlcw/DwtLmwTW1Hc/xM57HoXTvvdjXPW7G7HDzgfh6utuo2uRATdnmDNvAfbc/2Qce/IP8Kvf/hE77HIorrn+dhJnLNo8PPbkeJx25g9Rn60Xz+Gbb87APvsejfc/mC1V+1z9HUeB/J45rghhGNBkmhDwvWIVK2G6OUHgy71gj27gF+QY1qwjcRgE7PnlbVlIcoc3I/xCWsceXI7LExNSXPZq8u9FkV9cR3EpHNDx8G+IaORLRMfFnmBZHwQSN1co4MzzLsT9Dz4i55svRHhtyjuYMeMT2s7BeT/8BX562dXm2EicxzFdU9rO4d+nffp0TPQTxfP+8vvQWlFxqiiKorR8RGQkYoOlJOCkSWB5phpWqpjN4nVgzcBiiIXJgoWL8cz4F7DLrjuhW7fOUn1Nq2S98ao19cmIv/8uhDiOyHcR3L/8zR+wYsVKTBj/H0x7YzzOOvcUXPbr3+H1N94S8fnbq/+Eqe+8j8cf+hvee+NZHH3cIbj0F7/FBzNmI5vL4+nxr+Cufz2K9z78RK4XaThYZRl0aN8Jq1bX4L0PPkI2z2LPETFo2q4a8Tnn089QS6I2RyL03fenY3VNjfxmIuZcuncLlyzHu+/NwIrV1fTdpeU+amrr8OnchQhiG5/MXYBFC5bCdumMSFjOnP0Jps+aLaKUm3KYuUtzC9M/nE3rPyXB7MGl4wlJTM5ftAgrqldR8rAxc9YcLFi8jH7HI7EZ4JNPF9K5PY7nJkzBkqUrUU7n9bc7/w+XXHqOXEm3vIymtnKs7E22bRezP55LvzOLxG8Ez3NI85oq//9+T1ofKk4VRVGUlk/R+BsRkHhK2etp2liKKJPZ50UCt5N0sGzZCrz++js48IC90b17Z1nDgoObBPB641UzXrnmMCXnbOZrWSNMSZytrq7F21PfxVGHH4KtB22O8vI0Ljz/VNh0jZ59cTLy+QIefWg8jj36IOwybiTatqvCT398OhykMP7FV3HfI4/i9jv/gS7de2H/fY/HU89NQlXbMpRlKvDve5/AuF0Px8hxB+PwY8/BggULpHAgHmoSi/V1ddjv4GNw3oW/xmHHfg877HIwthu3Px59doK51laEq669CYNH7oc99j8BQ0btg7v++TAJvjTGvzAJe+5zEn580VXYaqudcc+9j2L56joccMQpGL3z4dhp56Ox934nYNbHn0mTg08/mYf9DjgR4/Y4itYfhkMPPRWLFi0VgXrq9y7CiWf8GCee9VMMH70fTfvjb/94gFJNjJNP+wEqUuW4/8Encewp55EYz+G4o7+H3//uZpO+QkpbFJNZtGgJDj/hhxi9y+HYkX5nl32Owvvvz5J7wdX8n78PrR3tEKUoiqK0fMjUGWNnRBmzfMVKEice2rapku+8joVZYhTZPLJoqK2px93//Dd69+6Dbt06yPiopk0mrZf9NR/43PjYt91mK1RVVYiHkquqExJJwIIpR+Jz172Pghdn8Mwzd6KiLIM//eVvOP/8n+Pii3+I8753IvoNHIsrfnsxLjzvVN4K9Q0NGDR0f+yyy3Bc85uLcflvb8C/HngUd//tD9hh++3w9rTp2HO/k7D3rjvgZ5eei1fffAsX/uiXuOLKn+PSi85BrpCXNq3LV63A0JEHIQ5C/O63F2HQlgNxyhkXoDYb4sO3n8Qzz03EEcecgZuuvxr77787/vDH2/GXW/+Jme+9gDfemoqDDj0Te+46GqefcixGjhmOH/30Kjz75DN46P6/o6y8HIccdgJGjhyOhx64FXsdcBqqa5bigXtuQ0M2i/0OPQHjxuyAu269BrvsewLenDIVv7/qp9h6m0E4+/yfoa4mj3emPI7p02fhwMO/h4MP3B0/OO9E9OzZDduO2I9+d2fc9pffkJg+GD26dcWj99+Mk8+4GC+++DL+c/+t6N6jK4489vsoL6vEM4/dItebYaGqGPRKKIqiKC2emEQmC02r+KYonjp36oh2bdus+c7ClAIcW7bhkHTqcR106thJepZ37tKFBGpXdKF5167d0KUrhZv41LlrFzluDnflcOdOUgVuztOc6zrQiYckClmMXvbT7+Otd97BdmMOwV4HnoSHHnoK3Xr3hS9V8TaCQhZhFMg2LHpFtFM4n8+hW5fO6N+3D+3Lx5jRw9ChfVsUCiEJ3wjnfP9UWjYcZ5x+Inr074fFi1eIUBZIGNt0zXO5HPbbZ3ccf9yhGD50S1zww7Pw2ccfY9r7M/DUMxPQvmM3VFLBYuob72GTTfqhdukyPP/8BFRWlNON8/HjC8/D4YfvJ21Kn332BZz/g+9ht11HYcyobfHC8/fjwgvPwOyPP8EUEshDh4/AtLc/wCezP8PALbfCU0+PF3HOaWLI8OE464wTMXbUCBx6yAFYsbIGfsGnY9oaIX169eiGrbccIMfvphwzcAGlI/ZCO3Q98lSYeeGlSRg8ZIh4ZN95611svfUAPD/hRcxfsFiuo/oJ10XFqaIoitLiEY+oCAAWDdy20bQTNVNxnQgKE0eQ70BZeQaHHLo/Yoqbzeax+WabYovNN6F5/2YxbbHZJo2O14QzGdPWlkV5Y9hvzEtc2yXhWcAB++6OiRP+g0P32xV77jwWN/75Ktooi67d2ornNV1eiYaGnAwtxdcyl88i19CATh06iPe14Puy35rqGlnP15fFm+NyR6QQBRKALM7C0OfLLb9tCgp87X107NJWtvP9BvrNTrShhdWrauk38gjCCPf8+wH88U934Jmnn8MRxx2J7iS+2bNNKhGplBklYPXqehRyDejRs5N0ZqqrrsZWA7fATmNHY8WK1fR7MT78cBZuvv1e/PHPfxdxe+QRB8m952Pk4/JpO2mf6rp0XqHst76+HhYJ0DxdJ26DKhTTEp+HXEvbQkN9HS2LMHfBfNx6xz/xpz/9DbXVy3ECie7kmsiPKGtQcaooiqK0eNj+m3kiTEk45QOa1vYST+IkOoFFErdv5PXceWX33XfE9Pc+xLR3pst638+LV87sz3gEm+QkAsjMk4l0E5+hnEdjjCikOasDEo3fO+8S/P2Of+G3v7kQP/7RmZg06Q0sm7ccY0YNJxFXhmFDBuPxh8ejpqZertWTz07EykVLMW777Umw8k7o2rk22rRpKyKUoojAsy1P4nt8jenagnvts5gryjq+PykvhTfffEeOw/PK8eYb78n5bNa/L7qTUE27wH3//CueeepO3HPXTTj95MOx3fZDkPd5iKs07dKMr9qne2e0b1uJlye9Lr9d2bYtfnftLfjJZVeiT7/+cB0P++65A5589HaMf+JO/Pyn5+CEYw5EGQl4+mkSuY4MDSXHzyMBuHScVijeZ4t+g+PwSA6cXryUJ/EYz+UOT0Dbdu1RUZnG4GED8cgDt+Hpp+/GVb+5DKcef4RU8SdiXFmLuYKKoiiK0oIRb5aoTtMjnKvqH330cbw6+VURMOK9ElioklSguMkyrqrmbTIZF/sfsCc+/vgTEajc+UaEhUw87FETnUQkUoiPkSYWT8m1MPNGFC+D6cXuYMSI4fjzTbdh+10Ow4FHn46zz/opzjjzZIzafhhdnwg/vfBMvPf+O9j7kFNx1gU/p3WXYO/99sQBB+xG+47RuWsHVK9cgaOPPRfTP/oELnszVy+XYZQYFqErVq5GbV09HeFazzV7qSsqqjBz5mc4+phzcMY5v8Cvf30tDth/L/Tv30s6YRXyeey8+/G4+pq/YMf9jsChx3LbUfbQxvBrVxS9nhY6duyA8889C//+x/04+pQLcPL3L8HFP/klYstF7+6dcOpJR+Hyy6/HeRf8Ehdddg2GD98Hf7v9XjmWlatWSccwhvdVX59FLR2vH4QoLy8Tb+xfbr0Tv77qz3J9V6xcRXEaJP7q1TVYuqparvf3zz0V9979ME44/Sf4xZX/h21G7Y4rr/kj75WOlxQsXStlLc7lRDGsKIqiKC0aFkAsWnjooueenwDHc7HloAG0zAwXxdqIHV88byzcOMgigj1jm2yyCV599Q0ZGqlb965rBFVRAza9iUnmjeDz42P/gkClr0aQBxg+bGsMGz0aM2d9jGxDHX5w/mm45OJz4dgkquiabTlwc4zYfnu898EMfDb3Exx+2L645upL0aFdG7qmPjbfYnO0adcen348B0OHbYt+fXtiZU0W++69M7p27ki/H5EAXI3RI4ZhyOBBcjw89mmu4OO6P96Ik044GttutQUmTJxAIvVgXH3Fz5D2bHTr1gW77bETZs/6BO+89R423bQXbvj9ldhq4Gaoqa1FLgT232dXdGjfTu7tDjuMwGZbbIq33pqKZYtX4NJLf4gLf3CqeDZ323UsOnXugsmTX8PSZctx5unH4tKLfyDNApavWIWtt9wCO4weLteptq4ObWmfe+++IyrKK7Dt4K2waPESuWx777UTli9fhe1HDMGwIVth2fKV2GrrAdhh1DCMGD4YAwZsjimvvYNZH8/G0YcfiGuv+Dkqy/mFBqaw8IX70IrR3vqKoihKi4ctHY+fadPH930Zq/LPt92F7t274ND99zYDq/MgnF/iTeRteRGbS/6wh6y+Lotp097FiJHDxQvLtBhxYbS2OV8KN+7Nn5BIB54n1diNYSH/TQWXXF0SlVRuwIrqWgzYehxOOfEYEnEXF2MY+KdZ1H7Z7/LxNP7N5Dh578aDvJZknYn+5ef4347/f61PWPs7X4zLXl6+vny9vux8Wit6JRRFUZSWjwiJdQWJ7xfWVC/z4rjR+oTku8zpjz2vURijrCyDMWO3l7aIZr8SrdnD5xlbLErNCZnrFIig585N3PFHqqGLsODiZRyHPdLJ+kSIcZg7E/Fyfm0sx+F98Zzh3+F1PDqAgSWq+c8FCBaUHJd7vMtvyG8bUcjbsfc6+d1kn/yb/D05B4aDHFfOhdbxMSTnwev4O68rFOg8KV6yjo+ZpwQ5H4qb7Jt/h78nv5d0nDLrTMephOQ3eBn/DsczaefridzWhHpOFUVRlBbPWlPHVdlGPM2ZOw+ZTFp6eItAKNbnf5VQMLvgf6Y6nKfGXsWWJjC+Sh7weX7VusZ8VbxkeePrJdG43aXMSciRyPtgxsfo1LEDevfoIqKwcXwOJ8uSfTUON55/ns/H+W982fr/tu+EZLuvEzfhfx1La0LFqaIoitKKKKqfL+O/rDIkEf5nxBZNIrj+F18V78uXf7Nr+mX7SJZ93eP7LnyT32gcd2McW0tAxamiKIrSCmBPJxm9oniRJcU5L5PlZuFXigcTnf/xerMtw9GTfbckvkoeNL6G/42vipcsb3y9JFojzynPuT0mR+G2mJ/fz5ft+8v3u26cb0rjfSUkv/Hf9p1s9/m4/227L/ut1oqKU0VRFKXF09jUcbV+HLEgZdETkSVkYcAigjs2rStuFEXZ+GiHKEVRFKUVwOKURacZ4N1xbTz55NOY8vqbMs6p6QDDcdRfoyilRsWpoiiK0uLhXvbsPWWvKPeS5vCs2bMxb8ECCcs6Ea/qNVWUUqPiVFEURWnxmLc+sQhlCWoEqFNWASvNg6ATsXl9pjpOFaX0qDhVFEVRWgEiPWVu2SxUzTiZZqxJ/i4rCVWnilJqtEOUoiiK0vLhqnuaJdX63AN82vszUFFRjs3690XMb+opvmNfO0QpSmlRcaooiqK0eFiacnV+Ij7Z8iUadO0yFaaK0hTQan1FURSlxWOEqfGcyncrFg/qum8eUmGqKE0B9ZwqiqIoLZ7Gpi4Z55SHk+K6fn5fO4tVM9j7WgGrKEppUM+poiiK0gpIxKkZ59R2LEx8+VW8++4H8n589qByT/618RRFKRUqThVFUZQWT+Oq+ygyPfTffPMtfPjRRxI2nlWe1GuqKKVGxamiKIrS4jG1+kZ8WmT6WIy65RWwMxkJ8zKJoY5TRSk5Kk4VRVGUlo9U2UvASFTLQi6fR6HgG8+pWUkiVdWpopQaFaeKoihKi4c7PJkqe0vepc+M3n47bD1ogIQdu2gO11T/K4pSKrS3vqIorRp5BLIe2chPwrVtIJWNgYxzyt7TokiVqvziPWgcVhSl9Kg4VRRFMXrlC/DTkVfJY5L+WMCwhvmCjinGiyget17k1eypk/gSQSk5fIPoZiQWj+9h8urStUNImXWKopQWFaeKorQeigqEH3usQ5L/ySyKeBYhjAMSLC68NQ2fkkCeJodEjUVClDaiP5ajrhNTjJDWeRKL9kSTR/EK8IMIjuPCIgHkrKN+ij/KoeSYVB1tMD5v6sIwgus6Jkz3iIeWStD7oCilRcWpoiitBqNNSU4WhSV3fuFlLFJ5IPY49pFyWZgY0bKqPo/Zy3x8utTBzMUFzF7poKY+woq6CPWBEZSeE6KqzKbJRbc2Nvp38dCvU4htetjo29ZFJsWi1UYUuiRfbdi0e574V5iYhBA9iM28uExZ//DA+8lVD0IqfFgO3p32ASoqKrDZZv2osBFKIYLvKXtSFUUpHSpOFUVpRRhhKp1j1ohS9nyycGFBEuOTZXm8NNvHFJpe+TTCZ8uBmjoSNXma0rSRx28WspChffBg7qHtgLQOonxAAtMHQk9ETvuOIYZ1TWFYX2DsFjHGbZJB28oU/Yb5Tf5tEap8TEWBSgfGB6lsABqL00KhgHQ6jT9c9yf07NUDRx51mCxLpVIiTtVzqiilRcWpoigtDhEYPC/+bwwv8UOpv4fHVbl2iNp8iJdn2nhgSh7PfxRg3oqsxGxTlUK/jhY272Jj884+enbw0LkyjY7lNtKkLHn/cUzb+xFW5iKsqLYxZ3mEWUvz+HRxjI9XFODnHVgZG4N7xNhvSAqHD0tjSG8+CpuOg9up2kg5xlPbGI7B/0XGqlj6znCaKBYJSIjmRYj++da/oUf3bjh4/33g+wE8z5W4er0VpbSoOFUUpWXCT7Ziz2wOyzCX9LiLeFHkw3EdEqU5PPRWFndMcDDhMx/IWujWzsbIzYAxmzgY1c9FdxKmVSkXbVIkJqMAQewgjEg0hiQoaZ+WHcG2Ijg0xeyBDT15FeaCuhCzF0V4c46PV+fEeGsOUF8foWOVj122dXHy2DT2HeDCImEaRqatqsOu1KKEYorStPhN+S7EfOOLF9L3fRGn11z/Z/Ts2R3HHXGIiFOXxGlM906r9RWltKg4VRSlxSGPNdF5LO9IMJJwtGIbAQU90pRxmMddr+bx10kBXvs0lPXbdfOwz+Ay7LOVg77dY5R7acS5CNnAQp62i0To2nBt88iMw6KALApgFpGhXZDWqtxslcfNTLkkdEjM1uZInC4M8OgHOTz/boR5i0PYGQv7DQZ+sVcbbNefq/tjBLRP7jRlWaadqhGmfC4qT78rnCYkSdAUBqEI0WdfmIS27dpg+2HbIvBDOJI4KJ5eb0UpKSpOFUVpETR+lCX+Rp4HsQ8EJBYth8RHiCmfAFc8VsCjH9XCC2KM6VeGw0ansc82KXQq85Cn3eRITLLXlfvgc80/a5VE3CRwO1GGHqJG9HA8cc/y73N802ef9+LSvspSNmzbx/zlOdz1poUHpgb4dGE9OrTxcPzoDH6yZwY923sI6Jh8is/NBr7MZ6rC6dshqUPSCIt/Dq4VoUlYVlNMvcaKUlpUnCqK0uJIhCT7H6MghEeitCabw40vAL9/1saq+loM7lGBE3Z2cOC2LrqX21hRoO0Cz/SkF22SeC15f0YmxkUvqVlLYf5LhAw/SovBBI7OW8hE/4I4RKUToCIdYeaKGLdNjHHPm6tRXVOGQb2AS/ZN44SRaYocwA8z4CaQpgMX7413RoHP/YbyzZFbRdeRm18wOs6pojQtVJwqitIiWOdRRuGIVFwU+/CcCK/OivGzB+vx4swAbdo5OH1UOU4Z56FPuwi1WRf1sY1yO6DtPBGSawSgiFJWLRSU741WFedr9AwrGzkGXlJcS8saH5dlRdIBKg5ipDOBiM835hRw04sBHv8gpAdyDqftkMJvDmqDblU28qEDzyrQdiRYeb+kdo1MVr4pnzd1PNJC8hpTFqk236vivVPPqaKUFhWniqI0a/gJxrKCfWCJpAiCEI4VwHZt3PBiDr96PMTK2gDD+9m4Yp8yjBqYRoMP5H3TxtOWPdCHwrIPfipuCH0iT1vzO+K0o4OvSFvIBwXcNcXHX58L8Vl1hNG9c7j2iEqMHegiF1jw7JR4dAWe8zmrgPpGNB5KKuRxTm0Hs2fOQaYsg169e9D6UJaxSdQOUYpSWjQHKorSrJFB9YuikiceJcrzHNSQqDvnH7X40b+ziPL1+N5OLv55ehtst5mLlfURfG6HKp2buAc/7yPm0rqIE1N9v36Q/TXar9TMU5h7+LMGqs+TSvYjnLmDhzvOjLHT5nm8OjeFg24t4C8TC8i4DsXlYyyeo1TzG5GlfDvEU0oX/+lnnsWUKW9QmAsL7Gvnm6PXVlFKjYpTRVGaHyz0krnoS56HyIaBvEp0zooCTvpLNf7yYoiuVRF+fXg7/PqgdqhIOagucI97hzQIP/5sEXoyFYXJmvB6Ys3+i/vlD/8O/ZP1Dh1LLmWjJudiaJdy3Hp6W5y7o4N8toAL/lnAZQ/VocBV0FZB5ly1L0KXr4D8yZVQ/idrm1hwlT6HrZQHi4ePkvRjruX6u/OKonxbVJwqitLsMJ7SdaVEQIKjzA0xZU4eR/1lKR59P41t+zm49dQ2OGF0Ctl8hCi0kbKMMBUPJLsxeR+ym40rSxLBGtOxpCIPHs1XhRbK4xR+dngaVxyaQVlZhCueCXDm3TVY3RAiZUfiGZbt6diNt3fjHnezhcQnX2+Gh/nicD4IUKACDYdtKawQRQGrKErpUHGqKEqzw1S/s7gzcxZsKbeAl2YFOObWVXjjsyrssnUO95xcjjG9M1hVFxlBy/H5w9tzmCZRLaJHNq4oSbx1/C/5pKwIhThCvp6Hl6rALcdVYtN2wF2TGnDCrXmsrPdloP4wpM1k7FYjUJX/zVoNzwF5aSz69umLrl26Stgs53gq9hWl1GiHKEVRmgXyqGLdkDyxKByTSPP9PNIZG8+/b+Gkf6zAgmofRw1tg18fWo52KaDed2WsUo6fdHxKPGhNBT43PiTps2MDEX3iMECbTArT5mRx/v05vL8owD5bZXDrqTZ6llvwkYLrmNdtMuJLJqHKc+WLGEtXvM7FNJSkg8QM8jcONbX0oSitDRWniqI0H0Q5kLwsPrX4jUqeW4/x02OcdEcei7IhTh5eiSsOycBBHvVhCh6/t36tGmm60o0O0XjwTDiyAjo/oGO5h5mLfZx5z0pMmwvsPMDFP84sR682GYQUzxHPqW2EKbsHVVd9BXyduHCy9hIlPfiNGJVii14+RWkCaLW+oijNAtaXUoXNVdn0kVeRujk8P80jYepjUW2AU0aU4XdHerBItdUijbQINpYjRpDI5vRpahivcKPjEq3EQ0gBKxry6N8VuPnETtiur42XZhVw8s0RlkoVfwyf3/OfXJfG+1DWha8PXWfTJCQ2vfO57TEJUxap3DyE/sk6RVFKi4pTRVGaLCwU1kwsKumPq7zzhQiek8WEGQ7O/NdyLKoPceLoNvjloRXw8zHytoUMiY3IckiTGM+YtCWUP1Z+TQvjuTPHlVQp29Jxy0XaTaGm3sFmHS386dh2GNY3hedn1uDM2+qxpJpHJ8hJG1Q6Q9ZWawWWfFESjOjkVMTDRnE4wvx5S7B0yQpaR6lKxKoRsIqilBYVp4qiNFlYLKydZAlYV5SlgLc+jXHaP6rxyao0jhtegSsOi+FGefGoOghFhLAYSTxlzUGsJeKI5wYjOPlNUtUNwKadbdx0XBWG9UrjkQ9CnHt3HerzrukkRbGlTW3xemnHns9RTD98TcOAB+F38egjj+GVV16VMItTSSd63RSl5Kg4VRSlyZF4r3ieTAh4fMoIrh3hk+V1+N7fC/h4GUiY2rj6CBsuibR8RELNdUmCkJrjKn2jSERwNAfJweeZCFRmjUilmedYqPGBAR0c/OmENti6ew4PvhPhonuzCEIfcRgjiIM1YlzmtGmyL4WvazFIc74uoU0TpRO5RsWVKk0VpfSoOFUUpWnCeqEYZEL62FYOKxtinHtnHm/Mc7DboAiXH1qBMopY5zhIxZ68SUm8h8X5GmGaCL0mTCJGeW5EqpnzheC5R0JqVQEY1M3GVYe3R6/2wM2vBvj1Ezm4bp4ukhGkDM9ZoDb9s954FC+vWD6+nvkghF+szpfrrChKk0DFqaIoTY51hAIJLJZY/N8PPXz/7hV4+iMPQ/rncMPRbVCVClHnO0hzPPGWrvUa8ry5YjyedB4058throKFlAOsbrAwdtMMfndkOdqVFXDl+DxufjmE65kxXwXanMW5Vu8XkTQhqUI+HO7YsROqqtoUrzXDF7r5phlFaSnQs1tzoqIoTQt5LLGoCmIEVggrsOCmfVz2UBZXPGWhT5cG/P3EDhja1cPKgiVV3ub989z72giQlgWLVPbu8ZwmujaRH6FdZYg7Xm3A5Q/UwEtncN+ZKey2ZTkKfgjPzqxxP4gY4+sil7V1itV1TF0xifik5PlyuDZdH7m+ZrV6URWltKjnVFGUJocICf5zAkQiTGPc/loO1z5XQJs2OVxxUHsM7mNjpc9tMc1jzAhT3rblCYtEOJlzY6lJ4tQLUVPn4tRRlThp13aoro1x3j0O3l0SIGU7CECiXjbmTdibTN9asehKqu5lIjHK85TryDi4PKSUXVzGk6IopUXFqaIoTQ8WCTQLwxjpFDBpTgE/e4CXWfj1HhXYZ+sM6uosEhQc2XjEjFfRzFsaXzg3+mLDge8WUJuLcMle5ThocHt8uLgOP/pXPVYFNlyKG5IgjWHG8JQmD429h62MxHMqnmeaIhmA32DGOV27TlGU0qLiVFGUJoGIAvkzIorkAhxSn0tq8vjBP+po3oDjR3k4cWwFahsoouXRA8wMom5gr5eZtzzWnltyuk5sI0WfIE6RTA3wqyMiDOkDPP8B8Mv7lyGyA8RBQAI1lOtZvLytmkR4xhFdjyjEqpW1qKmuR0RhHglCUZSmgYpTRVGaBCwyjXeP56YNYERC7KIHCpj6KbDTgBR+sV8V6goktmg9exFZp7HgaE1VsaaKPzlfC64dI1tw0bMtcPWRbdGjY4ybJqZw2+QAbsomEcavNuUhptiL2orl6ZrztxCGIRzHw/33/wcTXpoo4ajYk0w9p4pSelScKorSJDCeUxamoXT2cWwff34uj7tfDbB5DwdXHdoGFU4EnwVZUWSxRBNR24oEhaniN8JcvtPk0DWobvAwqnc5fraXB9eL8ZsHc3htbhYpz4ZPAtU0CWg9Iv4LSGGGz59fXWquYSHwEUSBhBPh3poKOorSVFFxqihKyRA9ysJAdAGLhxhhSOLTy+PlGXlc/ng1UuXAZfunMaCzg1rfgwcHUbE6PxkmqXUJCuM5FalVnHPjW9uysTof4YjhFTh6dAoLakL8+N8FrM7l6YpZdM1YnxlRlkytiySN0HUjy8fXzqerUuArSOFWlYQUpYmj4lRRlJIhVfMiDIxXj1/B6ZBIWNTg4KIHY6zKezh7XBoHbp0ikcVD/rCE5W2MuGrNHXxYlso14GtHc5uuG3sEAyvCz3dzMXqzNCZ/mMPPHw5hOxyFIrACk+ttplaFpBUz0dnLtctkKpBKpc11pI8g8RRFKSX0bNecqCjKxkUeOyyO5OnD//id+XlpH+mSkDrrnzW45eUAu2+ewi2nVsK2STyELixWrhHFZiWmrIWuJ19FvizZMESndIwp80KceGsdVgcx/nFKBY4YlkbOJ0FGFzh56LNAFWHWGoRq8Rol8Lfauiwcx0Z5WXqtOCVanXBXlCaGek4VRdnoiOdOQolcIKnge3DdAu58zcddEwro3aYMlx6UQqYslMH4udpaoqtu+ALcvIGvKb+6NWM74nEe3i+Nn+6dRj50cPF/VmPWUh8pEvehXHL6x57U1iJMmeI1SiZOT22rKlBZXibhxusURSktKk4VRdnosLeONVIiTVkwuV6Ajxel8KvHssh7Nn64p4Pt+njw613YPKCpnQz1k2ylJCRDRXEVf0QTj3FaW/Bx1PYZHDfExieLPVz6cB3FKRYJaC5NI0iItZbKM3OefJ3MtUrOW5bKsrWToiilRcWpoiglghVChCAyA6IX4hAXP9aAOYstHLYtcMLoNJbXkuCyuW++Q6Ih8WqpZ+sLiMdPAnRNTTiMbNhOhPP3ymDTLjk8MBW47eUaOHYehdA3g9C3MiFmTpcFeYSQrkFDfQG5hoKEVZMqStNBxamiKBsd8U6RiArpERSHBaScELe8Bvxnag5bdgcu3Kc9CYYINjdAtUzVM0+8nVa7/g/42tIlcuja5vPAFp1i/HDfjkhbNq58KsTbC2NkPB6cn64lRxffYSuA0hufK3uMgyCA63p44P6HMGHCJAmHtEzSlqpURSk5Kk4VRdnoGLEZIwpDpFwb0xb6uPaxVcigHBfs5WLTLhHqAnpANRIKprq19VRDf1uMiKfry45R28XKvIujhzo4bjsbn9UE+OWD9Sj4/HYtbqNKG1DcVgEXciT9sAA18+raajQ0JM0dTNpKhidTFKV0qDhVFGWjYLyla9v1sTDitpF5Cvz6kTw+W2rjgBER9h9SjmxDGinbo/iO8WaxrBBBa8SX8tUk18d2LPGeOrGLoODgB3tVYmAPG0++Z+G2idxLnd8nbzyJck9oG7lHLR45U0lLERWMQrpOJl2ZtZq6FKX0qDhVFGWjIKKJJjMznivHtXD7ywEemQYM7O6RgOKe04EIVxEJ9C8RUMrXw1wvDtDlo4n7kuVDoE+HCBftVgU34+OqJy18tJhf4WnTtS4Kf44vG7ZQJAkV01ExXbEJjHlqJMpbh0BXlKaNilNFUTYKbPTNZCGguWMXMHNhjKvGF1CJAs7dM41BbV3U5R3YLm9AE4kII2RlF8rXxFwuum4iUi1EbozaegcHDHFwxJA05i/P4ldPZJEPQkRRhDik+1L0oPLF5u1bnEgT3c3/LLiuSWBHHHogdh43VsKOw+2bjVBXFKW0qDhVFGWjkEidGCGs0EchsnDNU7WYvzjAHiMqcczwMlTnuarfgUXrWCKRVJBtVDB8fcQLKvNimESnG7qIbQdB4OL83TLYpLeDB6fEeGByHTzXp8JCKDfICFLeuoUJU0LSUPF68NBklmWjR9dO6NKxnYT5xQ48JJemNUUpPSpOFUXZKIjhp08YkVjyHDz8dgH3vOWjb9cY39/VRRiadqgsDkSY8rylee82IuL/pOtn9CZfzxi5ANiki40f7ZqW98tf8VyAeSvZa2gG8JdrznH508JEmins8CVZe17Gk2/SmMwl7SmKUmpUnCqKssEQ4y8iif5IE0QsEGi+qLqAa5+oQda3cPZuNgZ3c1Hn2/BIJEl8Qj1Y3w0WmHyxzXU019Ih4VmTdXHo8DLsMyjAjIVZ/N9jeTIEvgzd5ceB6eXfSLS1GDgNyjnRuVEpKAh8RCGJcioU8Tina9a3tPNWlGaIilNFUTYYLIwsUqWJN469Vq4d46rnIrw5H9h5SxvHjGiH+gZug8r6QCSVbMdCQQXq+sIILr6+PAB9hu7H+Xu1Qbc2bXH71Bye+iBAymsgocYdhCgeX/aWptE4HXKaoo8fBHAcF488/ARemfQ6bJs990ExnopTRSk1Kk4VRdlgsBgQYUrCgKvzHRKmU+bYuGdCLTpUOvjp7hmUOwXkYh51U7agaa0wFU+W8p0RkU+X0qEZT6sKFob2s3HKOKA26+LKxwtYUe8iRRZBvNvmNrQwimmKPyTQOTxv3lwsWbZEwlFULBTxtVIUpaSoOFUUZf1CwkZEZaIraR7J9wJ838flj9SSELJw0phKjNq0HPX5DFzuoEKPI5EFJA5ETElQhcL6QDQ+X0ua25ZDAtVBddbGyTvYGLmJh0kf+7jt1YK87pTb/Qo8pw35Y3bQvBFvcBFOj5xGvUwadtqTcJJmNcUpSulRcaooyvqFPaUshMT9xsbeAkkeGb7nzskFPDUjh6F9PJw8zkVDjtaTMOU3QYkOpX/ccUpZv/D9kMH2ac6X1yEVFoQ2ulY4OGenFCrSEf70bAEfLI7gsfeUlRz9cXzTLKNlSTbbNi93KBQCFPxQwtyDf81wWoqilBQVp4qirF+Kbfu4fSlXn/IwReypm1/t43fP+yAdhDP28NC3HMiFMgR6UTSRKODtWpgQahqY+0FXWQoLLL+43enSBhv7b23h4KGVWLA4xDVP1SPgwgTdMx77lAsKpllG8xdsjVMVj2kaUdo8+OADseMOYyTMLyRg1FuvKKVHxamiKOsVkjMifljQsNGPCjymZB7XPRtg9gIfew1OY79typDNW3Adsw1jvK0snZT1D3tOk7mZYiowpCwPYZzBeTuXoUcPG/95K8TT7+bgOQH8kFufSnmheEc53HxFqhGd5txdEqKc0vr17Y6eXTtJ2OZlLODNhVIUpYSoOFUUZb0irxqVqmAjZFLpAC/OjnHnpCzatynDubtVoNwKkZVBTdlPx5685it6mhvGq23mNt2j+kKMLXvEOG2nNOqyLn73VIBVWVrnGnHKUo39rRy/uQs3c/Sm+MTnIm/HKnaOEt1dTLOKopQWFaeKoqwXEq+aVB+TkWdBw+SjEL9/KodVdTFOHG1hRD8XtQUPPHaUFXum2rgYV9nwyJWmf+aKW3QbLNTkbJw0sgyjB8aYNKsBt0wKxHsahhyHlSzFFAHXfMWbiHJOl3wKEWToKHlTFJlBM4wUr2ve56goLQUVp4qirDfErJOBZw9UTAKAq08ffKOA594PsFnvGGePSqMuT7o0duDxa0r5NUValbpxoWttBGoiT2OEgYWO5cDZ4zKoysT484t1mLk8Jc0uQrqPcj+buWiTjl1yDhaJ0VCE6bNPT8CUKe9ImF9CIClYxamilBwVp4qirBdYYLLQYSETRRS2YyyvCXHVs1npYPP9MVXo2YkEacBxSezQNiwWWCKpt6pUmOvuOiFWNwD7bOlg38Fl+GyJjRueytF9CkSryZ3le9WMCxFrPfScPrkq38b06R9g7txPJcxvjTLxmu85KkpLQcWpoijrBRYvXC0akuHPByFsEjZ/nZjF+3Mt7LZZCodtV4ZVORI5ZPsT+y9iR76rICgFyXWXMRNiF47t4vRxKXRub+P+N3N4ZWYAzw0Q0v3kuFKIkL/m7Unljnp8/KmqcnjlaQlL21NapylRUUqPilNFUdYLIlZYaJJwKfMsvL8gxl9frkdVxsWZu1chkyFRIFXEHNdSQdoESO5DDAcuWYO6rIPh/Rwcu10KS7Mxfje+DoUCiTabhai5X2ZoqWZ4/7hUxMqazsO2eAQJCw25HLL5goTlOvDUjEW3orQUVJwqirJ+YLFChj2KHZrZ+MPz9Viw3MFhI4FdtiigoY6H6zFVq1KtryKg5Ky5DzRn3RbT/cnngVN3SGNQD+DJ92M88Da/h95CEPG9DUzbTf40t/vH5ygCm6S4y2k0wh677Y7thg+XMI99SgERqYqilBYVp4qifGtYoLDJF6FCEzfb89wIk2YW8O8pAbp1BE7ZsRx+4CEi22+EDdMMPW8tkkb3gWYczGUd9Olk4eSxadCNo0JGiJo8V3n7MvKCtM3kTcyNbDYkqY3PV4QoLRm85WbYvF8vCcs4p2tiKYpSSlScKoryrWFDz3JT5hK2kA8j/Gp8DRqyFk4blcGWPYG6AsW1IxI0XHXazFRNK4ALF3JbuJCRitFQH+HI7dIYM7Ad3pyTw80TcnAdrvz3ENN9lEJGc7uPxTSawOGIxLbpHFVU2zRrHEdRlNKg4lRRlG+NeE5ZqMQRsiRKbTvEg1MCvDgjwla98zhmTDmiWhc2CR4r5nZ+PFfj39RgQcbtLVmX8cD8DXEa7VI2vreThZQL3PxCgM+Wx/Ac7kgkMk4KIs0J4+U3zRHY+2vGOXWKw0iZUQlMem5moltRWiAqThVF+UYkBtxMtIDETBhZcC0fKxp8/OGFajh+jJN27ITebVzUxw7cyGskgFScNjVYaErBgUwC3UmkbQvVORu7bu5gn8EePl7m408v5ki4ckGE719RxMlfMdzU4WM1CVbGOeV0OOnlN/DutBlGoAb8xgE6t+ZwLorSwlFxqijKNyIRlzxPdCYLlJQT4ZbJebz5qYcdBnk4cqiD6nxEorUoYOjD79vnj9K0kHvCHnD6mDFo+dWm9N2NcO7OZehQ5eCOV328+Rl3juKhmMz9T3rus6Zr8shh8oGacU7ZazplyuuYMWMGnQsPpcXpks48SdSKopQMFaeKonwjEi8Zz3mKSKnwMERzl9m4+SUf5U4BJ40rRxsvQhhKLyiKLb45mhXnSpPC3Bszl+Gl+EP3tj7vYHAvB8cOd7FyZYxrx/t040OEEU3sfYyMQCVN1+RpfIichDntlretQrqiTMJrCl3yX1GUUqLiVFGU7wCLGfpPFv2GCTnMne9jjyHl2GcLG9UkbGyWBLyyGYgXxWC8p0BE/1y6g1Hk4ISxGfTq4WD81Ho8PT1Gyg0R8L1vJsKUkTKSHGxRhNL51dTXoT7Hb8LidGzOm+eKopQWFaeKonwjxLvGAoY+YRTDsS1Mn5fFPydHaN/Bw5njPLi2g4Jl0zoWLxTT6AGlGSD3l24b3zKu4m8oxBjYzcOpI1NYlbdx/bM5NAQxPLq3/DE0A0EniZCnWIaNihFh9KjR2GrLLSXM7U5NQUsTq6KUGhWniqJ8LdijlHzYyMv3yKeQjz+OL2DJqhAHbJvGmP4eavIO0hTNtN+jeGrvmw2JNjMijQoYloNaEqjHjExjqz4uXp6Rx4NvFajgYdqeNqZpex2NZ5TTrue5nDgxbtQwDNlqgIR5YH5ep0lVUUqPilNFUb4WLFYS0819ukMy9inPxuQP8/jH2z56tbdw5s4p+AWHBA3FofjJ6zF1+Kjmg7lnyZxEG025AOjV1scpY8qRs/P46zMhljeYvv3Gh873l8Vf073P5tjMuSXH2nicUylySZSmew6K0lpQcaooytfCeE45ECHiEH3PR8DVz+WRrbVx7A4utu5qoy5gY8/mnwUA/Rer35Q9aso6FO8Z3zu5zfRJk6VYEaRwxGAbO/Vrg8kLc/jXq7WwaTl3jIooTbCYbcqeU0m/MknSpcn02DfV+fyCiGRd0z0HRWktqDhVFOVrIUabDTh9At+H6/h4/F0f46eH2LKngyNHZ9CQC+E4iXFv7KlSb1RzQfygxXtmwuxVdBD7LqoqUjiVCiEpJ4XbJuWxcFUetpVFSNrOFESasLArimc+t8APZNG0d6Zj5uxPJRz6PPapilNFaQqoOFUU5WvBIoU1C/fSJqmC+ryFW14MkMu7OH6Mi83busj7/Ehh484x1cg3d7g3vtFq3PENqM3G2HWwiz0GpfDuvDRueSlHhRG3KOo4jchmTRM6NhHadJzs6eWxTV94YQLenvqOhOOI6wOadtMERWktqDhVFOUrSbxIPJcwi5AwgpOyce8b9XjxwxxGbmrjsO0yqM7S48Slh0rkUTwy8iJQlebMmjvIbYbpjztAlZNKPXWcharyBvz9jQI+XQoRrpw8GlftNzUPJAvPtZjjLKssR7osY46VBKqcp6IoJUfFqaIo/501Nt0SceI5wPKGCLdMDBFYIU4a7aFbBRDSeidOGR3DIkU9UC0ArtbnufGg8ssWVtfHGLl5CvttlcHcRQ6um8DjhBrxJ3Gb6G1f57DoZNhDWputR0Mua7ylXKBiT3ExiqIopUPFqaIoX0lSxSm2mw13RA8NemrcPimHKR/b2HUzFwcMTqEu4iGHOCJ7TCkeh5uY50z5DhTTAcNe0nQQ4+QdM+jSLsQ/Xwvx/gIeWsqWwosUTHjeaJsmgUmUEuSOUCxDBwwYiN69+0iYj1eOW9OtopQcFaeKonwlXN0p7Q5JlOZCHzaFl1SHuJvEaSrl44Sdy9Gu3ELOL25AsDwVndrUxInyreF7aaSdJb3bs3kPw3tnsP/QFFatDvCnZyNEkY8o4J77IW1g0k6TggtOxTTpyjinwIF774pxo4ZLOBnnlCJJHEVRSoeKU0VRvhIRGFJFH0pbUsuO8JdXCnh/UQo7b5HC7lu4qKvz4bJB50lcT2rcWxqcDkSgksBDbNMf32sLJ4+pQO8OKfzrnTxe+jgrb40KSJxKtCYmTo0wNc0U2LvP33mMU+4IlYhWOb9iWFGU0qHiVFGUr0QECRnyKOL3qQeYuTTCnS/5qPICfG+XclQ4DnJWGnZxnEgx7E1MlCjfHU4Hawoq9GFtWpuPsXVPGwdvb6G2Oo+/vhggtH04MVeZy0aybVNBDp/+SfIsng97gS0Z59SIVXnxgERQFKWUqDhVFGUdxICbwNowHPGa/mNSDp+uCLDHVi523CSF1TkLju3wm8klVuKBUloecm/lz9xjfgNYfSHAiSMy6N/TxePv2njyvQY4DlftixI06UeCpRd8LKuLgeI4pzE+nv0Z5i9YIuGQl9G60h+poigqThVFWQfxlrKg4DlN3MnFcWy8O4+r9GO0bRPh3J3SUtXPvaPY6Fu2iZt4oJSWjCmwuHSb/ZyDAZ1cHDvGRbY+i+snpFHgAfn5w+lA0lDTSBPsFRXpSX9ByAPuk5h+8lm8+toUCYdhJGm5KQhpRWntqDhVFGUdxNvFuoLmYRzSdw434PcTfKxYEeDIoSls2zeN1bkIblGocKREmKpxb+mI9IS8xNYD6n0bx2xdgc02cTB5RgFPvBtSmSVEgcVe3IRea8olLjpuCRbTaSrtIZXy1qRdWd8EhLSitHZUnCqKsg4iJGjiWSEK4dgB3vzMxjNTs2jf3sGJIzNSjW+zMpGBy43RT7xjTcFLpmw4+P6ajkMOUnCQCyz06uTh5BGV8EmQ/u6FWtTleWipAhVuKC1wWip6JJOpKcDnkc3WI5/ncVqNKOXj1NSrKKVHxamiKOtgxCUb64jEB49dGeG68QUsXe3gmJEWBvUqQ32WX2dpvE8qRlsXRmCSQOU5fTgd1OQjHL0dMKQ38PpM4N63fLi2TeJUNJ9gRO3aQsxGJ6nWJ+R1pXT8Pbr3QocOnSTMDVQECiuKUlpUnCqKUvRuSaBonGOEkQUe+nHiTB9Pv91AhtzDKaNT8LmpqVP0nhEqTlsXRmBKgFIJhel/IYrQodzC8TuUwY0C3DQpxuq6GC6lkYg3kmTFotZMJUGSqUmrHr/mjA7qsMMPxC47jZWwza+/4vWanhWl5Kg4VRRFDLIMoSONTXkiYx3bCCwff5sQYnUWOG6Yi0GdXWR9mLdBsTBhgULbqUBtnSQV4ewlrcu7OGSwhxFbVOGdD+vxtylZ2LaFMGwa6UOSNf1bO7fp+Hg4Kf5O/7hTH59NEzhWRWntqDhVFMU4S8kmF5sIkqCwYLsRnn3Pwv3v+9i8l4NjRjho8C14ZLwT31fiBSuZN0wpKfKqUirIeFSQ8SkBVaVtnL6jhXQ6hb+9BCyvKcChkgyPk2uknySzkmDS6FrPbVKo4knCslbTsqI0BVScKooisiFpR8htTKM4gB8UcOOzOWQbYhw7shJ9O7qo8dlw81hBRsUmxl29Ta0TcbRTkoho7pJArcs72G2LFMZulsJ782P8/dUG2FYeQWTGFV0DBTe2CBRxTD/JaTUKeRSBCAsXLMXSZSvpYOg7LeNYiqKUHhWniqIYj5F8WHraSLkxHns3xEsf5TCwj4XDRnjI5rk637QhNJ1hlFYPF0xY9PGcvaiRjQrHxuk72yj3XPxpUh7zlkXwHAshRy+mMdaAG7tA09hj6gcBbNvBQw8/hkmvTIZF4TDglM2FNE3ZilJqVJwqikKIxKCPJQKUhegNzxWQpSXHj0ijV1WIfEhxWITQJJW0G1lcKE0PKaRQekl67nP7zXo/wo6bpbHXkBCfzXdw4ys+iT9aG9LEApY/HH9ji8BGyXXN78u8+J2KXZwLNF0rSulRcaoorRgjEJIJ8tpJh4TE/W/5mDwzwLb9Uzhiuwzq8y5cx4VtuWS8bZo2vudLaYJQGuCPzCU9sMSLUU7ho7cvQ7qNg39PyePTpQEVekJEUSRJjbfZ6OKUj7MIHytPUWSOyRy7TYfGH0VRSo2KU0VpxbBRZmOc/Hfo+/L6CNe/VEDkFnDSqAx6VIbwyYibOEWPE4c2urhQmjIs60TiUQGm2g+xy2Zp7L1lgLkLgZtfDmWIhwgBRaSUxN5WEYQbkTUFMTpG24xz2q59B1RWVknYTvKCpmtFKTmUDzUnKkprhbM/e7ECmgdhhIwX41YSEt+7ZxlG9mmDe85Mk6iw4chTwpVtGBG1vO3GFhhKk8WYEk4XAQqULtqlI7w2J4+Tbm9AmRvhye93xNa9KV5gw/Zs0Ymceri9Km204dMS/Z4IaE67kfGR+gUetBdI8bin3LuLh5Pi89B0rSglRT2nitKKYUEhXqyIpKcTYWm1j1sm1NCaSpwwNoM2FSlYIYtSrs43VaGJiNjgYkJpVpi0weLPQZpMS0ODg+028XDg1hksWO7gjlfquBgkTUcoGutR1ossZ+X/hkZGFqBjlEIViVD2nqYzHtIpj5bbsoyPRcSyoiglRcWporRiRGAWRQK/IOdvr0Z4c16EXbeIsd/gmAQGG3IjHURM8D9F+RIkbbACNKkFMYu/MMLxoz10bgP8Y0oO78yjdOah+FpTFrIsB42o3VgkharGablx2KxVFKWUqDhVlFbGGkNMc9ETNFl2hCU1wN8nF5BxIxw7zkW7lIUgYuFAcSg6zxPDriifR9IGJw9xi7JnMkZtLoVtNglwwPAMVtbGuOGlLCL4MqxURGmLq9c5dTXShhsOPqwkzXO1PgVWraxBdW29rDRV/SaOoiilRcWporQy1nhLRWxKUHro//WVAj5ckMfYzSqx5xYOljbQA8KLYLGI2IieLaV5Y4aXokINzSM3ABrSOG2ch14dU3jo9Rwmz7aQsgtU8AmLgzexIDTbblDkN8wPBSGPc2rj/vsfxosvTaR8YMvA/IKKU0UpOSpOFaWVId4jFqb0j9v/cS/lT1bE+NukGpRnLJy2kw3PteDyuKaRLcKU4yrK10Gq6YulH4c+WZpv3dXDIcOB6mwKt06ohi9j5gYUhd/UJImxuPWGwyRhk45DeUNUDN8nkez7EpZhrhgusSmKUlJUnCpKK4S1QBhHJBJ8ssU+bp1YjbkLPeyzrYc9BpahPpeB4zrGryV/arCVr0eSZoxb3qG5gwbfxrEjKtCza4yH34nx+qwCUtzImQWhNAOg+DIrhjcSpiJfUZSmhopTRWl1GJMc0v+UY2P20gLufD1G23Lg1LEZxDGPacpV+aY6X15LuRE8W0oLoXGaoT+bPkEhxBZdUzh+lIvavIdrxq9CIXRoDQtYS7z3sp2kuw2T1sxuzb4dSvfcvMVzU/JyCQ7L2KcSZcP8vqIoXx8Vp4rS6mC3Vixjl9p2iJtfDLBoiYN9BkcY3j+NhjyJBrHka0WGVusrX5vGaYa1J38ch9JViONGVmCzXgU89UEa46fVw3a4012IMA6kep+r1zdYWpPdmn27dDxcjX/EEQdj553HIaawzYKVY7BQVhSlpKg4VZRWgLQzLU4sF7iTNPfQnzY3wN9f99GlfYDTx7Sh9SY+C4yk9/WaalpF+To0TjMsUmkW0b9CAPRuZ+GooWUIChZuerkBhbAAhIG8BIITH+tSk0Y3AHxIlKYlWdvGc9qhY1u0a1vJK4rjnHLS5/+KopQSFaeK0hpg4yvWWb7IxK+Z/MvEAMurgUOGWBi8aQoNhYjfMikiQV/jqHxnuJBDM05LluUhV4hx9HblGNDLxQvTbTw8tQAvxR5LFov83n1JeGbbDUQifht7SNcJF+eKopQOFaeK0gpge59UtRZCEqB2iLfn5nDfmwV0bu/jyO3aiwcLET8SSFCQhTY+L0X5bsiwUiw/KTnV+R66t49xymgPPhz88bkAq7MBhSwUWzrTFibdiYhcjzpV8oCIZG4+EEm1fiEfIF/gJgVRcZxT07RAUZTSouJUUVoBbHb5j0wy7IiEQBTg6hfyWFUb4vAhbTC8n4O6XAop7hTCYoLtcyNvkqJ8G6QavSgIuR1zmhRqIevikO1SGNrfwuufBnjwDRKnDglEKRgZgUgK0eyAE+16wohO07QlCEgK0zEl45yyII4CHkqK4qg4VZSSo+JUUVoBbG5ZaoaxBc8r4LmPbTz2doRNulg4c4c0GshYs2fLeFdN2z+t1le+K4kX0sw5Bcbwowidqiyctr0n6/7yShbLqZDkFMc8Fe8ppz8Sj5wO1xtS2DI75OPh/a9cuQK1tbXmt5L0LvEURSklKk4VpaVCxtYY3KJAoMmmf0FUj5ufb0C2poCDh6fQu0uEeu6hTyvNgOgsEAg10sp3hEWfpCeaJBVS+oopndU12Nh/qzLsuImFqXNt3Dc5gGWH8IMAYRhKOhQBuV7VqckHdECIiq8vdRyXJkfCcfF9VUksRVFKh4pTRWmhSPU8iwIy8GziQ7K6jhPh8Y8yGP+Wj/69bBy3fTmCQowMC1MeD11Ns7LBoLRFCdGGQyI0RKbcxgnjypGKXdz0ShbLamJ4JBRFzFJcLlexZFxvrNmV8ZrylIhU+U5HJr/HP6woSklRcaooLRSpnhfDy0NHxWJ6SRPgpmd91KGAE0eVYfP2DupCl4QsK1OWsOvTU6Uoa2H5x6mLtZ/r2MgHMfbYysOoLYHpCyzcNTkP28lSWiVpys1LTGzZdn3AAjSZe65LwjTEwQfvj7FjR1PBLITDb6ziXy3GUxSldKg4VZQWBgtSM5eZzAskSm27gMfey2LCzAK26pHBYcMyIkxdfgzEPJzP+hMCivIFSPNxCrMsGzZNQWijzHJw+ug0yjIubpuUxYIVpnlJxAOjcq88Fqq0TZKmvwviFeVjoH3JgPt0DL16d0O3Lh1pOX2nZeYIFUUpNSpOFaWFwZ4fNsDJYOJs110nQk0uwu9fiBD6AU4cBfRqZyPvQ8Y1FRFA8dVrpGwouP2oSV6sEC04toW6IMZ+A1zssTXw4Xwbt06soeUUhdYLnCZJMK6PdMn7kE9xXzyXIaQog0iYlxWXK4pSWlScKkoLIzG2FJIwV5N6doT73orx6vR6jNo0jYNHVqGhUOyhzxvRXBxVrGQVZQPAVfUmsXHBiZOcSZuhA5yxvYNMRYjbX40xZ6kv3lM/CikqiUeOuR7SJe+C97N2zsLUNs0IKCzNYNbTbymK8t1QcaooLRAxsGKAuTo/xspsjJtfypEYdXD0qDJ0KQ+RCxp5slg1sGBQr5GygWCvJf9x2uRkxh31uB10fcHGiE0yOGhIFeYvBf74XD3F5kHyAxGOSTr+zshOzI58n4QvHcx/HnwcE16eLOHQ13FOFaWpoOJUUVooLDT5Hfq2FeHuVwK8+UmIsYMc7Lutg5qcLW1NjRQtvjZSUTYCRpiyQDUefvZaOp6HM8c46NLRxT1vRnh7QQ4Zz0Ekccw23xnZidmReErp+/z5n2HZsqUSZh+tsF5+TFGU74KKU0VpASRVkTw3hp+HyYlg2wEWry7g5gn1SHsuThxbhg5lNgqhC8/hilVj+Tm+omwMOK3xh9OedI6iT002xvC+NvbZxsXy5TFufKlABasQtgz1VKxq57RN2ydp/Zuz7na8n/LyCmQymTX7N8elKEqpUXGqKC0ANviJKBWhSWGuuHTsCLdPzmL6ImC3gS723MpGfb0nr5EMI45L27Dx5/aAirIRkHF3JZ3yF/bsc+99R14pesaYNDr3cvHw63lM/ojEqcMitZi+eRvaRNL3t0GSuEnnSV7J5QsoFHyzfxaovF7miqKUEhWnitICSIxtYmD5NaUuCdNZSy3cPDFA24yNk3eykY4jhIkQFXFghOn6fROPonw1XCCSdCrJ0HhDXUSoDW1s1dPF8UNtrKqzccOkAq1zxJfJ0U2HpeK23wKTP4wo5nFWuWp/n733wPbbbydhh5ex75QjKIpSUlScKkoLITHa7BENuErUinDHhHrMWxZi9y0d7LhpCrWFFCwSrWu8pWSHxR+l9ljZaBQFIP+JEKSJh40giZoLHBw7og027VqGJ98p4Pn3CzI+by4IRZhyYerbwrmDf46zievxe/0tbL5FP/Tp1V3CjudKpG//C4qirC9UnCpKC8DoUjbfXF0fIG37eHshcOuUHNpVluO0nSqQIasrbw+PbfWWKk0C48lkbyiJQ1KO+byFTboHOG60g/pCjP97vh65EMg4JE55YH4RqGbbb4roYfonepgyDIe5XXZME4dN7QMdi0RQFKWUqDhVlJYAi82igQUCst8e/vzsaqxY7eCIITG2629hRd5Fyo4o07OVNoZaUUpJIky56p6r7eHEiGodHD7Gx1ZdPIyfaeHJaQ2wHQ8hrZYk+y2Trckb/Hv83+QV26bcQJMIU4nDhTeOpyhKKVFxqijNFTKi/OE52XgOSTjlpfHmnCwefBfoWmHh6LFlQMGBY9lwItcMz0NGWLZVlJJS9GRywYomNkj1CNG9ogwn70BpldLt9eMt1OdCEpKRdI6SdN9o+tpwmi/GD/xARO7jz07AK1PelnAQchfCb7hPRVE2CCpOFaWZQrZWRKa4fNjCs9cHEcIowtXj81hVa+PoURkM7WkjF3DVJRne4jYUYllgdqQoTQIWhZQmbRuFrIXDR2QwfJMYE2dH+OebBTji4TRRTPW8mb42XIIrpnmuzuf0P336B5g791MJx6R8TTb6BvtUFGWDoOJUUZorLDKL1aJh5CMfFWA7Fp6bXodn33bQr32EY3bw4OeBwIlgk21eM2SU2l+liSGFJfrzYgfcT79N2sNJO6eRdgPc9EweK7IxbCuQtqffxnO6TkwWobRt24pKlJeVF/fD+5WjUBSlxKg4VZRmivg/xeKad5Sz+MwHPn7/bIi6MI8TdijHoI42GkKKG7v0jy2yEQBqgpWmhoxjSmk4tC048FBfsHDYluUYuXka7y+McNuL9ZSEfRSi0BSyuHC2ruT8r6yT4injsNe1vroWuYashNlzaryriqKUGhWnitJMSQw0V9ez8EyR/nzgTR8vfRhjYA8Px4zIoM4363hYKRayEldRmiBmHFMzZ5HIHaAyro9zdnRRVg789WUfnyx14blUGOOe+xTnmxSypDmLiFIKSxOBCDvvshMGD95WwjaJYv58E2+soigbBhWnitLMWGM8i8KUB9x3yKyvbgjx5xdDhAhw9tgy9GwDZP20tNWzY8rqYse/vjFXlI0KqUYWjvyPZadL85UFD7sO8LDXQAefrgxx+8tZSut1kvZZnCaO068jKGX4NN43RfV4TFNi2PCtMWjAJhJ2aRnv5Ru1Y1UUZYOg4lRRmhlrjKdYUpoiEqdOjH9OjvHqJz7GbO7iiCE2qn0gxXHZY2TZYvi/iadJUUoFy1P+uJFDYhQ4c9c0OlQEuPnVCFPme5Teo6L31AjTryUoKU4Sj+f8Xv8oDE3nKAon7bFVnCpK6VFxqijNDPES0Z94TUPKxHaI+atj3PCSj7JUjO+NySBdwQOMS2yKyH4o0z71m7TRU5TSYQSi7fio8W2M7G3hgGEVWLEij1ue5yTNqtTkBRaTX8dzKo5WiW/yAYdtx5GxTmU510RQvK+zL0VRNiwqThWlGcK2mTtB8diMlhXi5pfqMXNRiLFbONh9mzRqsy6siH1OHJG3MFWm6jlVmgVJWo1JPMYuClEKp40qQ68uFu5/qw6vzMrBIeEahNyW2ojJz88/T1Iw4/VRwJkixsTXpuKdD2ZKOKS8pMJUUZoGKk4VpZkhBpSmkFRnxrPwwRILf38lQruKEGfs3Aae5fJqWPK+cg6oIFWaF9J5iT3+sS2d+XJ5B9v0tHHsCBs1DTaufqEBBRKYjmMbyUkJPvGgfmW1PJfoJDYX6gKKZ+O1Ka9jxoczJMzV+5xXVKAqSulRcaoozQxjfGmK8vDjAH96rgHzV+awzxAXu2wG1OQAl3K2mliluWKEKQtU9nBaVNCKkC2EOHpMO2zZHXj67QiPv8sD8xffGtVImH6luOR6fc43lDM4CseryGSogOdJWDajf18pbhVF2WioOFWUZoAYz2ROU0STazuYOjeLB97Io1OHNE7fIWWq+R2uwjcGludqa5XmhlTpS7pN0jHQEDjYpJ2FY8dWIQ5j/OnFnAjWpC0pk8z/F7bkCwu5mnoUGnLr5JOvtwdFUTYkKk4VpRkgxpOspjGiYrphkTi9bSKwojbG/kNdDOljoZB34bCA5fX0MWK2aHUVpbkhCdl4UR1Kz/X5PI4alsY2fUNMnG3huRk2HAcynNr/hPaV5AzuBMXV+NttNwIDBwykPMI99iVX0W9xHEVRSomKU0VpBojIJNvJRjQX+WRII3y4JI9H37fQvb2FU0aUI+enybY6kKamhJhaEbPmu6I0NyTtcsKnAFfhZ6M0ulVZOGS7CoQBcMuEZWgo5LgYtvbd+F8lLmU3skPppc95acedt8fgoVuKUHVc7kBI22qGUZSSo+JUUZoB7PGR6ksKWzIuY4zbXwmwdFk9dhtchq27p+DnHVh2jIiMKxthdZgqzR15pamkZUr//FJT20VdPsaB26SwVY8Yz37k4YWZIVynAJ/HPSWMAP0iUlCjTMGr+W1QjuOKKBVhSmFebqYv315RlI2HilNFaQaQSTXe0zhC2nbw4eIC7n2tgPZty3DctjZC9haxeuWYEq+oZBWlGWNeaWqq9WVOaTwfAn07OzhmeAZBvYs7Xw0QUFq3qWDGTVi+ynPKS3kfnEfkO8Xj6v1knFNZ/l+2VxRl46HiVFGaKGIi2TiLVaV/lkUiNIDlRLjnNR/zl1oYt3WEEZukUF/g9+cXt6J44iVSB5DS3OF0zKKRdSOHKHlzD/6GbIQ9hqSxaWfg6fcCTJzpw+O3RkmmITjfcF5IvjNF0cni0w8Cmkd4972PMPOTzyQcBqHZRlGUkqPiVFGaKOI1EpFJBpPmbDg9K4351SHueR2oqLJx1vYViJyQRKvYb4qhilRpmSTp27VsZAMbAzvZ2G87D/V1Af4yKSBhatNa9q7Sf843lCeSV5IyjWUnV+XbtoPx45/DG2+9JWFexj+inlNFKT0qThWliSJtRlmgspGlfyHbTjvEva8AHy/PY/9BEYb1c9HQ4CJDOZlNqkpTpaVi0jaJT8oYrm2hNu/i6FFA7y4unnsnxutzfGlzHXDHKM43tAXH/TJYiHKeqqgoQ3kmI+FItuPCoOYiRSk1Kk4VpYnC7eeMv9RCSMqUDe/C6hB3vZ4jg5rGoSPScMG9jh2QqaUtRM3KtorS0pAUTsKR+z05ZLr8EBjQuRz7DnOwqjrCzS83UKQCFeL84sD8XLBbmx8aOVHhWLbsK9eQR5DNS1janspHUZRSo+JUUZooSbW+HUfwyXC6Voh/TALeW+Rj101jjN68DFmfMjGJ1kSY6pimSktFqutZbNKc0zu3sc75EU4emUGvrhEeegeY+lmItOsg4BgUtXF2SIp6Eip2guIxTvv07iNh87pf3k7lqaKUGhWnitJUKVrX0IpImPpYUgvc/Vo1vFSEI8ZaaEvG1A+l8pIjm03EcCtKC6QoTJMe/KwlG3wLAztZOGDbDGpqcrjllSwiFBq9iGItMhyV5I8YjsNtTEPsvc8uGLn9MAnze/plC81DilJyVJwqSlOC9SgbYTGuxpBGkY0U5dT7XvPx/gIbOwzwsOfmFVjlAx4bVDG6xvBK5ylFaYlw+l4zZy8oGzAbPhXgDh7poUM7B4++lca0T7Owi+/c5zicnyQ38XbcVEbyCcw4pzE35C6Oc8qfNQJWUZRSouJUUZoSiXFkA0pf2bhy7+TltTH+OimPTNrH6SMzSLu8jrMvx+DqTlPlqdX6SuuAlScPpB9SIc3CkB4W9t8mjcUrC7hzomlPaj6clWhezBecW/g/L+P8wu1MLcpfUiBMMpyiKCVHxamiNCHWikzunR+hEHAP5AAPvhpi+kIfu2zhYefNPKzO2XAa6VCjZ8kIN1qmKC0XTussUCkfxB5cmk4cXYG2nUPc/04eH8zPU74pIAh9k58orghQUp+cx8LQjGn60cdz8en8RbJcevAXRauiKKVFxamiNCHINJJxLDpxyKCS2cXqbIxb3loBj1YcNrISmbIU29JGqDFVWhfi+ZTCmI0UZZbago3BvX0cPLACi2ocXP9KLSyu1+cBgDl/8N8a0UkFPz+ETds+9sTTmPz6FNlPxGO1URwVp4pSelScKkoTIum0IYOHcycNL8R9b4SY+rGDUVulsNsgB/VZyrhkkNfaUHWXKq0LFpDiOGUxyd85P4QOThxjo0ObCI9PsTF1ng/XI9FJKzmHcL5aQ9FDmkl70rtf9lPMT+vEUxSlJKg4VZQmwBpvjRjSWDpz2FaEVfUhbn05D5eM6PEjy9E+za8wBRxSp2xD1ZAqrRFJ943SPzdxqSk42LaPjX22SWHxyhi3TMzTGirJESxhkyxmMIXAMJtHXAiL+ykWDE0ERVFKiIpTRWkCJEaWEeMY2TLczf1vRXhzToQxm6ZwwACLDDBlWhKmbGzFkJLFbbytorRWPDZngYVTRqfRvj3w8JQUpn0WSn7hES84m6zJL8Vwzx690KlTJ1M4TNZzWFGUkqLiVFGaAGIcWZbSPIoDGVi/pg64bZKPskwDTh+aRqrCQRBalGk57lpharZVlNYLF89iJ0SN72JYzxQO2rYCS+pqcNfLEYnNiDQrd4yicDG/uK6LMApw8CH7YYcdRpN4DeA6bnFnvDdFUUqJilNFaQKwwZRhoCwSpwGLzhgPvl2LN+f4GNUvg122dVHfYMEhMxwVRWniMU3mitIaEcFJkxPzS005bOOo0Q7at8vg3mkhpn22Co4VoUCFvkSc8tx1PDgubccThVnhSl7iSVGUkqLiVFGaAGwUyWwiiizYjo2V9RFumBgi7QQ4ZlQVMmUuGVWKRzk2MbCKopiCnbw1irKEtD3NRdi+p4WDt3axaLWNv74SwEUEm8Rr0hxGRCjx+TDvRKWpopQeFaeKUiISgWm8pjQnqxhSgAcWv29KHaZ97GD45jb23NpCLpcY1aIRVRTFUMwP7D2l//TdRZ4KeUeP9dC+MsIDU228PWclPFKukYwWVRzTNI6weNlKLF9VLeE4onxI+9CCn6KUHhWnilJSEkNoBKpLOXJ5fYy/TaTvmQJOG1WOtq4Ln4wt214eFkc8RSpQFUWQnED5IckR7D3NFxxs18vBfkM9Ep8x/vSKR2uyEpnzTuAH9N3Cvx98BC++/IqEeWB+zoQqThWl9Kg4VZQSwUaSKxGNR5TbklKGtG3cPimHKXMi7LI5sNdWHqrJkLJolW3MTA2oonwBEpacnxCB3/8UhTZO3j6NzhXAw+84eG++D5vyWcgZrZjvELMgTYaSMjQOK4pSGlScKkqJEIFJE3dwCgM2kMDC1XW467UYZWkHp48qR9pLIQi4mwebXiNOEzGrKMq6cL5ggcrjANf5Lob2ymCfoWVYtSLAzROzlInqEEQFynZcrR/DCWkyL4aSiSnOFEUpISpOFaVEmOp5DgA+zR0rxJ2vpfDhpwHGDHCx88BK1OdiaSsn7enYeqooVZQvRQptnJlobsdcoLNIiMY4ZayH7h0KuPvNNKZ8WoeM4yGE6blfWV6Jskw5hVmSFpvLJCpVUZSSoeJUUUoFGUIePiomU+k4wJLqCHdPqgMyFk4bEyDj2uDXfScGk+dana8oXw7nDc5PMog+iU2bptogxrDeFg4dWYmalQH+MJ5rKnLw3AyCwMcRRxyKnXbaQcKOyyNiFAWqoiglRcWpomxM2IAW5+LloYkNaors4d2v5DB9YYjdBznYaYsy1BQiuA4PuW8EqRpNRflqOH9IFlmTTyzpHNUQWDh+VBl6d/HwxPsxJn5UTeKUo7kor0yhvCIt45xq9lKUpoOKU0XZiHD1vPHsiBUV2elYDj5ZnsefX4qRqQTO2TGN8hStiTl7Gk9O4jVVgaooXwfOJzFcOKgvWBjU0cUhI4C6+jLcMjkFPyzAstfmpSRfJXlNUZTSouJUUTYiMlh4UWhyp4wwishIhrhlQkQCNcTBW6UwejMXK3O2eFMFiavV+orydUmyDjcltS0bdaGNE0dUoE+XGI+9F+KVGT7F8VHfkEVDNouI8iJj8qXmMUUpNSpOFWUjwmZPhCbNfbKHjh3go6UB7nm1DhWVwHEjyykCrY0sBGsE6Vpvjnp1FOV/IzUU9IlsC25sIwgs9O+awpHbA7W1aVw1fjllJkfGOX32xUkSl0fMMBurOFWUUqPiVFE2MlyZz/KUO2xwzeIfx/uYt8LCQYMdjNzMQn2eRasxkMaLo8