1753 lines
257 KiB
Plaintext
1753 lines
257 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<div style=\"\n",
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" border: 2px solid #4CAF50; \n",
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" padding: 15px; \n",
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" background-color: #f4f4f4; \n",
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" border-radius: 10px; \n",
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" align-items: center;\">\n",
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"\n",
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"<h1 style=\"margin: 0; color: #4CAF50;\">Statistik im Data Science Bereich 2 (Streumaße)</h1>\n",
|
||
"<h2 style=\"margin: 5px 0; color: #555;\">DSAI</h2>\n",
|
||
"<h3 style=\"margin: 5px 0; color: #555;\">Jakob Eggl</h3>\n",
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||
"\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",
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"</div>\n",
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"<p1> © 2024/25 Jakob Eggl. Nutzung oder Verbreitung nur mit ausdrücklicher Genehmigung des Autors.</p1>\n",
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"</div>\n",
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"<div style=\"flex: 1;\">\n",
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"</div> "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Wir kommen nun zu den Streuungsmaßen. Sie geben uns Einsicht in die Verteilung der Daten."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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||
"source": [
|
||
"import pandas as pd\n",
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"import os\n",
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||
"\n",
|
||
"path = os.path.join(\"..\", \"..\", \"_data\", \"titanic.csv\")"
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]
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},
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{
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"cell_type": "code",
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||
"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"df = pd.read_csv(path, decimal=\".\", sep=\",\", header=0, index_col=False)"
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]
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},
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{
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"cell_type": "code",
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"metadata": {},
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"outputs": [
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{
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"<style scoped>\n",
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||
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||
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||
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||
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" <td>C22 C26</td>\n",
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" <td>NaN</td>\n",
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" </tr>\n",
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" <th>...</th>\n",
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" <td>NaN</td>\n",
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" <th>1305</th>\n",
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" <td>3</td>\n",
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" <th>1306</th>\n",
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" <td>3</td>\n",
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|
||
" <td>Zakarian, Mr. Mapriededer</td>\n",
|
||
" <td>male</td>\n",
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||
" <td>26.5000</td>\n",
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||
" <td>0</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>2656</td>\n",
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||
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|
||
" <td>NaN</td>\n",
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||
" <td>C</td>\n",
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" <td>NaN</td>\n",
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" <td>304.0</td>\n",
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||
" <td>NaN</td>\n",
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||
" </tr>\n",
|
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|
||
" <th>1307</th>\n",
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||
" <td>3</td>\n",
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||
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||
" <td>Zakarian, Mr. Ortin</td>\n",
|
||
" <td>male</td>\n",
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||
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||
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||
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||
" <td>NaN</td>\n",
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" <th>1308</th>\n",
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||
" <td>3</td>\n",
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||
" <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",
|
||
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|
||
" <td>NaN</td>\n",
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" </tr>\n",
|
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" </tbody>\n",
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"</table>\n",
|
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"<p>1309 rows × 14 columns</p>\n",
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"</div>"
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],
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"text/plain": [
|
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" 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",
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"2 female 2.0000 1 2 113781 151.5500 C22 C26 S NaN \n",
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||
"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",
|
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"1305 female NaN 1 0 2665 14.4542 NaN C NaN \n",
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"1306 male 26.5000 0 0 2656 7.2250 NaN C NaN \n",
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"1307 male 27.0000 0 0 2670 7.2250 NaN C NaN \n",
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"1308 male 29.0000 0 0 315082 7.8750 NaN S NaN \n",
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"\n",
|
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" body home.dest \n",
|
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"0 NaN St Louis, MO \n",
|
||
"1 NaN Montreal, PQ / Chesterville, ON \n",
|
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"2 NaN Montreal, PQ / Chesterville, ON \n",
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"3 135.0 Montreal, PQ / Chesterville, ON \n",
|
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"4 NaN Montreal, PQ / Chesterville, ON \n",
|
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"... ... ... \n",
|
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"1304 328.0 NaN \n",
|
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"1305 NaN NaN \n",
|
||
"1306 304.0 NaN \n",
|
||
"1307 NaN NaN \n",
|