ZSUb4JpoaCclmSf8jS+dkAx27vYVDPAOM/qsDr8ykn5hvQkC2YQqDZlEuAxYCiKKVCxamibATWrSq0ENJXz87jjQUF/GdKHu3bOzhrXBkZU/aSOhSDJvb+FCdFUb4BnG/ow3P2ovLAUvVRiL5tKnHUGBfI+fj9CyHqc3m4HsVjMcvvNlUUpUmg4lRRNgIiMNcIVDabPNKig5ufDbGkLosDhqQwtFuAugL3MCZTKpMRpSpOFeXbwz5R9qBatoOCH+Do4W2xzSYeXvogwkPvOmiXcaQmw7KNOeR6DUVRSouKU0XZCEhHi6LI5IHB+Q02L86Mce9bAfp0cXD22AwaLAeuFYlxlKr/ophd1+uqKMo3g72nQIoKg3VRiN6VAY4fl8Kqmjos67w3th02hHJbwKpUCoLicVUUpaSoOFWUjQWJzCCIEEU+wjDArc/Xoz4X4ejBHbBljzTqCzzWoqnOF0+Oek4V5TtTzEWsPeEhjdU5GwdvW4aRfWPMXl6FR6ZGsK0crTevNOWyoHhPk7miKBsdFaeKshFgo8dG0rJjpD3goXcCPPZBiE07Z3D4GKCBB9wXA0qilO2hClJFWS9Iz33KVDzqBRu8QuigG7+Fbcc0CrGLq16xsGgVpO2pyXqUCymu6VCl+VBRSoGKU0XZKFgw3S0c5Asx/vyyj1zOxmk7hNiic4BCgQ0oxxKHjbSRUxTluyM991lkis6M4TgxanMW9hzk4Mhh1biw/c9QOf8aiuNRXPaesjCN1ghURVE2PipOFWUDYdqKsmGkOXtuSJ26jo/73vQxYYaPoX0dHDCsHLV5MoqORJW2ceI0Vc+poqwfxHMqOZG/0BQjR/MOZWXYI/0khjX8HVWr7kZQ8y5Cm18XnKM8a9p+U0B2oSjKxkXFqaJsIExb0cQjynMLy7MBrn2pAO4ffPqO5ejRLoLv80A3YkPVFirKBoLzmIHyYhTATsf4bFVnfBz2QVxYjOjjP4sojRBQWZJLi4RW6ytKSVBxqijrEdOhwijMJMwe01wYwrYj3PZKgPdm+xg7yMGe27rI17tmnEUymKbmUY2homwIpKMh5UcpBEaWeUObF6Ci1/FAWVeECx+AvXQyRayi2OZtUZwnJTdLXpZFiqJsBFScKsp6JjGCbMzYEPpRCI9M3KxlDbj9RR/pCg+njylHl7SDnOUCEY9pSpHJEspcUZT1TvIaYJMv+UUXFC5UI243FFbPw+HkViCa+0dYoY+Q4tFaaa9q5CkXGjVvKsrGQsWpoqxH1npn2BCKw0XCrhvihgnA7IUhDtzGxe5bulid5x76TFHI8ly+K4qy/uHcxZMFx7FRWxfhwH33wKjtt0TQ7jjYlZshXvI44kWPwOZG4CbzSscobjPO+VhRlI2DilNFWY+wME3mURQVX1MKvD4vh3sm16FjewunjOHB9vkVprRC7J3x6IghNAsURVnPGG3Jec0IzTCw0LtPX/TsUAWU90Tc/yw4QQHBZzciztchgI84jBBxZ0bKx0neVhRlw6PiVFE2ECI4WaRaIa57xsKqVTEOG+FidF8XtbmYBGoxoqIoG4FiIbA45ymfDxAEPpy4AK/7vvDbbANv8euIF9+D2M5QXG57ytX7/F/FqaJsLFScKsp6ho0Ye0D5NaWuAzz/XoDHp+axadc0zhxTRsbQgk3LzcinHFNRlA2NaQduJsmlNPc8B06KcmDoA+Xd4PY5F5YdALP/CCe3EJHjwqJ8rJ0VFWXjouJUUb4riVelOGcjFnIXffhoyEW46pk6ZP0Yx41JYbPOHmpDDzZX6XP24ypD2YmiKBuWte1GgyBARYWFx58Yj4mT34OVLkeQrYbV6wCg2y6IV09H9PFtCC2bRCznZcneFDYhM1cUZUOh4lRRviPymkP2qhTn3IGCR0tMuQ7+NSWPF2eFGNXHw7Fj0sjmbTgUlWPKaxWLPYgVRdnQmM6KTER6M50C5n32GRYvXoLYcckY2gjSLtD3fFiptrDn3gJ71VREjsdbcA6nvGryrmZZRdmwqDhVlO+IvOaQjR7PoxAFBHDhYF51Htc+X48MUjhldwdd0hYaohg2WzYWsrQNbULbqRtGUTYmRlzGSKUpd3ppDiKwI7gNBaDTaKD7YQgLCxB/cj1sytPS5lSmYr7VPKsoGxQVp4ryHWFDxSKT5yFZuSAgY2bncf3zwEfzY+w6MIW9tilDbT6Aw+3ZKA57X9hCio1UN4yibHTYF5rL5uD7PmVBG27k0ZIQdki5uP9pcLzeCBc/DH/JUyRcHcRhjrIu13iwStU8qygbEhWnivJdES8oV/Vxz3yg3LUwZS5w98R6dKiswvl7plFJK0KaxK5xtaB6XhSlhNhoqI+w227jMGzEIISFgrzBjf6RCM3CrtoWVv+TkPLrYM/+HaLCSlrHvRgpDgtTzsiKomwwVJwqyrckqdpjscm+UPGG0qIC/fvj0zksXQUcMcrHqP4WagoObBKtdpwiw8Z/6nlRlI1J0rabZ67rgPQottxyIDbt0wfwC7BYfEqeJrNYWI2w7zFA2yGIV0yGO/cf8B3Ku3Gxir8oTrV6X1E2DCpOFWU9wBmJB9xPOzGeeCfAQ+/E2KSnhbN2yKCOjKBj2SRHPcQ2e1nZuKk4VZSNCQtJFqj8GlP6JlX5uZyPIBvCpkUxDxlFa7jgGNkBQq8LrD4nI7IqEH56I7zaT2mlQ3k3ojys+VdRNiQqThXlW2IMnfhLRZjapDpXZm1c9XiIvF/AuTuk0b+jLR4aXicGUYQpB/m7oigbizX5lfIfhyMKp9Me3BQVGovClT9ccHTgwi3Uwup+FKxueyCqmY1ozg20IZlMybuckc02iqKsf1ScKsq3xFTpkZGLIuRJndqWj5ufz+ONeTnsNCCFw0ZVYXU2huNwtT8jVlHErBo1Rdm4mPxq5mEYoKrCwssvT8ab02bASqcRRr4ITsmgEc8o39ppuP1OBdKdEc+9C+GKCQhsl/J8ICKW9yX+Vvkz+1cU5buj4lRRviXG20IGicRpuRti6gILf5pYjaqyFL63WzkqvYBWsSfGiNHEOCqKsvEx+dXkwzCMkEoD0959Hx9/PAeW68nYxFx4pAgkSmkDy0UcrAba7QD0Ow5WbgXiD69GHNWRbLWRdGqUoeToOaBV/Yqy/lBxqijfFjF0ZMtsR6r1r3u8DouWWzhkWIRdtghRm7XhUA4TD0zRMCqKUhoSYcpzx2bTF6MsU4aysjJaTsKUBWcSp1iOtCwHUVwLt89ZCDsPhbX4GThz7gEcEq5xIHG5DSqXQJNOUoqifHdUnCrKN0CMEX+KBozfNOM6Ph55ux7/ecfGJl09nLMrGTvfheU4lMFozp2hyOipOFWUpgG3N+X8mMtlUShkTf4Ud6kRmJy3jTfUgRPmEWd6w+53Ciy7HP4nf0BUNx8FytdxFJh9yTNBNlUUZT2g4lRRvglsxOjDc6muty2sagAufyJEPqrHmWMrsWXXGNkCi1H2xlAktVqK0qSwbRsNDRHGjBmJQVv3RxSEtKxY6EzyNntDZaj+FM2Xwel8NMIu4+DUfoh45lVkPCkubWOTqJUcrtlcUdYbKk4V5RuQvLrQimKEAXeCCnH9Cw14b14e+2yaxpHjXNTWlCFKcZs09piyxTIeU95OUZRSYfIhzx3HQX1dhOHbDcGgLTZDnM+SOHVk3VoozIKVX2uad2F5HrDFBYDXE9GCv8Ne+jQCOw1EIUXlwqjmb0VZX6g4VZT/BQtSdouIMKXvZLOCKILnBnj9Yx83Pp9Fu4oMztqnAm3goEC5yomK7dfEaBmDl8wVRdn4sHg0edAUMB3XRS5bQJQlQyhV9CaPrp0oPlf1Rw4oOwOFVbDajYDb7zjAb0A84zogu4zW0T7jkPZJ+Z0fEPKcUKGqKN8FFaeK8j8QgSkdHsgIiW0zhqvBj/HbpwKsrEnh5BEWRm/moKYQweE4tJ4/iadVUZTSYrJhUaDSxPkyk0nBTRfHOS16TTlsJq7W54/J9hEPwB9mEfU/CU67UcCqCfA+uYWsqMPZnXcp+25cIFUU5duh4lRR/gciMNmLEvFg+yEKYQDHsXHfazk88W4DBvd2cMKeHsIsGSWbrBQZNbZUYuzUUClKE4EFaVF8RhEJUwtT3piK6R9+AivtUraNZJ3ElHybzCUn09yFExRged1hb3o2YrsMwbxbEa98BwURrgFoD40KpPxjsjtFUb4hKk4V5X8gvhP+I+MVktHxSKjOWlGLK56w4ZJIPWfPFPqXZ1Agg8edKpKtFEVpSrBoNKEojFBeDrz22lt4f8ZMWG45wigwKz+HKZxasONIBCr8WqD7fvC6HwGrYS7s2b8lsZtFVCzActmUkdeksktVUZRvjIpTRfkfmGp9Izf5xYaW4+O3D3mYvbIehw4uw8FbW6hpgHSysCLHGKTEQimK0iRgbyZ7Q5kwihHRVJZJI+VxtX4g3tEvw+R/I1D5CSDLQhvBoHNgtxmAcPGjcObeCdtJ0Vp+yxTFkd9iMfxVe1UU5b+h4lRRvoKkai7RmhH9Szkh7n/Txv1T8+jZwcX393AoXro4EL9NxomyFMVVk6QoTYvPN69xbQu5bA6+X5B1sfR6+iKyFQtUnvEzgcct9qk0Wt4PcZ9zRIhi9h8Q1c5EYFHhNDQeWImqNSiK8q1QcaooX4EYLBKkbJRIosIhlTqvOsblj+bhh3mcs1s5hnRz0BBYcCmSxKc4azpPKYrSZDCeU87TMTzPRjYXY9shW2PTzXtIG1RbejKaOF8F529+FsD2AR5+qs+RsLscCNTMRDjzaooRoWDnKaKp3+fYiqJ8c6ggyOU7RVE+jzFmSRVgCM918f17a3HjswXsPtjB308sRxDyK0pdMUGJSWMvK3tbZWNFUZoEjU0dhyMSpGUZGx3T8wDfhhlK3/hrvkqgrtkHNy6NfFheGfz6ObDeOBZxw2pgxI2we50AK8zRcyGDiOLxnhVF+WZorlGURrDxkU/RCPHMD1mYAo+9txp3TqxF1/bAhXuWI+2mSIgaYcpCVDwqNBdfqwpTRWlSJIKT5xx0HBeFfADkqIBJC+LYWRPnq0i2lfFPrTTiQgCvahDsfmfTshoEs64FGubTOn73fmRqUeSZsq44VhTlv6PiVFEaIcZHXJ/mO7+80KNcsmR1jEsfKqDeT+G8nT2M7m+jLhebMU0J0xZNjY+iNGU4f7NINHOsO84p5WXJxhz4CkRoSnV9EdtBVGgAep8Aq/Me8Fa8h2D2VbDkbVNSXC3uz/ymoihfDxWnitIIMT7cbjSyZEzTOCABalv43dNZvD/HxtiBHk4b62J11rRRM2aHJjI8anoUpelihKURiUEQIp2OMX36h/jk04WwUi6iKKB1a2tNvhTK5JLP1xRE2SsawLbSsAZcCJT1QjTvDoQLnjCdJGmf/BxZ60Gl7fjvv/2GoigqThWlMWI05I+MCnd08nw88X4Bt74MdOkI/HS/MqSsMgRkbNiQJQ1MjTBVeaooTRnJ3iIMY5SXW3hpwmS8/e4HsLwMiUmz/r8hRVDJ8ib/89yxbERxDey2I4FNTkKmIY/4w0sR1c9FYLuwQ/OYMM8Wfkb8jx9RFEXFqaI0hr0q/AkRIeVEWFht4eeP+agr5PGDncoxrp+DOj+Cx1mHDE3SO19RlKZPUrNuRGgM1/XgOjwcHC/7+qJReu3zNvSJKMCdnqKoFk6f0xF03w1Y9R7w4eVwogihzW1P2WNrfp8fF1rFryj/HRWnSqsnMTIyp3/8CSIyHo6PXz9Zh7dnBth1aw+njE2jutaB5fFGPKYpWxn+U0OjKM0JHoDfIutXyOeQz+dJLNL3rxjn9MuQIiwXZGVicevR9gEitxLxgAtglfdFOO8fiBc+ROLUo9/zEXIH/0adpBRF+WpUnCqtHjFMLDD5j4xNSMYj41r491sR/ja5gK5dQlyyVwYpHl+b4tgxGSP2fBS9puxFURSl+eA4NnI5C5tu2h+9+3RGzMNCUaH068MFUvPMWLMZCVQENbCrxsLa/HR6TniIZ1wGr+YzBE6KItBv8POCN9BHhqL8V3ScU6XVY3IAC1SyLVEMl4psc1dF2OsPK/DxMhe/OiSFc8Y5WJ314FmO9OA3sHEyAnXNIkVRmiSNTR2H2YuZJj3ZsWw+7MCRd+eTbKWs/HXyc3FfidiUyaHCawEO16rQc6Iw7Sx4C55Aod8xSA3+B0InDxcZ2rfZuVbtK8pXo55TpXVCxsloUlONzx9+PSkbrCAq4CcP1eGjRSH23srBKSOrUJPLUGbhMU3ZcIn5Ehvz9QyZoihNgUQQ8swmARn4VNTMc4tRrmrn4Z9Yb64VsV8N78fkfbNPrt6PSZjy+Ka0ve3CG3ARUL4prMX3I5h/G+23nAq2oWxp5Cz9l7+v83uK0rpQcaq0TlhgshHhOX21aR5GEVJuhNsmxXhkSoTNunm4dL9ypOyARCt7Q9hwme309aSK0rwwIpKKl5yHJWzJOKeel5I8nSz/ph0cWYzydiJKaVNpgxrkgcrBiAZdADf0EM3+BdxV78O2PToCU/eSNAn6pr+nKK0BFadKq4QNCXtBZR5HKIQWPDfEO7NC/OaJahKrIc7fuwxDuhaw2nfgFr0piTAVYasoSrPB5HWT57lDVCoV49O587B4yXLAdaTWROJ8Lc/pWhJhKoKX9s9SM7JpmV8Pq8dRiHoeCq96KQofXQyQaKWflt9PhKm2WVeUL6LiVGmVsD0g80ChGD57LuIcGgoxfvpwDRau8HDcKBdHbpfB0gYXnk1Gy2zGlkiMD88VRWk+mPIkC9QYYRihotLCU089h8lT3oaVzpBoDNas/6aIMJU5i07LtDvlKvwwgLvZJbDabQtr8VPwZ/+B1rMQDuV45BlUnH+b31WUloqKU6VVktSkGakZI+UCf3o2j2dnR9iyV4wL9q4kvZqDY3licBRFad6IY5MEoMVjSFGet2jicU4d16bl5jnAz4Ni8fNbIXug3zDeUPqdKI+wrBfCgT+B7baBNftaYOUrFPZMByz6KY4qv6oFXkVZg4pTpVXR2DvBpiCkr2knxBtzgd+Pz6KNV4ZLDnXRqwLIRmnxglgxKVc2ImYzRVGaKUYAskA133O5Bvj5kFbEsKkgyk+H76IRZVN+ZtBHqu0tF1GwFHHXfWH1PA5xfiXiGb+AVahBaIWI/cjMWdCq51RR1qDiVGlVSPswMUFsosz/bB645OHVWF7n4NgxEfbtX4VlvgUXnhiatW3DVJ4qSvNl3fzrUx7v3q0z2neoghWRQOXGoMT60ojyzKCdOSgHgnrYm54PtBuOeOkLCGf9nkSpJ0NPWfzeVDo01aaKshaLMo9mCaX1QMmdq954zl5T17Fw+WOr8KtHCth+Uwd3nNoWXdNADSK4EQ+cLRV1JEw5s9BXFaiK0ixpbOqkbSh9d2wf7dOL5XXEDk2sUTmLr48qdikEyzODfyuA5bRFsHwi4ndOhmU7sIbfDXTdm54zBYrDz5qIflf9RYrCaE5QWjyJUeK50Zcx/DAkYerj5Vk5XP98HlUVDi7cvRLdKzzUhQ68yOWY8mFrlcwVRWm+JKLT9Nq3EVM+9yi/2xReK0wlynpBnhv03LFYfAbVsLruCLffSYizq4Dpl8OqX0yS1Cb9yp0ujadVNG3xmaUorRUVp0qLRwwSP+yLVocH23cdYGU9cNGDdaiuTeHccQ52HuRiVZ7bnpGR4DfF8GZsXBRFafYkwpTnJkjPAdelZ4HLVYgiJHmd6Rz13eH9SZMgNrOyfxLBQQOifufD7jwMWP0GnI+uIivMr0M2Txo5Rv4rHquitFZUnCotHvFC8MM+jmR8wSgKYds2fv1EPaZ8ZGGXzX2ctXMFcn4Ed41N4Ko43kw9GIrSUpDak+LkujFWrFiB6praNQKRl68vXSj1NOyhpTDvMrZd2H4O8DKwtrgSQborgk9vR7zgIYpAvx/5VHAujrVKk6K0ZlScKi2SNQ94niff+eWBAVfnh3jwrXr8dWIO3TvGuOjAMlSkYxRi4y0VQ0L/jZFaT5ZKaVIkxj9JJ1868efLlkuyWiseGq/jlMMfnifTmvXF8DrLGk3Mmu9JnM/FTbZdu2/Zap04jSdZW5y3dhpfE98PUVVl4ZFHnsJLk9+EVVa2dpxTubbfHeOJ5YARqLJvJw3H92G3Hwlnk1NhR3lEH1yMsO5T0rH8+uRAtjPHypsU5y2U5J58q4k/X7Z8A09f97iV74aKU6VlQg96qaIT62AkZkDiM5UCZi8Occl/AkSBhbP3qsLofhnU57jlFz1QzB+hD5eWTFJtyvMvnfgTF+dfWM/etbWFlsbrpEqYvWWNpjXri+F1ljWa2J6t+V78XR4K0xg7+SXZt4mb7IfXf/V58LY8V9Yi14OuSxhScZWvbcTeSrnQvJbmJt76Qt4mx/dD9s+Q2Q1r4fb+IYI+u8OpnQXM+DGcSBoT0c+bpkXSaas4b6k0Tqv/eyreO9mOr2uyrNF+ivnmC+H/Oq3dL9+i5DZ9MZ6Z1ln3P+Ip3x4Vp0qLRAbCpknaktHk02PEJvvDVfc/fWQlZi3ysdfWHs4e6aI67yKy02QYivDDpRhUWiaJdyOZ5HWSNA/DAL7vI4xoin0ENA+CgKZQmoOY+Eb00d8X9mVxIrNCWsrxfVrG+yvADwpmn7T/WN4OtLb6ds22JELMb5gpCH14KQuZMhvpNIsWKlDR/nhby+Ip2Y5fh8n7C+XY+XjNdz5Ac6yKgUUDXw/bseFQhg/ovtClMnnecovXc/3mfjNWMt2rZL88j+g+OhG8/r9BoV0/2J8+hPxnN5JF9qR6P5R0UNyO5gwfW4u4k3QSSZqUcypOXFgIgqiYhpOJ8g3lGZOeTXxzD2ni9B9Z0pEt8CmPhpRn6EuBts/T5NN19CkPNf6NL514e8rfvF/bNhOHJc8HX4zP8BvGCpTPfJqHdGxJfvt8POXbo+JUaZEUH30yD/lhQQ861w1w3QsF/Geqh817hLjsoArQY4UMhQVPnv9crW+E6fo2UErTwhgPI1R4YuPCoi6TcdG+vYfKyrVTVZVLc04bJl6SutbO18ICkY2pTcKngrenbavapNC2bYrCZl+plCO/tS58HDRj3UL74BGFqij+8uXLMGPGDHz88SxaGaG8ggpSbE154Pbi7/N2fA4OqS0+9o4dXUrr/NajxseqNMbccwtlmTTdD9Mhii6s5HuTNtYf8iQpPlfkdrAnNE7Tg2k1grb94W5yMYK0B+vDPyJc+QpZZR5Wigs4HJ3jFtOGWdDs4XPiqyF5r7iM29oW/KykW8/zaJ5MKbpPSb4zyP2RCSQOqXABerZ73LHNkSlF26dp8hwz+SRcWUyuc1+LQc4jYVSg33GwdMVKfPjRLHw4czZWrK6WZRGtW7Pdmm3o+GlKuS48iuPYNu2fCxON9q98Z+ga6xVVWh70KJKSFz3XkA9yKPMcvDQrh0P/4iP0LfzxWA8HbpPB6lxID5e0xE0emgkqUFsubPCKb7EkoRiRQXRoAj74YAZee+11vP/+h2hoyErcXr16YMzokRg1ensSmeWoq4vWeFc+//hkQ1dVlcayZavw0ouTMXXq21i4cAEJRw9du3TBgIGbY6+99kDv3h1QXW0MLnfOM/sxbQ4dJ0ahkMf1f/grnnzyadTV1tCx2ujfrz/OPPs07L//7nQMeUq3dMCUctnA8rEvW7YcTz89HtlsFnvssTs22aQP7cekY03LRlSshYUoXed8LTpklqGSRCoPJ8VlVWZDXS9TYOB987H4xvvntUf07iXw5t6CQpexsLb7D+x0Z7gUN6JSjs3H3cLuX2OBysLTcTgzWpj50RyMf34iLM+W5RVeBkccfgDKK0nMcwzJtOYaxpSH2QNek62nvPY6Xpr4KpavXIGGugZ07dAJQ4dti513HInNNu23Rtx+/r7ycj6Sv9z6T/z1ljtRS9vysXVs3xbnfe8UnHLC4RJP8igHireirj6H+x98FKtXr8aYUUMxcsR2IoBZ0PI5aZ777qg4VVoMUg7nqjATMsvomRRbPpbVAwdfvxKvf+bggt0d/Hz/tqjJ8QMkovhcoU8PEjIUvLXSsjGPPJ5IDJKB46rz2poaXPO76/Hww