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"1308 NaN NaN \n",
|
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"\n",
|
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"[1309 rows x 14 columns]"
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]
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"execution_count": 3,
|
||
"metadata": {},
|
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"output_type": "execute_result"
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}
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],
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"source": [
|
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"df"
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||
]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
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"## Spannweite"
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]
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},
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{
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"cell_type": "markdown",
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||
"metadata": {},
|
||
"source": [
|
||
"Die Spannweite (auch \"Range\" genannt) ist ein einfaches, aber nützliches Maß der Streuung in der Statistik, das die Differenz zwischen dem größten und dem kleinsten Wert in einer Datenmenge angibt. Sie bietet einen groben Überblick über die Variabilität der Daten, indem sie die extreme Ausbreitung der Werte darstellt.\n",
|
||
"Definition der Spannweite\n",
|
||
"\n",
|
||
"Die Spannweite berechnet sich durch die folgende Formel:\n",
|
||
"\n",
|
||
"Spannweite=Maximalwert−Minimalwert\n",
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"\n",
|
||
"Die Spannweite gibt also an, wie weit die Daten auseinanderliegen, jedoch ohne dabei die Streuung oder Verteilung der Werte zwischen diesen Extrempunkten zu berücksichtigen.\n",
|
||
"\n",
|
||
"Eigenschaften der Spannweite:\n",
|
||
"* Empfindlich gegenüber Ausreißern: Da die Spannweite nur die Extremwerte betrachtet, kann sie stark von Ausreißern beeinflusst werden.\n",
|
||
"* Einfache Berechnung: Die Spannweite ist leicht zu berechnen und schnell verständlich.\n",
|
||
"* Begrenzte Aussagekraft: Die Spannweite allein bietet keinen detaillierten Einblick in die Verteilung der Daten, da sie keine Informationen über die Verteilung innerhalb der Werte liefert (im Gegensatz zu anderen Maßzahlen wie dem Interquartilsabstand).\n",
|
||
"\n",
|
||
"#### Beispiel 1\n",
|
||
"\n",
|
||
"Nehmen wir an, wir haben die folgenden Daten:\n",
|
||
"$$2, 4, 6, 8, 10, 12, 14, 16, 18, 20.$$\n",
|
||
"Dann ist:\n",
|
||
"* Maximalwert: 20\n",
|
||
"* Minimalwert: 2\n",
|
||
"\n",
|
||
"Die Spannweite beträgt somit:\n",
|
||
"Spannweite=20−2=18\n",
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||
"\n",
|
||
"Das bedeutet, dass die Werte in dieser Datenreihe sich über eine Spannweite von 18 erstrecken.\n",
|
||
"\n",
|
||
"#### Beispiel 2\n",
|
||
"\n",
|
||
"Wenn wir derselben Datenreihe einen Ausreißer hinzufügen, z.B. 100:\n",
|
||
"\n",
|
||
"$$2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 100.$$\n",
|
||
"Dann haben wir:\n",
|
||
"* Maximalwert: 100\n",
|
||
"* Minimalwert: 2\n",
|
||
"\n",
|
||
"Nun beträgt die Spannweite:\n",
|
||
"* Spannweite=100−2=98\n",
|
||
"\n",
|
||
"In Kombination des realtiv niedrigen Mittelwertes ($\\bar{x}=19.091$) kann man hier somit vermuten, dass ein Ausreißer dabei ist.\n",
|
||
"\n",
|
||
"Im Vergleich: Bei Beispiel 1 ist der Mittelwert $\\bar{x}=11.0$, was in etwa die halbe Spannweite wiederspiegelt. Also sind die Daten kompakter, als in Beispiel 2."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Die Anwendung in pandas ist sehr einfach und intuitiv\n",
|
||
"\n",
|
||
"range_of_df = df.max(numeric_only=True, skipna=True) - df.min(numeric_only=True, skipna=True)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"pclass 2.0000\n",
|
||
"survived 1.0000\n",
|
||
"age 79.8333\n",
|
||
"sibsp 8.0000\n",
|
||
"parch 9.0000\n",
|
||
"fare 512.3292\n",
|
||
"body 327.0000\n",
|
||
"dtype: float64"
|
||
]
|
||
},
|
||
"execution_count": 5,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"range_of_df"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"---"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Interquartilsabstand"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Der Interquartilsabstand (IQR), der die Differenz zwischen dem dritten und ersten Quartil darstellt, ist ein Maß für die Streuung der mittleren 50% der Daten."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Der Interquartilsabstand (IQR) ist ein wichtiges Maß für die Streuung einer Datenmenge in der Statistik. Im Gegensatz zur Spannweite, die die gesamte Verteilung betrachtet, fokussiert der IQR nur auf die mittleren 50 % der Daten, was ihn robuster gegenüber Ausreißern macht. Er gibt den Bereich an, in dem sich der Großteil der Daten ohne Extremwerte befindet.\n",
|
||
"Definition des Interquartilsabstands (IQR)\n",
|
||
"\n",
|
||
"Der IQR ist die Differenz zwischen dem dritten Quartil (Q3) und dem ersten Quartil (Q1):\n",
|
||
"* IQR=Q3−Q1\n",
|
||
"\n",
|
||
"Der Interquartilsabstand umfasst also die mittleren 50 % der Daten. Datenpunkte außerhalb dieses Bereichs können als potenzielle Ausreißer betrachtet werden.\n",
|
||
"\n",
|
||
"Eigenschaften des IQR:\n",
|
||
"* Robustheit gegenüber Ausreißern: Da der IQR nur die mittleren 50 % der Daten betrachtet, ist er unempfindlich gegenüber extrem hohen oder niedrigen Werten, die bei der Spannweite das Ergebnis stark beeinflussen könnten.\n",
|
||
"* Nützlich für die Identifikation von Ausreißern: Datenpunkte, die außerhalb des Bereichs Q1−1.5×IQR und Q3+1.5×IQR liegen, werden oft als Ausreißer identifiziert (siehe später Boxplot).\n",
|
||
"\n",
|
||
"#### Beispiel 1\n",
|
||
"\n",
|
||
"Betrachten wir die folgende Datenreihe:\n",
|
||
"$$12, 13, 1, 3, 10, 4, 7, 8, 9, 18, 14, 15.$$\n",
|
||
"\n",
|
||
"Berechnung der Quartile liefert:\n",
|
||
"* Q1 (erstes Quartil): 5.5 (25 % der Daten sind kleiner oder gleich 5.5)\n",
|
||
"* Q3 (drittes Quartil): 13.5 (75 % der Daten sind kleiner oder gleich 13.5)\n",
|
||
"\n",
|
||
"Der Interquartilsabstand (IQR) beträgt:\n",
|
||
"IQR=13.5−5.5=8\n",
|
||
"\n",
|
||
"Das bedeutet, dass sich die mittleren 50 % der Daten zwischen 5.5 und 13.5 befinden. Werte außerhalb dieses Bereichs könnten Ausreißer sein.\n",
|
||
"Beispiel mit Ausreißern:\n",
|
||
"\n",
|
||
"Wenn wir dieser Datenreihe einen Ausreißer hinzufügen, z.B. 30:\n",
|
||
"$$12, 13, 1, 3, 10, 4, 7, 8, 9, 18, 14, 15, 30.$$\n",
|
||
"* Q1 ändert sich zu 5.5 und Q3 bei 14.5, IQR=14.5-5.5=9.\n",
|
||
"* IQR ändert sich nur wenig, obwohl der Ausreißer hinzugefügt wurde. Dies zeigt, dass der IQR robust gegenüber Ausreißern ist."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Der IQR kann wie folgt berechnet werden\n",
|
||
"\n",
|
||
"Q1 = df.quantile(0.25, axis=0, numeric_only=True, interpolation='midpoint')\n",
|
||
"Q3 = df.quantile(0.75, axis=0, numeric_only=True, interpolation='midpoint')\n",
|
||
"\n",
|
||
"IQR = Q3 - Q1"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"---"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Varianz und Standardabweichung"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Die Standardabweichung und die Varianz sind zwei der wichtigsten Maßzahlen in der Statistik, die die Streuung oder Variabilität von Daten um ihren Mittelwert beschreiben. Beide Maßzahlen werden häufig verwendet, um zu verstehen, wie weit die einzelnen Datenpunkte von ihrem Durchschnitt entfernt sind.\n"