4+jhsKpNFfxUuIhAxPz2xoo7rbbbouf/PQH2Gmn0WScWByywaS0RvHEq0r7LS/zSFA+h2uuuQ5zPpkvxi8RnxyPv/fp0wfnnXcWTjj+MNRnfdm3ZZlGJex5TaVtfP+8n+CB+x9EeUU58gVfPDRMKpXGjTf+AXvvvQuJZ1KexWJVJmPjBz+4BP++41ZsM2os7r33TrRpQ6LHnAJNHK91Y0QDz801kXtPBYEuqYWyntswylxmJry+SZ5RoOcOSAxbVBgJHQt2IQd/2jHA4rfhbHIe4mG/lzaoXCiJ6d7JcFRFmrvoaSw5wiCASyWrhmweN99xH274418xb+FiWG4Kge+jU7tKzHjnBXTq3EG8kyYvRfCp1JXOlOHlydNw0c+uwLR33qX8Z4kHlXdv2hGzyGyD888+GT+64HTwC1ekUErXjyfOizyU2BXX/Rm/uOwaEsDtkcs3wKFlKTeNbH01fn/d5fjB2SeI95UFdOBnKX9W4Mr/uwM/+/HP0HPTPnj+yXuwxeabyP74+BgVpt8dFadKy4FTMnsi2LBQsuavLBhcEqen3RHgjlcbsOsWwN/OaE/Cgh+MLj38E0HKTzQ2GrwjpaViBIrx2LDnhbQeVq5ahdNPOxevvzYV7dq1IyGYItFYiyDIS9yysioybB7q6mppbuPGP/8B++yzC+rrjceHq9m5rWibtin8/Y77cemlP6flDqoq2iEIA+RyeTFclRUVZPgc2q6BhGUDLr7kAvzwh2ehtjZfrL6MUF7uYMKE13HSiaeT8fXQv38/nHXGifhw5hz885//Qk11HYYNG4Z/33cbwsghIx2ic+cM7rrrIVx44cXo0KE97r77DgwduiWJbDaoLGr5nFWcroup1nftCN1Ti+k73UMSi6wt2CJuMG1RfEbxsyYuCtTYovSRysBe+gH8qSdShOXwtrwR4SZnUcFoNVJxFZVB6D4mgraZ38pEcvCcxdxrb7yLX/7qerw0aRKqqiqpAJYRocltPju0K8drLz2I9u3bFfOuTc/tggjaZ56dhJPO+DFW12XRtk0bEfq5bAN8bp5TXkX7SSGfL6B6xTKcfMJh+MtNV8NmBwTvg/KaRyL04zlzMWbXgxEFjnhLf3TBGSgUAlz3h79iVXUtunbpiMkvPICOHTuIIE6lU5hMz4mDDj9bhOydd1yPQw/YY41wTkRp8pxRvj36xFJaDGacQnog0IOBH3/0/CHjQ2LixQLuequATTpauPygSmScWKr22dslcWkyxsI8NJWWSyJMzRce69LGVVdcJ8K0S+eutB6oq68lATgUp512Eo444jC0IcPXUF9HhrOKtnVw8U9/jo8++kw6KbEoFeFZ6WHiy1Nw+eW/JoFZJnHrG+opThrjdhyLXXfbWYRpbW0tysozJILb4LrrrsPjjz9P4bTsg4/L9WK8/vpr8p0N62mnnYLTTzgYl/7sAmy99dYkTCx8/PEnmPvZAhLKrjQhmDlzHu3rejKwAb7//e8VhWmhWFUqJ1qct274+jaepFq/kJcONHLj6amRLN9QJM8oedbws0oWkqjJh7A6Docz4CLYfjn8D38Le8VrpEnb0bFxIYm242L0Bjy2jQWfgbnOFn5/w+3Y+8BjMWnKGyIAC7mc3BMWewGlZ/asUlSJy1eA84VNBa7Zc+bh/B/9kvKYL3kpn8+RKM1i1OjhOOjg/Whf7bF69Sp4KQ+duvfA3f96DDf9+e+U3z0Rr+xZ5X1Om/Y+snURFRbzOOboA3Hmqcfg+2efgP333006Mq5YXo333ntf4tI/1FLB8tJfXIPlS6hAe9LROGT/Peg4fePRLZ5Xcm7Kd0PFqdLskQcCPxrkjx/hQCHKk/EOMGFGPX7+eJbfzYKL9i3D1r3LUF+gb+wioQeIfOTBw3/6QGnpcFphoihAWZlDxmkmnn7mBXTo0EF6x+fy9fj+D87A/ff/Hb/97SW44Ybf4l/33o4tBm4qbTkrqyqwdOly3HzzbSQkaT8hGUtKP2EQ4cY/3YrAj5FOVZCYzaF3n6649bYbcPfdN+H2O24Qb+fAQZuhvr6ahCO3Y3Px5z//FdXVOWk7x8fGyZK9qpyOuXNHx07tsagmgF+I0L5dO/OKTY5TnwUPi8Y9m6+84g+YO3M2dt9zF5xy6nG0jqsXi6/fVSP5BfiScDvjNm0t3P/Aw3j+5ddBJQZEMJ3Uiklkg2CeN2vnXECy4cFhwRrUwel1LOxeB5EenY/ovZ/AbliCgHvw09Fx9OKTbk06bo5wZ6IkXf7z/kfgR7YUtLIkTHfbdQe4lLCT6ne+SMWofPJ03py2Hdx0y534dN4ilLVNo562q6xI4283X4OnH/477rn993jhqb9jvz1Ho3ZVrVy3irZtcP3Nd2HWZ/PheSav8cT51HZox1aInj17ihhmUdyjR09Zn83lsbo2K2H2xF597Z8xYeIbGL7dQPzsp9+X4+GmF+aOmmPWPLd+UHGqNHvkgVD0QvB/biKYoQf6wtUBzrk/i9V1Mc7Y0cHR22VQ0xDBtSmWbEMPO32QtDLYgBivOnc8mjz5FVSvrpYewvX1dRg3bhwuuug8Eqk+Vq0KsHy5j6227IvLL7+E4rviTamsrMLLEyZi3meLTfu0lIOpb7+HqVOnoqKiUgQrVxtefPGF2HmnIVhdnSXBmcOQoQNx2WUXi3FlsVFeXo7p06fjlVemoKI8aQ/H7Uq5tzYdIxlEFszlZS4JYRt+yOKJ0ysPd+Ogkra5++4H8PjjT6LPZpvi0p/xMXKVZTFPUFQ2qmosDUaQGM85/UlBgJtc5Ome8jUS4SfXi1ZuBPhY+Lkl3lS6RfSNH0jAoIthtd8BzsqJ8D/8BWxeZragibdp5veUr3XxHNpWdkTD8hoM6N8H9/3jJlzx20spnfOwThzPRE/gs+dmKsuWrcQTj72I8ooKKhhSQSObw49+eBYO3G9vqXrnGode3bvj+t9fiZ7dO1Fezkt1/OJFy/DUU89JR8Lk8jlUiOPaD945e1PldbY0RXQMnEi4gxM3A+BjfeK5V3DDTf9Em6o2uObqy9CpczsU6PdsaWdh7o2y/lBxqjR7xNgUDQoVZOkRESNHCvWH92Yx/bMQuw5wcOFeNmoLpipH4sk2FJfmSmuCDaO5/45jYd68eWYppYs8CdKdd96RREsMeZNYUXhWVwcYOHArbLbZJuI9LSvLkIFchrfffheZjCXtVidMmCRV9o5rS7OAIUMGY5dddsKy5dzu05Vp5YoCRo/eDmN3GENx68Uw+oWAtp0o3lD2wrBg6dipHR2D6a38Gr+9iNLpp3MW4sPpM5EmI8tTn95d8ebbs/CnG2+ETefxwwt+iG223hT1dQFtm6Rxc158roq5FnRVZC7V5EXvnA3uYV1szynXy8Tf0MgxyDOouEDMcS1srwfsgZejULEJnLl/RzjndorksJtebioXqJvzPeVj5+vM6TvjFPCTn56JZ5+8G3vsOha5+nqKQfeChV7xHJMzZa8mbzdp8hTMn7+M8l4G2fos+vbqgWOOOECaArAX0/NcFHIkUHt2wYH77yo1EVzp7tDyZ559UcZD5cId76trt860Z+5I5WH8Cy+hgQor1bV1mDBpMuXlFFK0Tf/+PVBT24Bf/epa1NWswg9/eDJ22WkUCvmc5Gtlw6DiVGmWiLjkx5Y8wHhuloVhXjwi1z1Tg/vfCbB5Vxe/PqKKHoI2goCMEhvu4sNRTDjNldaDsXckSByTfvg1liJI6MOijscoJX1ZRFIYeAzGdLrYIYW/k1HlYWO43Sd3qAspXc38aCat4TEPgUKQxTbbDEJVVUp+j0Wo6Y1vk9gFhg8bhoAKSrbtkXFL4+PZn5ABDckYWqivD7Hvvnujffu2JFpsPHD/IzjogFNw4glnkLhdjdqaauy91+4iYH/5iyuwcN58HHDAvjj66IOkA5R4ZYvp2wgYOWGlCGd3vixSPczXSF6UUCy0RsmzYGM9E9Y+g+T3WaXGGcBfDafDdrC3+CGt94BZP0e86EWEDg/QH8gJyPOv0dSckHMl+LhvvvG3+N2Vl6JN20oRl1SMgxNxBjRpmEnuhim8xXhvxifwwULUQoHy0YCB/dG9S3uKzwVOzmt0PanAxnF32GE7ys90fei6eZ6FOZ8uonxSJwKW8/Ho0cOx7dYDpSr/pUlvYc/9T8Qe+52At6d9JO1Yhw/dEoO33ho//9Xv8cbr72DcDiNwwXlnUDmBRxlIi2c1gX83uR88Kd8NFadKs0QeQDE9DMzTXT4+PRC8lIv7ptbj6mcCtE1F+OUhldiqY4h8zqYHiVglia+0TtiA8cRV6Oyl5LZlDHvRuGp/4sRXUPAtMnI8UH6IgMQrD6A/7d338Mknc8Rbw7BhW7JwATwSlDW1WSxZskx6//JyhwRiv3795HdMeiNkZpHQBfr27Q035UlcNpKLlyxGdU0tpU8zYHjfvj3x29/+SqotV6xYiYkvv4JZs2ZLnHE7jsElP7sA//d/t+PFF1/Cpptvjosv/jH9JrejMyLHGEmTR5Jlyrrwda+pDXHooQdi7E5DEeQa4Jg3cZQEFjOcXMyjyUHkV8PtdRyw6fdg1a1EOP1sWDWzYVEasYpiWu4r/zXD+8vny3msb7/+0m6ahSl/p1xprgWn3WLchOSc5372Gc3NMt62b9++kt45D/OnMX369EUF5SN+4xbXhFRXr8aqVTWSLzj/lZdlcP11v0D/Pl1RvaIGk1+Zijff/AA1FGfLAf1wy1+uweNPT8Att/0Tnbp2wtVX/BTt2lTQb/E9ML+RHFfjcPJd+faoOFWaDUlplOcy8dM8shDG/Oq6CGk7xLTPAlx0T4A6emhdsHsZDhjkYEWWStMpSuqhJw9z1aatGSPc2JDx6xKHDNkSPKZpFPuoqCzHK6+8jptvvgfl5R46tHfRsZOHmR99hquuuk7apEqv3GI6rKuvFy899y6urasVccttTdkw8ZBUPFQRfZG4icHl0lTbtjxcFcWV6kUbdXX1CApJdbyNmuoCDjhgdzz4n3/i/B+cjeNOOBwnnHgMrr32Ctz3wB10PLNx6623oaysDBdd9CNsvlkP+v0cmWX+bT4vM7QV/ZhMSX5hkrnCwgbo3LkzOrZpS88GrtYvrijB80GSBv0wNzMy45qGsPwcidMfIuq9B+LqmQjeO58KTNUSjzv0sUdfCuhyf3kvybzpw3mBjzsIkuHOCD54ug5m3drbkJwS99JnVlfXFNt5ciExpnvYTsJrtzFDVPF+2ratogJlmn7HNBXgoddWV1dLHF7PonXEsMF49sn7ce2VP8H3zjgC3zv9cApfhOefeRDpTAoX/fwa5PIBfvLjszBm1Ag0NNQX70EsPf/5HFjo8pTkNc1n3x0Vp0qzIXmg8ZwfLvIwstgQ8zD6IeY3BDj9rgZ8Rob6uOEpnLlLGqvzPjx+HWBEDzbulUkPc7O90hpJbAZ3OmrIBhi7w0hsv/0IrFq1AjysFI9neuUV1+KYo8/AL375O1x04a9x3LGn4a0330K3bt3EAK3BcqhQxGmQx140ry+UUSDMSlr+xTRrUzLkKOzFaZwOOQ2z0LBiflNVioRwhC0GbIJLLzsf//eHK3HNNZfj5FMORkN9gF/84kosXbQIhxxyIA49dB9kScO0a1dGYtWTpgFt2ri0D+P5NT9hft/kF/m5Vglfg2Ri08dNIHhMy7gQw2FBWGxzmnSu3LjwcXH65Dk/p9KUKHyE9MxyB/wcUdVWcBaPB6ZfioBW+1wQYT1NcY0Qornsx/xvyjS+DyxMuXmF5BteRh8TR2ZCEuRrw3Ch0txDM+fCJc+lc2vx+W7Wm7zGedaCGb2C81mYNOWhS8Uilwtz3HHqB98/FTfdcKVMPzjvdHTq0BYXXXIFPnz3fey1x1gSrcfIb5aXV0hBlDsf8qtSpQNV4+eCsl5Qcao0GxIjz3N+BPODjN8wzuXpAiXli+4t4M1PYuy8aYxfH9ABccgPqBQZm+IDWzbSUm1rRgw/pRtOAyzeuCr9sst+gh49emH58uViaCorKzB58uv461/vxJ1//xdmTZ+OXXfdDUceeQTq6oz3lIVNJsOGiQ2gMYRJ2kyMo6TT4neT5sg4kphlQxYEZtiitetMmub//J07a2Ub8qhenUd9XQE1NXnaBrjxxlvw2quvYfCwoSScfwSPBPX7732Aiy/+DY49+mScdOIZ+OUvrsKcOZ/I2Kvs3UnOl36K5uZYWyPmOpu5uRbcG9ulAkPRG168NEnnypJgDswEXTo+frd7ZiicrX6FsLwNMPMuxHP/CM9J03H6FNdsw5vxCXB6aurwtf6y6euyxtNaTNfMmrlckLXfGQ7zdeF8KsuL954vGs85P3Oe5J73PHGnR976b/c8hPvufwZ9+vfCb3/9I8pPlfhk7gL84jd/xP6Hn4Z9DjsZ51z4K7z+xltrBGrj31W+GypOlWbFmsxP84CnMBJv0dVPrMa9rwfYtJuPXx/aCe0yNvIBC9PkwW1gQdscHuDKhoLvPRtDC47loa42wKBBA3Dnnbdgpx13IMNUh5WrliP0eZxcG23aVuGQow7FTTddLemIRaUxZgG6dulKYpPHNU3L8FLcC5g9NAFpBn4FKsdPOnEkIpQ7YvE6GYKG9sP7a9OmCpmyFB1VUOy1L4dIcUn80sQe2rbt0njppddx++13oryiDBf86DwM2LwrHnn0eRx3/On42x1344XnJ+LFFybir3/5G4468hQSsW+hrIyP1VTxy37F7LZeknvBBZOqNhYe/M9jeGHiFFhlZQhj7hxF16eElygpPHFHO67tseMyWMEioPMesDb/FeBFsKZfjWDJIwhsEqhRlo63OFA9/UuOX+ZNFL7+Xzb9L7gZA9OuMiPeTt6E89DSJavMPuicec7nzh0WeV5d3YACv2OB8rLvc6/8mO57OR+EPAlMfDNngclwM4CP53yKK678PwSUdy74wZnYbsgQvDntXex/yMm46uo/46mnXsbTj76Am2+/B3sdeAL+89Dzsn1Tvu7NDRWnSjOCHycm80f0MEGQR9q1cdvk1bjyWQttKkJcfmgltu0ZojqI4HHqZmPPD6LipCgMGzWGq8I5WQwbtgUJlb/hPw/fj8svvxQ/+vG5+M1vf45///su3HjT9ejQoS2mT/9QDBAbPi+VwuZbbEYi00Iq5aFP314kSovCldZ/8vFcEkBi/tZJd2y75syZyyGpziyQ5ezWtRsJ1ArxcibplD1AbD45Pne6Wr2qGldccQ2qV67Ccccdi4MO2gOffLYSv7v6WmQbsmjXrgoHH3oAdtttF7Rp1x7Lli2n+NeitrZB9pP8thE/rZdEPPCctQh3ZFtJ11beYc8fWl7S54QUpo3AiiNOB6bAY4Wr4fQ8Gla/c4DcUljTLoC78n2ETjnF5cKHbEr/zLyk57CeSVIsjz3K16V/ow5QacqHs2Z9QnnNl2p2ji3r+B/xyZw5qKmtA7+djfNt9+7d0K1bF8kRySXiOU/JvecXalz6i9/j4w/n48AD98LZpx2LfK6AX/z6Wnw8ey7ad2qHffbcASeecDS6dehIdyhF8a/AosXLJP8nv618N1ScKs2GNQabwkHAPfMdPPZBAZfcH8KxIvxyrzLsv2UKq2sdadsn8MOeHhbysNeHhlKEq+BcEn3z5i3EhAmvYvz4N/Hs+NfQtm0lvn/+ibjw4vNx6mlHYcDAzSi9Rfj4k8WY9s40GTifB+Jnb+cWW2yCgD2nGQsDB2wh6ZPTWDqTkQH56+vy8ltJ2mMDGIYW3n77HTGC7Gllz+qAAQNIJLPxZKsqW9BkBAob1PJyG9de+ye88/ZUbLf9SPzoR+dKnClT3sT8BQsoToj9D9gbd9xxPf5x918xavsRUvU5c+ZMTJ8xE2XlZt8sTFtztT5f80S08YyvLxcsuOe+3J9GwrBkJCKJA+aPHmEeD/JJAjULDPgx4l5Hw6n5FNH7p8POLkZoZyhSUsXPnaTMPloKfA0Y7hDF92fw4K2krSd7Urlt9fTpM7Bs+Uo6fe7gxOlcrprMX3/9dQpym1NuUhNi0036o13btpJnknjmWvF95+GmPNx267148KEnsMmW/XHlry5AhtLILCpsTn3nY3pmZDB0yDZ44L6bcecd1+DoI/dGQM+SeQuX4OVXXpN9SvU+H7DynVBxqjR55OEhD2w2/0ZYZFwfb30a4aJ/1WJFnYXTxnk4aVwVarhnvuPJWHnmkcP/jNExDyNFMWmKRd+7707DccedhjPPOBcnHHcqjjn6RHz26QoUclwlyO80t9C2ysPtt/0NixcvI+HpIJvjd+9vi003641criDCb+zYUSQwU+LBqagwb356eeIr6NjRo2UBxQnQvr2DKa9Nk+p2bgbAqdmyA4zZYXu2n5RW+XGcpFGSxHEBbdu5eOSRF/Hvex9EZVU5Lrnkx/IOcq6pX72qVjyvYVQgg72NeF65Od4WA/uT8M3Td2DlipVSlUm5hiZTsGut8D0XHUKIWKePX8hSYYMHd+cISYm2tMhziv9ozodrk+DkV5yaexjCHfRzhF1GI176BsL3zoJVaEBg2TLiRBRzK/zip3i+Rnw1f/h1vnxe248YjB5dOyDbkEO63MP8hStx38PjTW0IZaRsrh7ptIeFS5bhsSdepnxeJlcuoPi7jN1OchgPBSX5oXh9uBDouim8+/4s/O4PtyJle/jZT87CoM36y/pVq1chl8+iQAJ22OCBSFNctkMjhm9HOzCFzOUrV6+51q28gmK9oOJUafLIQ1qsB5VKY0seUvNXxTjn7iw+WuLhyOEWLtunDA057mTCw7DQk4Him4c8b6coBjYeJklYyGYjjBw5Ar169hLj1L59eyxZshgXXnQZPvhgBupqa7BgwUL8/Oe/x513/gPt2rVdY3yOPOpI6fHPZLMBhg7dlgQqv/mpTryWXMV4xZVX4dVXp6FNmxRtm5L3+F922W+Qz+dlLNR8Lo/h222HMaN5eJrGPf35OHlEAUdekXrN734vr1g955xzsPseI1FTUxARWkzmMrEniM+BBUzxEHm1rOTvkhdoSWvPDebe82gJNt2rCPvtvydGjtoGYS5L199c9yZzkehg5NnHc36qWS4cEtJ+VVu4W16DuO0WsOc/BWvGT2Fzz3762LEp4MiHtuXzNfe++SPXgtJ4ly4dsd8Bu5BYzMm14VcGX3ftX/DkUy/RfXVRXlaJBYuW4AcX/Apz5y2RNqS5XA59+nfHYYftT6KSvaY8MoO5vhxm8lTQu/hnv8Gnc+fiiKMOxInHHIH6On5jlVgU8dSa+xFJ0x0uDMrbpmh7I3YN5hnR2nPad0fFqdLkkYczTWFk0YMgh+qsjzNJmE6ZE2OXzSP86vD25mERc7WPeTBwCdv88XdFMRjjwkPY2GSwQvTp0wnHn3AkVlev4pWoqmyLCS+9jKOOPAkHH3w8DjrwWNxyy+3gV5by22CWLl2K/fbbH3vtuTOJxECMIXtQWFieccapSKU9EZ+ZTDnmf7YQJ510Nk455VycfPL3cfRRp2DmzA9JrFbCD/LiiTn77NNkGCgeh9H0+k88XrF4f679/Q2Y8f672HHncTj33NNIpJrxUPkcMmVpOY+YBAl7ddtUOOLZXb5sJS13aVeRGOZkvFW2ma29zWkCpwN+u1C/vv3Qq0dnulQkWGwWK7SyiVwiMzSS3DQ5JHmqUaHGa/BhVW2JeNvrqATTDfGcGxHMvoHSRYaKJtw5ij15pn0mb27EUvMnuQosLs/93inoRiKVX1/qpR1U19fjuNN+iH0OPQPHnvZj7Lnf8Xj8qRdR2S5DNsNBXXUdvnfWiejetTMV4igPSb4x14bfKsj56Ma//gPPPj8Zg7YagN/+6iIqQFryYg3OMzymsEv7YdEvbUsd7kDFz4Nl0szHovyWyXBh1RQK1HX63XEuJ4phRWkyyAM1MRQUlk5NUQHZMCZhmsfDb1nYtm8BfzihLbqXe8iF/OrIoteA4/LG8sc7URSDpI2i4WCD5PsxhgzdGsuWLserk1+nZR6qqtqI4WqobyDRQoapvEzS47LlS7HjjuNw/fVXkCHiHsOcumzxguZyETbfvBfatm2LZ559geJbqKxsI+Ofzpo1RzpIyfBTZSkSrw2oravDBReQaD3pGFRXF0TkJnAzAG4OcO+/Hsf1/3c9OnTqhN9fdwV69epFgoqr7h3JF5VtKvDQQ49JFf+smbOwdHkNnnzyZTz26FPyZqv+m/TF+eefRb+blvMRo8k5QuatDyPSzPnLuLKWTdcpj0qrVkZmoAUUiT1qHLv018gcBqcxnvHxmqX8KtwobIBb1Q8o7wZ76SSES1+icEc47UdRAiJhyr39i9uZh6ihKd775Ai5g+CSJcvxz/sepYKCaWJRTvnl9JOPEnEoaZie8ey57NS+PTbdrB8ef+RZNDRQYZAKfFwtP3v2p5g+YzYa8mYUDH5N8IolK3DmaUfhlz/7vlxD81593jvvi4eTS2HK1Gn4/g9/Ke9i+PP//Qrbj9hWCp0O5Utui9qhQwc8+cRzUvCbN38hPl0wD2+8NR1///v9qC/kUU4C+fJLf4jOndpTfNo5/UBrzWfrCxWnSpNEHsaUyXnODyWp2KIH7kUP1OOO13xs3qGAm45vg0FdLDQUWJiufQAz+mBQvgwWKI3TBqctx42x+x67kpiskJ6/ixYukrac3BaRvaAN2TppR3ryScfj6qsvp3jtaLnxlpp9cJU8aFmI7UcNRr9+vfHutPexaNFiEqc8PBSnY5CAzVOcLNqRYb300p+I1zSb9cUDwyaa43BbSO4c9d67H+Gss85F3YoVuOTnl+Gww/YqVuebAcf9IEKXzu0o7GI8iWE/KMirV6e+NVX2wfvi3xhBRpabHbBBTmiteSO598n5c7VseZmHNmkuhBQ7yIiwkKeNxGkqrBHWNDOOcBuh3wC0HQF45cDKicCy5xCXD4DTditKSJywuejEAsw0GWmK913uCc2j4jEuWLAEf/rLnZTn8qijwqFF4vHcs06QjoimhoJjWzIyxpYDN8OIkcPxwfsf4rO5i5DN5egcWXzaKOQLqG/IobKiAhdfeAau/M2FUojkH+PrINaimB4WLl2Jo447F59MfxfnnHuqDMbP+ZYLgbyePa1ci9GpWxc8/OgzVGgtkDB9FxMmTkEd/QYXQH956Xk4cL89Je/xMcpRNsHr3ZywKHHIfVKUUsMpkb1apkcxf2EDQqGojgx4GX71WA6XP+qjV5sC/nB8FXbdPI3qLA8JYzxJjD4QlK/DOo89i4frsUmA2vh07nLp4Tvzo5moq21AOpNG/359MWr0SGy5ZV/U1/Pg/WuFqUlvSfUpp1df3sW/YMEqPP/Ci3jzjTewdOlySdNdunTCNttsjd133wX9+3eXt0DxtvKGM6lm5P1wD3IbM2bMIqM7HW3atsW4cWNpmRnCin93zaFb3FvZwv33PYx///t+qWLktqf9+vXHKaechH322Ql1dfyKVI7M/8yxttY8ktxzPn8e57SyysbTT07A5l3zGLn9EIT5HF2looCRa9X0MKdgxDOPIsFeRMtrA//jK2F99CcEmY5IDb0Vdrd9EQd0Pk5atkuQs2pC95/vCR8N5wT2nK5eVYMXJ74mZ8jnlvJc7LnbOBKHqeL949jmPvKrgrn/QS7v46mnn8OzL76KpStWIZ/NomObCgwdOhT77rv7/7d3JmCaXGW9/9f2Lf1NrzM9W2YmCZM9Q0iCSURjNKwGkgAhEZFHxIvyIKKgPirKvcpF4XpliRrwAoKQBES8JEQFg3pDiEASIOtkX2cmyyyZmcxMb99S233/76nq/iYZkvSkM729v+766tSpqlPbqff866w4Zv0aSUPYgl7ecnkNyvSF4fF9emzrDnzvez+Ud72Cl//cmejr7dESE0/EPeG+rG/KPof/89vX49Ofugx33n8f8iDHihUr8CtvuQDvePubkUmcch+isp+cIt3GwWPi1JhDOGGqxa7yT4OVyVcru/z5xLUdvP8fm2j0JPj4Rf244OQK9kxo5oAamLLen2FMF+baMMpxnG3WX+upu8SFllHTcZlEt2jO6P6ilNvIvl2JPZcpItmYqd7jwmCn/EkCSfwkvsruExJvO51UBSnRtEyPNRUmu6eqy/aiNUVgTh2H27k3Q7aVk+ZgABTDoyMxdu/eK4l4IMuDqMs1jIxM5TS5oLmzO8ZipUzuEnkgw8sj/MVH/g4vPjLEm9/yenRG98nzCTW3ce7eJvcMxVJOLcqPF0r8vOfDCB78PPLe1Qh+4jLkS38Wfhpr7yVlgx0Wiy+EGFA+R36MlSUPPw7XbRRHdXPvj6vW47Yv36tuJv1kM3cUWZa/JGX1G9cIcvfOPWovBoeG5AORfRuzlwSXFpU8NVxjepg4NeYMpeGgQKXx5TKL6z/5nXH8wZXy5Zp08KGLevG2nw6wb68zNi7xncIMgvFc2N/s0c14w0Z37PYp0yI9ervtGM9csaiLXlNxzMU3F1e7oRhIc9cpP8NgowzOOTGhdDmlxcZCGW/detdXIie6y2O7ddxGN+XZitu1zmf4rhjSiWMmyBRausPk9Tl3eazFSPkRS3E6tDTAJX/9JWxYF+D8C16DZHwUAcdgV206R++RPEraRp6fDrOqcUGeuVxTIHYzvesP4T/6ZSS9xyM67SvAwEnwMva3W9HtVZrOoeevcZpzmco4zrhbxlXO+a5MxX8373bzmaqffLSVl8YBDDSey8Tc1RJ6TZbM6TJ7gJE99ZiS3hRF+QxPb5X8MReVblYD0cZUvNfFdnzXyveUYXNdiR7fOGim7qRhzAKloaEtoMHgnGYmbieSuGa49Psj+KMr9olnjD84r4q3/qSP8VExWKETpyVmCIzp4BKTIgFzqZDOAz9CtVJTYcdx990UTgpEbuOiWrnvlNtNbpmtgaOwIqJR9vU4ChUTNBdmmYCV+0+FM+XmNjxumQgSN586rpyths1GXAzfJZ58h7gvhz0tw506t3LfxQjtDK+f80w+HNgau9Ua1S6EeP/yTFUpDdDcpXyGxWOUp6ruQEQSCY/7CLI1r0Ywci/iW96GeN9diCUO5nlHt6VtLW0uKeezhbuWrjgtc8Z75oaW8+515bzbzXeE2/J9CwP2YFHRzvR1//2EKfeZeg/KMFidwB3L1ecmup43tnATiuQoknfadx+aWuIiccidq7yLT3mvjeeH5ZwacwQaTOfiR2wYxrjiR22880vASHsM/+P1dbzvrD7sa7ZkS4oFjkXuijdpDBiNzSgYBw3jXhF9yrj09DjlNmI87S4a7KZc53Jn6NaZ4kytSxzVKeEdTNzdb/uu03hq+NMIclHg7o+DHdZXqyHuufsurOmfwPoj1yDrZCpUyHSex2xCscmGo5qLKh8nWSRirdNBeufvIN7+LwgHT4F/ytfg9b8IfpbKdvzI4p786Yo8C4UXIOLrPZY/997Rpwhfj0XH/seb7vtsHBgTp8as4mKfM5KsdJ6J3ozCHF+7pYV3XdrCk+0M739lhN99zRJMtHIk8oVake3Y5YvrmN9xMIm8YZCnmkBGoWeyiuX6A8U1Fxb9uYGblXSH63Y9uDi73/nKrnqYrnDpnjqWrp32MRYi+983V4xbrwVYWt2GpBVrkbenndjz/s39+0XRJEZQTpZz5+eJAI0r8vHeiYGNvwZv6zVIVpyJ6KVfQtY4HEHSBthISvZRUTtP48ZT39nnwsFe58Eci9g79/wwcWrMChrt+PJ2Rb9EDGpUFWF6U47f/PI+7Jyo4LfPbuOPXjes/VHGXgCOxFjuYS+/YRjPle6kjvUIRZaJIO1gVX07gkCEmupVFgOzDuH8qvGml6aCk8OYduCFPcgnngDueCeynTcBw6cCJ38Fee8RCGQ9S5743aKt0p9iR82uGnOB+fUGGgsGNYBFYsFfzTGthvjqzQl+47JR7BwL8duvyPH+c5dq/VOmG75sX+7B/ZnYlD6GYRjPRGkzOC+7+anXqwgrrpsitmSft5Q5oR6FdSRf+k0RostFkH4W/orT4O/6AYJb3wSMP+ByTkWJaz/S/OP9kNtRzg1jLmDi1DiEFFKSorJIJFxLSTdW+GXfm8A7v9DB7riD970qxQfO7UMz9RDLV742KNEwSCFsaUxNmxqG8RwobQ7nHAKz3uPhuv+6AbdvvBd+VNWugWij1L7MM8p6p5zrNXAc/tYEsvoK4MS/Q7LyZ5HsvhX40VvhjdyG1A+R5hNIvUSrU2kPKXJfyp5S3L8ZV2P2MHFqHDJUT9IAFuKSwjQXA8l+TC/5zhje89UWJvI2/uS1DfzBzw8hbsn61EfEr3s1mq7FNCcVpgyUbsMwjGmgo0P15Lj11jtw732bkYcV8XNdEql9mW/QJLqfwkaK7fQjBO0JePVheBs+iXzFK+HvuQnJD38JePJGZH6PVr2lRXaNSwtBWghdrc9qGLOEiVPjkKG5FoXhzJy0RBjU8ZGrx/CHV2ZIxB7+ybk9eO8r+9DuZOjIMkccV4Mpk2sF7SbDMIzpoPanEJ+cWJWIY7bXaizmLvyLbeczZQ4obSbY7VEyLhc6hOikzyNf/QaEo/cgveXtwM5r4IdlB/1y/bIPbSwnClOdG8YsYeLUeEGgoKSGLMWkW1YPJGILA3Q4+iI+cOUo/uQqduHSxAfOreA9P9eD8dEMecD+5MLJxIIJB7MFyoTFMAxjOpTClHP2c8p+klvNMXRa7OdU1qfyU6yfzzgbqdaSP3KdVYSdFrKKj+DES5CtvAjRvvuQ3fw2JNv+uRhBKhaxHiPNY5po2c3Zb7Xk8/t2GPMUE6fGC4L7Cu8ylIWBS2Ue+in2dHL82mV78JF/TzHQk+Cv3jiId/9MD/Y220jYVx8NpLaoLUcHkUAMwzBmAHao3mzmOO30k3H88UciT2IRcQsrOSzroOYsu/eq8DVXQD76X/JRZC/6DQQTTyAXgZo98jnkfg2Jn8FXO819CoNtOajGLGFdSRkvCJSVNGx0OWMnwjTOEEXA1lEPv/7F7fi3uyIc1Zfgzy8cxGs2BNg7IntVgKpsnHG4Rw3JQYHLcAzDMA4Gl9RxEhHqJUjl47e3J8BQZRuSCTbKDGU1Ber860rqgKgJLgRqaU3lHmQhhzqtor35z+Hf93nxDIDjfh/BsR/Q7UJ21s+hbwVXlcplMBjGocTEqTFjMCqxKIkGjn/qzlOk4p+kOeoiPG9/FHjvP4zhugeA4w8D/urNfXjpOhGm4xSuvo7QonWgZF4WwXFuGIbxfNgvqRM3a1oi6+Cwnh1axM+xPdjzKVl4NqcUmZleJ+0rohqyhz8L//6PiVDfg2Ddu5Fu+F/Ioz4Ecl8gAt33ij5SZHNmoPIOmj02DgUmTo0ZRs2XE5XiimXus6uoKMS192R415f34P7tEc46KsPH31rH2oEI4xMcQxxiCLmr7CszFakMwwyhYRgzAFvjs+iec5oVirV6FRiOtiJLY7E7PjyOr+/Tdi2AnNMumMqXuaDORjN/uAWEK+BtvxLY+EEk8SPwVp8Pb8PFyBtHIMyacr9EwMq2ejfMFhuHEBOnxozhohINWCLmL5dEIBKrFiMUo/jZa8fx3/81xs5RDxedmuNDFw5iqJpjtBUgCsT0UYiKOi1zS0npNoFqGMbzpTupy/MMtXqA22/ZiMMHR3D0MeuRdTqyJligQqzMOeW88BE3hzvNK4NI99wIb+PvwRu5C/nSU+G/+HNIlp4iAjURrS52OJD7IjuqhTd7bBwCFtbnoXHIocGfmihNc6RizNpxjjBIELdzvPuKNt73fxOMjHn4rVdH+MRbB9EXhZiIK6iGvhap+SJQS6PHebfbMAzj+UJbUn7spmmGej3Hdd/9AW7b+CA87YSfHdxRgC1Em0ObWsx5ffxn/VovhNfZg7DvZASnfg7p8pfD33UbspvPAx7/R617GnM/EakUprw7k/aePjT6xRrDmElMnBrPi1JIuolFRWKmUh/1Sor7diV4y2fH8Omrx9DbSPFnvxTgg+c0xBjmiFMgYP0nbl8aOzV0btkwDGMmoV3pFqg0M/VaDZVq5GyO2C+dUYwtYMpGUuJyHiJQaZDjvrWonPJppOt/Gd74dvg3vxPZPX+EIJuAx279cor3LnvPHFW9WbyXC/ymGYccE6fGc8aJRopI59Y/znVKkaSpdv8URR18684Mb7h4DP98WwcnrGng73+lD+84vQ+jHSDxA1e/lKkBf0tjp4bOLRuGYcwktCu0XTQvtFms195pNxG3xG6pYAuKbQrRtkARS8sfndTS8pqjGJWJBJnfgL/h4/BO/CBQ6QHu+gukN/8S4rH71G6nWUcbrLJaBLuo0hH/ZNLuptTNAA3j+WPi1HjOOMNNEelyHsQ6UasqceohChM08zb+4hvjeMun27h3N3DeqVVc/o4Qpx0eYN8E63NFMk0NQ6rhGIZhvMCUIqrM5Wt3chx77FE4fN1K7YTe9c288MVpSZnzSYHpZYEI1FDmch/iffAOfxdw/N/C6z8Z/pZvIPvR6+BtuQpJUAXHKmCT/5z9UPNWMRkQRzn6n2HMBNYgynjuqCEqjbssyCxj/84yZ//Vd25r4vevmMC37gjQqCd475m9eM+rxeDFQAfckCM+Pf17yASqYRgvNPsndRk4vn6tAiytbJPFXBv+qFET27Yg+jl9FibvRyFQXat8j7dChGYbXtRAPrEF2X0fRfDIVch7KsiP+B3gmD9GGPUgTxO13V7RJ7VIXQ3LMGYCE6fGMyJSlJZKXSUswhfzLcI0RxTIF7TY8X+4PsGffnMUD233cMwa4AOvH8B5J2ZojVbR9DNU2F+eBiV7MjyzYYZhHEKeLk7FL+1gVc82EVuRClRtJCQstg/mSTtP+8zlnPa6A1T6kGfjSB/+PLJNFyNIxxAPvRqVDX8Kb+AMzT318lj2Y1WtLkGvgRROcfPWWyaEMR1MnBrPiDMqU7ml/I3zRIyUBz9KsXlPjA9fkeLzt0zI2gC/cGqED7y2gnX9NexqyZd4KMI0iZDR6MnOriiJ4ZihMgzj0LFfUidujhDVU/exvLoNWSICizaOokyE62LIOd0P3hqxy7wHbKbqrD0bQMU69n4a9CPb+e/A/R9GvmcjouhwxCf8LoLD3wHPb8DLOvD9SIOhoWdQpYl3aYhzG8ZzxcSp8Sw4YUqBmogxz8RdCVLx7+CrNwT40NV7cPc2H+uWhfids+r4xZ8W456maMchP6bFPomRP8AXtX1FG4ZxKOlO6tigJwg9bH7oQawdGMHaNatFoCaiS301V4vv45l2nnZZzbP8iINj8kPuSV5B7neQBSvgTzyM+KH/g2zbFxHGbWDV+fCP/58I+k9iXrTskopIDTUDQsMQNEyz+cY0MXFqKGU0oPk4UIRos/hGBGk1CPHIrgQfvLKDy29rIulkeM1JIf74tQM4aVWE0Tb7OQXYr74W3wtWlG8YxlygHCUqSWIsXRbho//7c3jxESEu+sXz0RkdQegz55QNNt32ixKx392lWy5poKcI1aAOhGLjH70a+ZaL4e2+A+hZj3z9ryM44t1Iqr0I0nZRxM97yYwN7r8/JlSNZ6MrS8tYzKixkElNkszLiYaJuaW1wDUg+OR1LZz9N3vxhZtbWNmI8OELqvji2wZwzPIEe5tacwkBg5J9qEdLYapf0oZhGHMC2rYclUoVUcR+TulFAaZmcFFDK642W24K74u2wNd7wnq5bSRxB8Ga1yM49VJg3duBdAv8O9+P9KYL4O+4VhKAqmwfyS6xiFS9sXpPu9MVw3g2TJwaCg0RW2zSQFOEZmmCOGUuQ4rAT/Dd+zO84dMj+K0vjeKxHRFef3IFX/mNCL95dh86GdBu1xBqcVgRnhr6KWGqOaeGYRizhNo4EUZOdLGfUyDuNBG3EzFcmfz7Yqvc+sUMtaNKSppssd1y1woP/vgIOO/sBWqrkJ/yl/Be8nmky86At/3/Ib/xInQ2/h7y5qPI/Soy9tKSdpDmncn7vtjvr/HcsGL9RYh75GJwVEDSh1aoiAYym0hyNEIx2CI2N+3M8bFrWrjs+gRjzTZOOizEO1/ewEUnVbTQZiQOEdKhuC9kwzCMuUZ3UhfHMQYGK7jyn76BY1YCZ73iJxCPxgjkC5udzLPo3zgQhbhkw7EgRiLu0B9C1tmO7JHPAo98Afn4kwj7j0W6/r3I174NeaWBqN2GHzGhkIlJj4ZEmGYwTEs7jP0xcbqY4ZNXg8DcUhbfQ4QmPRLsGknwxR+08Klvx9i8PcCypS28+YwG3nNmDSt7gX3tAGKaUPEqNC8MpMvgiNssjWEYcww2hOJXN7vDY2v9apRhWXU7fEkG/UxsltaVZA6ridNumH86adwncUKV9j8L5daFkjA8+QNkmz6FzhPXIOpMwBs+G96L3gesOReh3HfW+fU8PgPuwH+GSwcDtzTDmMLE6UJHHm85CsjTH3SGRIxFJl/BFT8Vu5xib8fDP9/Uxif+cwwbH4lQq3k476QQ7zqrilPWVdFKMjRj+f71fUS5GBt+9dKmSOAmSA3DmKtMJnWc+ewwSYRVFmNFbScCEaOqjwrMlv149D4WNl/RYUwlLaB/1CPuFNjxdaSbLkW+50aEeQPpmnPgHfHr8IdfxZsrYTTl3jO3tCLPQgLruvcMXIOXB+I0a3kweyaLCROnCxx9pSlMJ19wN+NTT2TyvQShn2OkneDrN2X4zHfHccOmphjrfpx1NPCrZ1Zwzgm+7BJhvMPhR2kraFQYjIZeGBAGbBiGMTdhUseJRfZZnrh+TmsBVoRPIC1GO1LDKJg4fRYKm68z+WGfqFoPjMKUwr+yHEF7KzqPfw3po59DtPMhpPUagnVvhLfu3fCXnqk75/Ic9E5rv4PunjM31YUrLvGyJ7E4MXG60KFBppjkWMhanMWunjJE7OtJaHZa+NrNGT753Rg/fLgFpCFOXxPgl8+s4g2npuit1vDkhEQUMTghKqXZ0H1Lo2E5p4ZhzHW6k7pMRFQYAjt3bMXqxiiWLRuSr/VUt7H6ps+M3sfC5h+IDG3Rp3IPJY1Jo174E5uQPPoV5I9fhWDkYcQ9g/BXnYdw3X9DsOwsDYrPw2eVCx0KlYOoTqU05bwUr8biwMTpPMYZCQpP9yIfGPdqJyk7mM4RVZzv9hHgXzdmuPTGMXz/QVfh9KS1Ed7xsipee1INQ31AeyxAh0YizBHmTtjSSmjLe7MThmHMI7qTuiRJsGw4wsUf/wI2HB7igoteh87oPoR+pOvtQ3t6lCkQ04aMxfwUmOLOM0l3wjqyoAaM3gdsuxx49JuAiNRsST/S4VciPPxX4Q28Clm1gjDrSFqUwfMlodK6qRSqLLmju/uZ0F0c057VgsTE6XyHwpQCtXhRyxdYl2RdKu+0a03P0T5aeGgHcMXNMf7x5hZu3SIr/BwnH+HhF1+2BBeeCCxd4mOkU0GeSJjy8evzxZfAaHxcsZf8sy7QfobCMAxj7jPVCX+CoaUB/vriy0Wc+njDm85BPD6CgM12LOd0+hTJT3e3ga47QTqYRiXIwhpCr4Fs7D4kj1+KcOu/Idu3CZnoVm/oNfDXvB1YeY4s97O5lIQjaRbliTZOkzCZzhXHcQ5LgxYyJk7nMfro9IXld6WTi3mWIss5wkmOQIvuU6Sphxs2x/jSDU3828YEj+5uI6rU8DPrgQtPr+KVx4ZY3fDxpAjZOPbBTqIK++LCpF2gS41M4TYMw5hHdCd1FKfDwyE+9tG/F3Ea4cI3n4t4dFSEaaDWzXLjpkd3zqmK0sLt1jDFSMSZIfNC5CGXe+GN349s29fhb/0W8n23MmFBOnA68nUXIlhxAfy+9RqqSlMOLeszbE4Mm77FcexZLUhMnM5hpvNokrQjApWilGPfy4ssbNnj4Zrb2rjythTXPNhCqxWhvy/Fq4/2RZT24KdeVMGSGhs65egkng45yldeYkVhUAzDMBYG+4vTGENDFVx+6RU4bpWPV/z8TyMZbWk/p8QEz8zAO67Vzsr7qc9AJvoFNWRhiHB8K9InrgW2fx3Yfa08G9lkyVqEy85BvvZ8BIPybKoDkh65sfupfTV3W8N8hufEVbKtPcv5iYnTeQofGovs2dDJ5ZCSNkbawM0Ppfin21P8x+1tPLwrlY0CHLkyxLkn5rjg5DpOWBXCjzrodAIRpRXtyYOTIi8yY4TrGJlze7ENw5j/uJTO1WNkP6eeGL0saWJFfRciah12LE97p3UeS5tqPC8oQuWeUqA6Hcn0hVXEZJXcZz4HP+xBFoh/ug/57tuArV+Dt/M65PEO2VfSp/5T4a0UobriPOS9J8ALqzoADNtJ8HlqGqXplIRBf3UJXFCHMR8xcXqoKe62K5pwOZT0dL/EvU18zbofDB8TzSr7kmM98TCQuRpQXwRmijsfaeObd+a46q5xbHwkRtIK0Nvv4WXrqnjDSwKcdWKENX1VxGmOiU4q9jcSgSoGmq0qeUwtipF5aTjkBHVM5eJ8DMMw5jPdSR2taZYl4KBFK2rb1d6xI37PyR4neIwZgJkcLi3R21/eVn0U8nEQMCc0h5+yKplsE9ZlW/l4GLkT2PEfyJ74DjB2PfxmjrRnGPnSMxAsPx/+ypcjb6zX4DhpXeK8Ka5A9o8kLH5tyGL5yMWtyZk4JlPWYr171s7XygvnDiZODzHli9FdN8dRfF0KxRZqTOnO+YUoojKs8sWJ6YO94z7u2Brj2vvGcc3dAW5+JMd4K0ZNvkKPXZfhVcfJdGIDL17poa/iY287Qpw44en7fAUlTFXIPFa32zAMY+GxX1LnuW6jKiEwHFGcsvGNL5/6LsfUxOkLDB8F0z+mO1zkjM+H3Un5zDxpwIsqyJLHke+6A/6Oq2X+XeTtzbJahGrvYUiHX4qo/3x4wy9D0ns0fBGlPoPIE4SamOlB5Fmytb8s66HERe+uxM4du/CZ8jZmGROnh5ribne3aiw9+QIxd9S9KOxvjwvFm4MU20Zi3LK5g+/cG+O7DwK3bMsQj8t21QqOWtXGy4/sxWtOTHDS2joGGyGyuINm4qMlYpRDxwVaibyLMmgibvtqNAxjocJPfX7os75innfE4HmYGHsSK3v2oNFoIE8yhJ7YTfnztYW48UJAyUHtr8qjSHI0s0YTIyZEHBAhRpZH8rxEZgbybKIW8omt8Hb+ENh1NfxdtyJrbkfix/DrS4He0xEOvwrp0EuBgZMQRgMabnkITwSrW2AOLX3KhM+tJ27bcsmYbUycTpP9XqxpM/VSqBDNJiQcH6l88ckCaqz4VLwiZKwT44HHgB9sAb7/UAs3bGrhoT3yhd+soN4DrB/28JPrc5x9XB2nHFbDikF58TJPGzgxI0DHMJYgg1z8+SfBqiB2wRuGYSwaupM6jgg1uDTC315yOU5c5+H8N56DeGxUu5KizTSRcujRp8NnJB8Gmrspbs2/8TqyHCBj/dOwipRZOM3NwM5rke26Ef7IPfDG7wa7VEWtH1hyNLyhlwFLfxLpkp9A0HsksiDSJ8qcVS9vi4s550wLfc1x5RMn/J2KJc8d5rQzjbV4M3OYOJ02crucytNIXEbG8ibqkluhDn0BnEvfO333ZFnbMHkt+dEe3WTKMDae4+FdLdz8qIcbN3Xww0cz3LfVR5ObiXgdHghx3KoIZ6z38FPrgQ2rAgw0uH+COGaxPSv05/rVrwKaIfOY+qbLmRZue4EMw1iMlP2cxjE74Q9w8ccvw4bDA7zxwtciHt+HwAst13TWcOmUilIuilNTKklDdZmilOt8EZYBG0UNiP8EsuYj8PfcCm/fjejsuQUYvQd+p6nB5T1DyAdfgqD/dKDvNOT9J8DvOUyS3T4NkeFrlhCrE+gIVfwvnz/XyrH1JByseueWXXqqyLKeuf6ojzEDmDidJnq3nMrTeJhr5/aMkywq4uvDYUIlQhfrfflU047sJ2OtvABCLNtu25vg/h0xbt/Sxp2P+7jt8TYe2JlhfFxEZppjSSPD4cM9OE2M5ylrA5x6hI/1Az56enwkmbyWSY5EDsrcUJ8VwSeP4dDzk5/yJSpm+pVnGIaxmOhO6pJExOmyEJ/4WDFC1Jtfp/2cUpzSPJqNPPSoJOUjknuvd79YZAKmSS7dk7DtBUUqR5KqyC413SBrbxdxugkYuRX+3h8h3Xs78vZj7MBbM4TS2kpgyfHw+05EPrABGHgxgt5j4YVLNVQe16XQzo08dvOMv5Kua3sN9dG0lefM9JfRhef31DTYOHjmrDjlaWlW+eTp8aE795Tr0KPSUyIjx6dvy8tRYYf3PEeJtIGcr+8lvKuyJc+SwjVCs51g24iH+3fluHtHhvu3ZnhwW4I7tqfYOSrX2ApZ9o7+nhxrh3xskA+7U4/ycexwjqNX1zFcDRFJ+G0JrtXRV9JJ0eI9YHVvHlHOTPzKYxuGYRgl3UldLGJleLiCz/ztl3HcygDnvulsJGNxUc9fLGhpXI05QykEpxoSl88og5c5SZlz2NOQrfXpLQlmexfyfXeJYBWRuucW7fg/bz6GLOnA1469G7L9YfAGjkU6uB554wTxOgFe7UgEFRGsQYRUNtMjyk/opRIsz8OJVtUpAT9oXC8PLh/2hUaP7JwHQIUyV8ucYlnvm+4zv5hHOafF3d7P1c2BfA+85STFlRezqXnpKHz4YPnAn26vKD5Z0YW1YEKMjmfYMZFi274Aj29PcOfuBA/sSLBlN7B5Z47dEx6yloQpETzs8bG8P8Qxy3ycsDzFcasr2LA6wuFDCRo9ASqsuC0CuNWpiAgW5N2j+OXlMPqXp+jqugh8SWSd67ZDVxmGYRgF3UkdbSt7LWlNjGBlbTd6Gqz3X6oQZ1eNOYY8mwM1JCZlIycdjl9+yhJNdvQPry7rE0lCRcQ2dwBjm5GN3w5v3z3IRx4AmlsQxk9qPeQsBCKvhrQ6jLznRfB6jgX6jpIg1snyeqC2Fl6lgTxcouks02JOT4strCLQdX6OcqunbD3tuMZwn2GfcvVT5/OMOZ1zuj+8u/LA6Z2JINOazeKe3MzlH7pF+WUE5qRfWcxrlEX50fokxZeXK253rTfp0v0moY9b70SofIQlOSbaCXaPhtixN8Xm0TYe3QNs2ZXgsV3A4/ty8fewu5mj3ezIrnKs0MeSRhXLezKsW55j/XCE41YARy/3ceSgj6G+Cho1EZRiGJM8kWOkSOJQJK+cky8vk1xDKHMNS18DvYjJMysW9afsT67wMQzDMAr2E6dME2Q5knTE9XPKNGBK+Jg4nXv8+JxTcRXPVn/Vm+KQy0xDJf1mgyoWyfuRLFfFHcDPO/DSJvL2VmD0fuTjm5BPPAxMPIB8bCu8zk7ksl6DCiSIqAGvOiTi9DCkIlax5AgE9bVA/Uh4NRGzlWFZt0yEa03iT6SpNbOuOH9abJITdfLDxUOeNyef56oreU38cf6TaT9PROtEy73QE6Obp8h1cn384/1RsSPrnLf6zzemJU65KS/SZRO7Z6aDNEyX4obp/FnQxyb/NBbsgJ7noEUv8hD1sfDhiVjlA+Gz0GHNNODyIJxEKOpc9yjmPHtP1oRot0QUxjmaiYedoxn2NGPsGk3wxGiAPWM+HtvX0mL53SNVmSawq+nhyaZEklgiUhaLdpWwoxADvRmG6zlWDdawaijC+qUJjhwOcdhS4LAhWVetoidiVxbyosjhO7J7IvN08iayWkDh0ggmC1yeXO38XFQ2DMMwDoZcZEMmdjcKcqys7hZ3qmlMmUIUZtiYVzC9LNLNbopMKJds8ocpaCHsWBwvQhWoiO6jAu0gTcaB1hPwW1u1u6pwbJPMNyNtbYbf3iab7BLhOsECUD1ULMH4UY9ogAH4YR/86lpkzHmtDYq/uClk2YtAWIdfW42M2wY9ojz6kIXsKUDg6Uk4PBOeLSUq42IhVVnrT/Umz1vPXRZYtc+tJcycYxdodIlG0MZdXM/pOdIdXDc/zp/oMdxbU242Ux92B5Fzqod3zkNGeYr8DnHHz0ScpiJK0zRX6ZnEHhJReh02FIoDtNsJxtspRmTlSJP1PoGxTo7drQyjY6mIThazi5+I0t2jHva2PIyLzkxEqO5rZoglPHihTC05pNz8yEdvNUW9EmF4SYaVfSI2+wOsGAyxbhBY0+9jsDfA8h4PA/UAvXXZLZCIJDHXl3Oi8GXjJW29n8vXG4PnxKuZfJjdj4J+Toa6teU2hmEYxvRxmRvslD1Nxdj74s5aWBruQqVS1SSWOXD8s5zTRUCZ3IqQK1SFzCUWUKz6bGTFeQ6REwhEJ/hJE1myA2jvRt7cKdPjyFuPyLQDQetx8X9C1o8hjPdoppUm9RIwCz6pOrOwIsENwBNxmlV6RaQOwqvWZXmpaOQh0Qt18V8hy30iZBviNyw710Uu1ER/yHYioLOwqn4eRGBQsXrUEoHsywxDEdh6HbJJMe9mSks8P8pw9g9P35oZCb9k2jmnPJ1MbnzgJ3j4iQx3b5P7RvHf9bXCjMCEm2ZiBGSudT3kjy3M+bWaSWSImWUo62OZtdMUeSqCMss0JzFLfUx0ZBsJsyPudlu+c9mhvFz+hOjTWITmuIjORD4rOrK8p0lhKttKYM2E3SrJ/vIlLLvJRvKYOt05p7KTHIsPVZ+l30G14mGJLPZVcgz017BE/AdqCVb0J1jZqIsQDTHU66GvASxteOgXgdqo+oiq8uUt5xSKsUtEKHMYUQrmRM7b5fK6HF1+pVPo8ouGZ8FfnpphGIZx6GAaxrqmadpBX18Fl1/2VRyzKsTPv/YV6EzslSSBnfBTosxkMmvMZcq0mNUFOPlZmSfJmFAM8c1qhFoqK+LAj0S6uGogHHY1YwYWqweIeEVnH7x4t2iUJ+C15aMnbyIeFwHb2SnhjiNpbZd9xmSblts+nZhUAxwnQEvteSiZ8lAmrmKPBBURq3lF69CyagKLiTOKWO2pgOt7Jc7KPKzJflXZNpRte5D7ImYDdo/G6gyyn4RFsavHZBUHT9azyoNs46K8L9pc/Lhe9AvfBPWX7dTN8ylwpbviN3wawrBfc225elZyTim4+Hha8mJXgxifuc7Hu78cotErGpBfB4oTZL7HsYvdbdeL4BXKSfNozHLmRwkvjIf3uCzijSKO61m4QkmXMzJovQlX5BLK1XM3Ft1zTOQg4H6ZnIs8DD9GNQzQK6KxGsj5RT7qco97qikalQoGxN1f9dDoEeEpz2hAhGavuCsSzqA84155rnV5Pg2ZN8RPnBI1+aimYBY74w/nFOA8V85LtEiel+kW94N+XZsahmEYhxhNX8QYp2LE+8XI/+Ull+PFR1Vxzjm/IGt3yiSJg3IgK24sDsqU+qlxgP7l1A23U2VSTFQPnOguVUO536hMbXFOACJiVZF29sgkbohfa0R2GRNhwaoF4g9xJ7I9M9g82TeRbUR/iYe45bgc6YzdajFzMGcpL91yTNYb5JyRnWIrlWXOKSbpr0K7OC/1L8+P4fBaCBUQ9+M+4uTUDcOqhIhPvQF+33FytdRt1EG8H8+faYtTHjZOWyLqPHz2Gw/hXZfci4YoPxavu4AoNuU0ZdsMLflaEKmpIxTJwbJY7hkvmCI3kfD4kNz2adZkIztZZOOltsw78oXRhi8PJtD6QE6QRvLMfVH5fRErs2f8KMCgKExPhGokftUKh+lMEQaBnKPsI4qRopYilAK3LRdQlXNPJMxEzplfyrFYKh6VQrMj56dnyIet4lrP3P2JF4V2Ibl12TAMw5gHaFLnbDrToXqtgoce3IyBJcCa5SvQlkQ/YFGp2XbjYJD4VaogHS6V7ow5my4TjvoiCOTjR9wpi+KjiuibTDReJHpQNFMai1u0jKz32Q2WqpIEOdu1ZDKnmORXFasMiCD1KFQpTmUK4nG3LXNws452FhBVRBMFiXxuJegNJVxf3KKRGqKR2LsBtVEQiLbyU9ZalOOKVvNz1OtUQESuhn7cVt6LQLSPU4CyLeVR6iHzG/iZd34Tg8uP0/3lR693JphmsT5PmkUisd7kf7nqW7j4bz6FvsE+OVFZV7zQTr5xobzIYoX4upks64WIW3NVuZ08EFX17gFncoF8SE4IcrV77DxdneRLRWbqTrjV5HrKSIpddu/E/RkxRHxyY1kKZcpkG5WgcuyArfa69g80Ikk4ujUn8ddz5ETcduUVGYZhGHMfTQIK6I4qEZ7ctVsS5Cr6+/sRJ5KSMF2VdVbn1Dh4qBFEOUgcYiadVhdQNcKeA6h7ZJI4xnVcztj1FTWG6B8qE10pqsTlWLrtXVdZ/GiaEn4528SU6BCs3JdhTEZinoVMLpgpPxcG1zk/tw3h3NdjyhquFgf9Mq04qx4OrpcPvKrMP/2pP8eL1q2WZRf+7OScysnwpVVBKC+yLzcn1PHgDcMwDGN+MbJ3n6RhIXoajcLHMIzpkCRtFc0+68KyiqZWGXj+TDPn1G3KeZqyqF2X1G9mtLJhGIZhzDyaUknaxQwWzWiRRY+jBAla8ieUCaulZ4ZxYPge8f3gPGNObZprOyCfGZXiOVOlDtMSp1OUp6fv+tSZ2httGIZhzEW6kjpmrpDJ9KuYBWGoxZOetm41DONpdGs+OotXhVJyJqvDHFTOaVm0r26ZnnKuhmEYhjG3YCJV1ItjzikndivFhIuNfYMggO/54nbV1wzDeBa6hF+pC2fq3Zl25YBuYUpK15SPYRiGYcwt2PiE6RTTMOachmGIK676V3zne9erm36uuathGM+J4nVxTa/YsGrmPuoOsljfMAzDMOYPrjWxc8dxikolxMcv+QxWr16Jt7zp9UiTFF4oyauIWMs5NYzZZWaaVRmGYRjGnGZKcFJ7Ml+mUokQReFUaaBl1RjGnMDEqWEYhrHg0aGkizpxWZ644v3WhEzNwm+qq0TDMGYXK9Y3DMMwFjzlIDKEY+uzX8bNm7agVq9i1apV2nc3654SK9Y3jNnFxKlhGIax4OlO6vI8EYGaI4oqXELG+qhCKUpNnBrG7GLF+oZhGMaiIssk8fMDzS1NklSFa/cIiIZhzC4mTg3DMIxFBYdbpAhlMX4YBurmKDecW66pYcw+Jk4NwzCMRUGZK+o64Pfxzau/he/f8AN1088wjLmBiVPDMAxjwVP2X+qK7lms7+Pu+zdhy+Pb1M1upKwTfsOYG5g4NQzDMBY8pfAsi+45r9frqFSrU8X5VqJvGHMCE6eGYRjGgqcUpG7uGj91JkYQN8edn/wxd9UwjNnHupIyDMMwFjzdSR3H0WdR/h13bESjp4H1Rx2lfkEQ6HrNRTUMY9YwcWoYhmEseLqTOjZ+ohitVNjPKcfaj1Wsat1TwcSpYcwuJk4NwzCMBU93Usf+TSlAKVA5L0Wp5ZwaxtzA6pwahmEYiwqKUIrVarWquad0lwLVMIzZx95GwzAMY1FAEcpcUeacUqBef/31uGPjHeouc1ENw5h9TJwahmEYiwKKTwrUMqf0v667ARs33l3kmjp/wzBmHxOnhmEYxiJgSnhSjFKHnn32z+GUU05BnrkcVcs5NYy5gTWIMgzDMBY8+yd1OeI4mWytnyRsrR9MilMTqYYxu1jOqWEYhrHw0Q72KVBZ5zRDGAa46Yd34N57HoQfcGx9y6cxjLmCiVPDMAxjEeCEKed5lmlO6TXf/jZuveU2+B5b72e6lWEYs4+JU8MwDGPh011S73naEf8ZZ5yMY48/St2GYcwdrM6pYRiGseDpTurYbRQJw3BytKgg8EWzsqGU9XlqGLONiVPDMAxjwdOd1FGQcplTd+MnGyHKMOYGJk4NwzCMRUEpRn9csleuM3FqGLOLiVPDMAxjwdMtTH+c+DRhahhzAxOnhmEYxqKgW6AeiGcTr4ZhHBpMnBqGYRiGYRhzBmuSaBiGYRiGYcwZTJwahmEYhmEYcwYTp4ZhGIZhGMYcAfj/XU3Gs1YYMdEAAAAASUVORK5CYII="
|
||
}
|
||
},
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"\n",
|
||
"(from https://www.timescale.com/blog/how-percentiles-work-and-why-theyre-better-than-averages/)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Durch die flexible Wahl von \\(p\\) erlauben Quantile eine feinere Analyse der Datenverteilung, was tiefergehende Einblicke in deren Struktur ermöglicht.\n",
|
||
"\n",
|
||
"Die Berechnung von $p$-Quantilen (auch *$p$-Perzentile* genannt) händisch ist nicht relevant.\n",
|
||
"\n",
|
||
"Die Berechnung von Quartilen erfolgt ähnlich wie bei der Median Bestimmung. Zur Demonstrierung dienen nun die folgenden Beispiele.\n",
|
||
"\n",
|
||
"#### Beispiel1\n",
|
||
"\n",
|
||
"Betrachten wir die Zahlenreihe: \n",
|
||
"$$10, 12, 7, 8, 1, 14, 3, 4, 9, 13.$$\n",
|
||
"\n",
|
||
"* Erstes Quartil (Q1): 4 (25 % der Daten liegen unter diesem Wert).\n",
|
||
"* Zweites Quartil (Q2): 8,5 (der Median teilt die Daten in zwei Hälften).\n",
|
||
"* Drittes Quartil (Q3): 12 (75 % der Daten liegen unter diesem Wert).\n",
|
||
"\n",
|
||
"#### Beispiel 2\n",
|
||
"\n",
|
||
"Angenommen, wir haben die folgenden Datenpunkte:\n",
|
||
"$$5, 7, 7, 8, 12, 14, 14, 14, 19, 21, 24, 25, 25, 27, 32, 33, 34, 36, 40, 45.$$\n",
|
||
"\n",
|
||
"* Erstes Quartil (Q1): Hier liegt der Wert bei 13. 25 % der Werte in der Datenreihe sind kleiner oder gleich 13.\n",
|
||
"* Zweites Quartil (Q2): Der Median liegt bei 22.5. 50 % der Datenpunkte liegen unter diesem Wert.\n",
|
||
"* Drittes Quartil (Q3): 32.5 ist der Wert, über dem 25 % der Daten liegen.\n",
|
||
"\n",
|
||
"In dieser Datenreihe ist der Bereich zwischen dem ersten und dritten Quartil relativ groß, was darauf hinweist, dass die mittleren 50 % der Daten weit gestreut sind.\n",
|
||
"\n",
|
||
"#### Beispiel 3\n",
|
||
"\n",
|
||
"Angenommen, wir betrachten die jährlichen Einkommen einer Population (in Tausend Euro):\n",
|
||
"$$15, 18, 22, 25, 25, 30, 32, 35, 38, 40, 45, 50, 55, 60, 65, 70, 75, 80, 90, 100.$$\n",
|
||
"\n",
|
||
"* Erstes Quartil (Q1): 27.5. Das bedeutet, 25 % der Bevölkerung verdienen 27.500 Euro oder weniger im Jahr.\n",
|
||
"* Median (Q2): 42.5. 50 % der Bevölkerung verdienen weniger als 42.500 Euro im Jahr.\n",
|
||
"* Drittes Quartil (Q3): 67.5. 75 % der Bevölkerung verdienen weniger als 67.500 Euro jährlich.\n",
|
||
"\n",
|
||
"Diese Daten zeigen eine recht breite Einkommensverteilung mit deutlichen Unterschieden im oberen Bereich. Erneut ist der Abstand zwischen erstem und drittem Quartil recht groß, was auf eine signifikante Streuung zwischen den mittleren Einkommen hinweist.\n",
|
||
"\n",
|
||
"#### Eigenschaften und Nutzen\n",
|
||
"\n",
|
||
"- Quartile und Quantile sind widerstandsfähiger gegenüber Ausreißern als der Durchschnitt, da sie die Datenstruktur nicht durch extreme Werte verzerren.\n",
|
||
"- Sie bieten eine detaillierte und präzise Beschreibung der Verteilung, was besonders in der Explorationsphase von Daten hilfreich ist.\n",
|
||
"\n",
|
||
"In der deskriptiven Statistik sind Quartile und Quantile unentbehrlich, um Daten strukturiert zu analysieren und aussagekräftige Visualisierungen zu erstellen."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 20,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Berechnen wir nun Quantile im Dataset\n",
|
||
"\n",
|
||
"first_quartile = df.quantile(0.25, axis=0, numeric_only=True, interpolation='midpoint') # ACHTUNG: Interpolation beachten! Siehe Dokumentation"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 21,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"pclass 2.0000\n",
|
||
"survived 0.0000\n",
|
||
"age 21.0000\n",
|
||
"sibsp 0.0000\n",
|
||
"parch 0.0000\n",
|
||
"fare 7.8958\n",
|
||
"body 72.0000\n",
|
||
"Name: 0.25, dtype: float64"
|
||
]
|
||
},
|
||
"execution_count": 21,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"first_quartile"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 22,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Selbiges funktioniert auch mit beliebigen p-Quantilen\n",
|
||
"\n",
|
||
"p = 0.42\n",
|
||
"\n",
|
||
"quantile_p = df.quantile(p, axis=0, numeric_only=True, interpolation='midpoint')\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 23,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"pclass 2.00\n",
|
||
"survived 0.00\n",
|
||
"age 25.00\n",
|
||
"sibsp 0.00\n",
|
||
"parch 0.00\n",
|
||
"fare 12.35\n",
|
||
"body 130.50\n",
|
||
"Name: 0.42, dtype: float64"
|
||
]
|
||
},
|
||
"execution_count": 23,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"quantile_p"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 24,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Bzw. können wir natürlich auch direkt mehrere Quantile berechnen\n",
|
||
"\n",
|
||
"quantiles = df.quantile([0.25, 0.375, 0.5, 0.625, 0.75], axis=0, numeric_only=True, interpolation='midpoint')"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 25,
|
||
"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>pclass</th>\n",
|
||
" <th>survived</th>\n",
|
||
" <th>age</th>\n",
|
||
" <th>sibsp</th>\n",
|
||
" <th>parch</th>\n",
|
||
" <th>fare</th>\n",
|
||
" <th>body</th>\n",
|
||
" </tr>\n",
|
||
" </thead>\n",
|
||
" <tbody>\n",
|
||
" <tr>\n",
|
||
" <th>0.250</th>\n",
|
||
" <td>2.0</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>21.0</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>7.8958</td>\n",
|
||
" <td>72.0</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>0.375</th>\n",
|
||
" <td>2.0</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>24.0</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>10.0083</td>\n",
|
||
" <td>120.0</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>0.500</th>\n",
|
||
" <td>3.0</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>28.0</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>14.4542</td>\n",
|
||
" <td>155.0</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>0.625</th>\n",
|
||
" <td>3.0</td>\n",
|
||
" <td>1.0</td>\n",
|
||
" <td>32.0</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>24.1500</td>\n",
|
||
" <td>190.0</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>0.750</th>\n",
|
||
" <td>3.0</td>\n",
|
||
" <td>1.0</td>\n",
|
||
" <td>39.0</td>\n",
|
||
" <td>1.0</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>31.2750</td>\n",
|
||
" <td>256.0</td>\n",
|
||
" </tr>\n",
|
||
" </tbody>\n",
|
||
"</table>\n",
|
||
"</div>"
|
||
],
|
||
"text/plain": [
|
||
" pclass survived age sibsp parch fare body\n",
|
||
"0.250 2.0 0.0 21.0 0.0 0.0 7.8958 72.0\n",
|
||
"0.375 2.0 0.0 24.0 0.0 0.0 10.0083 120.0\n",
|
||
"0.500 3.0 0.0 28.0 0.0 0.0 14.4542 155.0\n",
|
||
"0.625 3.0 1.0 32.0 0.0 0.0 24.1500 190.0\n",
|
||
"0.750 3.0 1.0 39.0 1.0 0.0 31.2750 256.0"
|
||
]
|
||
},
|
||
"execution_count": 25,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"quantiles"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 26,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Man kann natürlich auch wieder über die Zeilen gehen (macht halt rein statistisch wenig Sinn)\n",
|
||
"\n",
|
||
"row_quantiles = df.quantile([0.25, 0.375, 0.5, 0.625, 0.75], axis=1, numeric_only=True, interpolation='midpoint')"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 27,
|
||
"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>0</th>\n",
|
||
" <th>1</th>\n",
|
||
" <th>2</th>\n",
|
||
" <th>3</th>\n",
|
||
" <th>4</th>\n",
|
||
" <th>5</th>\n",
|
||
" <th>6</th>\n",
|
||
" <th>7</th>\n",
|
||
" <th>8</th>\n",
|
||
" <th>9</th>\n",
|
||
" <th>...</th>\n",
|
||
" <th>1299</th>\n",
|
||
" <th>1300</th>\n",
|
||
" <th>1301</th>\n",
|
||
" <th>1302</th>\n",
|
||
" <th>1303</th>\n",
|
||
" <th>1304</th>\n",
|
||
" <th>1305</th>\n",
|
||
" <th>1306</th>\n",
|
||
" <th>1307</th>\n",
|
||
" <th>1308</th>\n",
|
||
" </tr>\n",
|
||
" </thead>\n",
|
||
" <tbody>\n",
|
||
" <tr>\n",
|
||
" <th>0.250</th>\n",
|
||
" <td>0.5</td>\n",
|
||
" <td>1.0</td>\n",
|
||
" <td>1.0</td>\n",
|
||
" <td>1.0</td>\n",
|
||
" <td>1.0</td>\n",
|
||
" <td>0.500</td>\n",
|
||
" <td>1.0</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>1.0000</td>\n",
|
||
" <td>0.0000</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>0.5000</td>\n",
|
||
" <td>1.0000</td>\n",
|
||
" <td>0.0000</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>0.5000</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>0.0000</td>\n",
|
||
" <td>0.0000</td>\n",
|
||
" <td>0.0000</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>0.375</th>\n",
|
||
" <td>0.5</td>\n",
|
||
" <td>1.0</td>\n",
|
||
" <td>1.0</td>\n",
|
||
" <td>1.5</td>\n",
|
||
" <td>1.0</td>\n",
|
||
" <td>0.500</td>\n",
|
||
" <td>1.0</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>1.0000</td>\n",
|
||
" <td>0.5000</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>0.5000</td>\n",
|
||
" <td>1.0000</td>\n",
|
||
" <td>1.5000</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>2.0000</td>\n",
|
||
" <td>0.5</td>\n",
|
||
" <td>1.5000</td>\n",
|
||
" <td>0.0000</td>\n",
|
||
" <td>0.0000</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>0.500</th>\n",
|
||
" <td>1.0</td>\n",
|
||
" <td>1.0</td>\n",
|
||
" <td>1.5</td>\n",
|
||
" <td>2.0</td>\n",
|
||
" <td>1.5</td>\n",
|
||
" <td>1.000</td>\n",
|
||
" <td>1.0</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>1.5000</td>\n",
|
||
" <td>1.0000</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>2.0000</td>\n",
|
||
" <td>2.0000</td>\n",
|
||
" <td>3.0000</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>0.0</td>\n",
|
||
" <td>3.0000</td>\n",
|
||
" <td>1.0</td>\n",
|
||
" <td>3.0000</td>\n",
|
||
" <td>1.5000</td>\n",
|
||
" <td>1.5000</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>0.625</th>\n",
|
||
" <td>15.0</td>\n",
|
||
" <td>1.5</td>\n",
|
||
" <td>2.0</td>\n",
|
||
" <td>16.0</td>\n",
|
||
" <td>13.5</td>\n",
|
||
" <td>13.775</td>\n",
|
||
" <td>32.0</td>\n",
|
||
" <td>0.5</td>\n",
|
||
" <td>26.7396</td>\n",
|
||
" <td>11.5000</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>8.7271</td>\n",
|
||
" <td>8.7271</td>\n",
|
||
" <td>5.1125</td>\n",
|
||
" <td>1.5</td>\n",
|
||
" <td>1.5</td>\n",
|
||
" <td>8.7271</td>\n",
|
||
" <td>2.0</td>\n",
|
||
" <td>5.1125</td>\n",
|
||
" <td>5.1125</td>\n",
|
||
" <td>5.4375</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>0.750</th>\n",
|
||
" <td>15.0</td>\n",
|
||
" <td>1.5</td>\n",
|
||
" <td>2.0</td>\n",
|
||
" <td>82.5</td>\n",
|
||
" <td>13.5</td>\n",
|
||
" <td>13.775</td>\n",
|
||
" <td>32.0</td>\n",
|
||
" <td>0.5</td>\n",
|
||
" <td>26.7396</td>\n",
|
||
" <td>35.7521</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>8.7271</td>\n",
|
||
" <td>8.7271</td>\n",
|
||
" <td>26.3625</td>\n",
|
||
" <td>3.0</td>\n",
|
||
" <td>3.0</td>\n",
|
||
" <td>14.4771</td>\n",
|
||
" <td>3.0</td>\n",
|
||
" <td>16.8625</td>\n",
|
||
" <td>5.1125</td>\n",
|
||
" <td>5.4375</td>\n",
|
||
" </tr>\n",
|
||
" </tbody>\n",
|
||
"</table>\n",
|
||
"<p>5 rows × 1309 columns</p>\n",
|
||
"</div>"
|
||
],
|
||
"text/plain": [
|
||
" 0 1 2 3 4 5 6 7 8 9 \\\n",
|
||
"0.250 0.5 1.0 1.0 1.0 1.0 0.500 1.0 0.0 1.0000 0.0000 \n",
|
||
"0.375 0.5 1.0 1.0 1.5 1.0 0.500 1.0 0.0 1.0000 0.5000 \n",
|
||
"0.500 1.0 1.0 1.5 2.0 1.5 1.000 1.0 0.0 1.5000 1.0000 \n",
|
||
"0.625 15.0 1.5 2.0 16.0 13.5 13.775 32.0 0.5 26.7396 11.5000 \n",
|
||
"0.750 15.0 1.5 2.0 82.5 13.5 13.775 32.0 0.5 26.7396 35.7521 \n",
|
||
"\n",
|
||
" ... 1299 1300 1301 1302 1303 1304 1305 1306 \\\n",
|
||
"0.250 ... 0.5000 1.0000 0.0000 0.0 0.0 0.5000 0.0 0.0000 \n",
|
||
"0.375 ... 0.5000 1.0000 1.5000 0.0 0.0 2.0000 0.5 1.5000 \n",
|
||
"0.500 ... 2.0000 2.0000 3.0000 0.0 0.0 3.0000 1.0 3.0000 \n",
|
||
"0.625 ... 8.7271 8.7271 5.1125 1.5 1.5 8.7271 2.0 5.1125 \n",
|
||
"0.750 ... 8.7271 8.7271 26.3625 3.0 3.0 14.4771 3.0 16.8625 \n",
|
||
"\n",
|
||
" 1307 1308 \n",
|
||
"0.250 0.0000 0.0000 \n",
|
||
"0.375 0.0000 0.0000 \n",
|
||
"0.500 1.5000 1.5000 \n",
|
||
"0.625 5.1125 5.4375 \n",
|
||
"0.750 5.1125 5.4375 \n",
|
||
"\n",
|
||
"[5 rows x 1309 columns]"
|
||
]
|
||
},
|
||
"execution_count": 27,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"row_quantiles"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": []
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "Python 3",
|
||
"language": "python",
|
||
"name": "python3"
|
||
},
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.9.20"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 2
|
||
}
|