|
||
]
|
||
},
|
||
{
|
||
"attachments": {
|
||
"mlr-nonconstvar-1.png": {
|
||
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"
|
||
}
|
||
},
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"\n",
|
||
"(from https://www.bookdown.org/rwnahhas/RMPH/RMPH_files/figure-html/mlr-nonconstvar-1.png)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"#### Definition der Varianz\n",
|
||
"\n",
|
||
"Die Varianz misst die durchschnittliche quadratische Abweichung der Datenpunkte vom Mittelwert. Sie wird mit der folgenden Formel berechnet:\n",
|
||
"$$\\text{Var}(X)=\\frac{\\sum_{i=1}^{n}(x_i-\\bar{x})^2}{n}$$\n",
|
||
"Dabei ist:\n",
|
||
"* $X$: Das Dataset, i.e. $X=(x_1, x_2, \\ldots, x_n)$\n",
|
||
"* $n$: Anzahl der Datenpunkte\n",
|
||
"* $x_i$: Die einzelnen Datenpunkte\n",
|
||
"* $\\bar{x}$: Der Mittelwert\n",
|
||
"\n",
|
||
"Die Varianz gibt an, wie stark die Werte in einer Datenmenge um den Mittelwert schwanken. Ein kleiner Wert bedeutet, dass die Datenpunkte nahe beieinander und um den Mittelwert konzentriert sind. Ein großer Wert zeigt, dass die Daten über einen größeren Bereich verteilt sind.\n",
|
||
"\n",
|
||
"Bemerkung: Die obige Formel gilt nur, wenn die Daten die Grundgesamtheit respräsentieren. Ansonsten (für Stichproben) wird die Formel\n",
|
||
"$$\n",
|
||
"\\text{Var}(X)=\\frac{\\sum_{i=1}^{n}(x_i-\\bar{x})^2}{n-1}\n",
|
||
"$$\n",
|
||
"verwendet.\n",
|
||
"**Wichtig:** Wir verwenden (außer anders spezifiziert) für die folgenden Beispiele immer die Formel für die Grundgesamtheit.\n",
|
||
"\n",
|
||
"##### Steinerscher Verschiebungssatz\n",
|
||
"Es gibt auch eine Vereinfachung für die Varianzformel. Dafür sei $\\mu=1/n \\sum_{i=1}^{n} x_i$.\n",
|
||
"\\begin{align*}\n",
|
||
"\t\\text{Var}(X) &= \\frac{1}{n} \\sum_{i=1}^{n}(x_i-\\mu)^2\\\\\n",
|
||
"\t&= \\frac{1}{n}\\sum_{i=1}^{n}\\left( x_i^2 - 2 x_i \\mu + \\mu^2\\right)\\\\\n",
|
||
"\t&= \\frac{1}{n}\\sum_{i=1}^{n} x_i^2 - \n",
|
||
"\t2\\mu\\underbrace{\\frac{1}{n}\\sum_{i=1}^{n}x_i}_{\\mu} + \n",
|
||
"\t\\underbrace{\\frac{1}{n}\\sum_{i=1}^{n}\\mu^2}_{\\mu^2}\\\\\n",
|
||
"\t&= \\frac{1}{n}\\sum_{i=1}^{n}x_i^2 - \\mu^2\\\\\n",
|
||
"\t&= -\\mu^2 + \\frac{1}{n} \\sum_{i=1}^{n}x_i^2.\n",
|
||
"\\end{align*}\n",
|
||
"\n",
|
||
"#### Definition der Standardabweichung\n",
|
||
"\n",
|
||
"Die Standardabweichung ist die Quadratwurzel aus der Varianz und gibt die durchschnittliche Abweichung der Datenpunkte vom Mittelwert an. Sie wird mit der folgenden Formel berechnet:\n",
|
||
"\n",
|
||
"$$\\sigma(X)=\\sqrt[2]{\\text{Var}(X)} = \\sqrt[2]{\\frac{\\sum_{i=1}^{n}(x_i-\\bar{x})^2}{n}}$$\n",
|
||
"\n",
|
||
"Die **Standardabweichung** wird häufig verwendet, da sie in **derselben Einheit** wie die Originaldaten ausgedrückt wird, während die **Varianz** in **quadrierten Einheiten** vorliegt. Dadurch ist die Standardabweichung leichter interpretierbar.\n",
|
||
"\n",
|
||
"#### Eigenschaften von Varianz und Standardabweichung\n",
|
||
"Empfindlichkeit gegenüber Ausreißern: Beide Maßzahlen sind empfindlich gegenüber Ausreißern, da sie auf den quadratischen Abweichungen basieren, wodurch große Abweichungen stärker gewichtet werden.\n",
|
||
"\n",
|
||
"#### Beispiel 1\n",
|
||
"\n",
|
||
"Betrachten wir eine Datenreihe:\n",
|
||
"$$2, 4, 4, 4, 5, 5, 7, 9.$$\n",
|
||
"\n",
|
||
"Um die Varianz bzw. die Standardabweichung zu bestimmen berechnen wir zuerst den Mittelwert:\n",
|
||
"$$\\bar{x} = \\frac{1}{n}\\sum_{i=1}^{n}x_i = \\frac{2+4+4+4+5+5+7+9}{8} = \\frac{40}{8} = 5.$$\n",
|
||
"\n",
|
||
"Nun berechnen wir die Varianz:\n",
|
||
"\n",
|
||
"$$\\text{Var}(X) = \\frac{1}{n}\\sum_{i=1}^{n}(x_i-\\bar{x})^2 = \\frac{1}{8}\\left((2-5)^2+(4-5)^2+(4-5)^2+(4-5)^2+(5-5)^2+(5-5)^2+(7-5)^2+(9-5)^2\\right) = \\frac{1}{8}\\left(9+1+1+1+0+0+4+16\\right)=4\\, \\text{EH}^2$$\n",
|
||
"\n",
|
||
"Die dazugehörige Standardabweichung ist dann die Wurzel, i.e.\n",
|
||
"$$\\sigma(X)=\\sqrt{4} = 2\\,\\text{EH}.$$\n",
|
||
"\n",
|
||
"In diesem Beispiel beträgt die Varianz 4, was bedeutet, dass die durchschnittliche quadratische Abweichung der Datenpunkte vom Mittelwert 4 beträgt. Die Standardabweichung von 2 gibt an, dass die Datenpunkte im Durchschnitt um 2 Einheiten vom Mittelwert abweichen.\n",
|
||
"\n",
|
||
"Wie würde die Rechnung mit dem Steinerschen Verschiebungssatz aussehen?\n",
|
||
"\n",
|
||
"Lösung?\n",
|
||
"\n",
|
||
"### Beispiel 2\n",
|
||
"\n",
|
||
"Berechne die Standardabweichung, für folgendes Dataset. Es repräsentiert das Ergebnis einer Umfrage, bei der die befragten Personen angaben, wie viele Urlaubstage sie dieses Jahr bereits verbraucht haben.\n",
|
||
"| Tage | Anzahl |\n",
|
||
"|------|--------|\n",
|
||
"| 21 | 5 |\n",
|
||
"| 14 | 10 |\n",
|
||
"| 25 | 40 |\n",
|
||
"| 31 | 49 |\n",
|
||
"| 35 | 30 |\n",
|
||
"| 21 | 16 |\n",
|
||
"| 29 | 50 |\n",
|
||
"\n",
|
||
"Lösung?\n",
|
||
"\n",
|
||
"#### Beispiel 3\n",
|
||
"\n",
|
||
"Betrachten wir die Datenreihe $X$ mit den Parametern $a,b\\in\\mathbb{R}$. Wir wissen, dass der Mittelwert $\\bar{x}=77.2$ ist und die Varianz $1183.16$ beträgt. Berechne die Werte $a$ und $b$.\n",
|
||
"$$X=(32, 111, 138, 28, 97, 89, 101, 51, a, b)$$\n",
|
||
"\n",
|
||
"Lösung (Verwendung von Computerprogramm erlaubt)?"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Nun berechnen wir die Varianz\n",
|
||
"\n",
|
||
"variance = df.var(numeric_only=True, skipna=True, axis=0) # Achtung, diese Funktion berechnet die Stichprobenvarianz, kann mit ddof geändert werden"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"pclass 0.701969\n",
|
||
"survived 0.236250\n",
|
||
"age 207.748974\n",
|
||
"sibsp 1.085052\n",
|
||
"parch 0.749195\n",
|
||
"fare 2678.959738\n",
|
||
"body 9544.688567\n",
|
||
"dtype: float64"
|
||
]
|
||
},
|
||
"execution_count": 8,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"variance"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Genauso kann die Standardabweichung berechnet werden\n",
|
||
"\n",
|
||
"std = df.std(numeric_only=True, skipna=True, axis=0)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 10,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"pclass 0.837836\n",
|
||
"survived 0.486055\n",
|
||
"age 14.413500\n",
|
||
"sibsp 1.041658\n",
|
||
"parch 0.865560\n",
|
||
"fare 51.758668\n",
|
||
"body 97.696922\n",
|
||
"dtype: float64"
|
||
]
|
||
},
|
||
"execution_count": 10,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"std"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"---"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Normalverteilung"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Nun beschäftigen wir uns noch mit der Normalverteilung. Sie ist ein essentielles Tool in der Statistik und modelliert sehr viele (zufällige) Sachverhalte. Einige Beispiele aus dem Alltag:\n",
|
||
"* Körpergröße\n",
|
||
"* Gewicht\n",
|
||
"* IQ-Werte\n",
|
||
"* Notenverteilung\n",
|
||
"* Laufzeit von Prozessen\n",
|
||
"\n",
|
||
"Außerdem ist sie auch in Gebrauch beim Normalisieren von Daten (siehe Normalisierung)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Die Normalverteilung, auch als **Gaußsche Verteilung** oder **Glockenkurve** bekannt, ist eine der wichtigsten Verteilungen in der Statistik. Sie beschreibt, wie sich die Werte einer Zufallsvariablen um einen Mittelwert herum verteilen, wobei die meisten Werte nahe am Mittelwert liegen und die Wahrscheinlichkeit für extremere Werte nach beiden Seiten abnimmt."
|
||
]
|
||
},
|
||
{
|
||
"attachments": {
|
||
"images.png": {
|
||
"image/png": 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"
|
||
}
|
||
},
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"\n",
|
||
"(from https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcQ1iWPhC9cNM1uGHf6YzjJzWonw0HR3EYKMMg&s)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"#### Eigenschaften der Normalverteilung\n",
|
||
"\n",
|
||
"Die Normalverteilung hat folgende Eigenschaften:\n",
|
||
"* Symmetrisch: Die Normalverteilung ist symmetrisch um den Mittelwert.\n",
|
||
"* Mittelwert, Median und Modus sind identisch.\n",
|
||
"* Glockenförmige Kurve: Die Verteilung hat die Form einer Glocke, wobei die Breite und Höhe der Glocke von der Standardabweichung abhängen. Je größer die Standardabweichung, desto steiler und schmaler die Kurve.\n",
|
||
"* Asymptotisch: Die Enden der Verteilung nähern sich der x-Achse an, berühren sie aber nie. \n",
|
||
"* $68-95-99.7$ Regel: Diese Regel beschreibt, dass:\n",
|
||
" * $68 \\%$ der Werte innerhalb einer Standardabweichung ($1 \\sigma$) vom Mittelwert liegen.\n",
|
||
" * $95 \\%$ der Werte innerhalb von zwei Standardabweichungen ($2 \\sigma$) liegen.\n",
|
||
" * $99.7 \\%$ der Werte innerhalb von drei Standardabweichungen ($3 \\sigma$) liegen.\n",
|
||
"\n",
|
||
"Definition der Funktion:\n",
|
||
"\n",
|
||
"$$p(x) = \\frac{1}{\\sqrt{2\\pi}\\sigma}\\exp\\left(-\\frac{(x-\\mu)^2}{2\\sigma^2}\\right)$$\n",
|
||
"\n",
|
||
"wobei:\n",
|
||
"* $\\mu$ ist der Mittelwert (Erwartungswert).\n",
|
||
"* $\\sigma$ ist die Standardabweichung.\n",
|
||
"\n",
|
||
"Eine spezielle Form der Normalverteilung ist die **Standardnormalverteilung**. Sie hat $\\mu=0$ und $\\sigma=1$.\n",
|
||
"\n",
|
||
"#### Beispiel:\n",
|
||
"\n",
|
||
"Angenommen, wir betrachten die Körpergröße einer Bevölkerung, die normalverteilt ist:\n",
|
||
"* Mittelwert $\\mu=175\\,\\textrm{cm}$\n",
|
||
"* Standardabweichung $\\sigma=10\\, \\textrm{cm}$\n",
|
||
"\n",
|
||
"Berechne mit Hilfe bekannten Prozentwerte die Körpergröße Intervalle für eine Abweichung von $\\pm 1, \\pm 2, \\pm 3$ Sigma.\n",
|
||
"\n",
|
||
"Nach der $68-95-99.7$-Regel:\n",
|
||
"* $68 \\%$ der Menschen haben eine Körpergröße zwischen 165 cm und 185 cm ($\\pm 1 \\sigma$)\n",
|
||
"* $95 \\%$ der Menschen haben eine Körpergröße zwischen 155 cm und 195 cm ($\\pm 2 \\sigma$).\n",
|
||
"* $99.7 \\%$ der Menschen haben eine Körpergröße zwischen 145 cm und 205 cm ($\\pm 3 \\sigma$).\n",
|
||
"\n",
|
||
"Diese Verteilung der Körpergrößen ist ein typisches Beispiel für eine Normalverteilung, bei der die meisten Menschen Größen nahe am Mittelwert haben, während sehr große oder sehr kleine Größen seltener vorkommen."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 11,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"from scipy.stats import norm\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import numpy as np"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 12,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Nun werden wir mit Normalverteilungen rechnen bzw. uns die Graphen ansehen\n",
|
||
"\n",
|
||
"# Verschiedene Werte können hier getestet werden, zBsp.: IQ-Verteilung: mu=100, sigma=15\n",
|
||
"mu = 0\n",
|
||
"sigma = 1\n",
|
||
"\n",
|
||
"z = np.linspace(-4, 4, 1000)\n",
|
||
"x = z * sigma + mu\n",
|
||
"\n",
|
||
"y = norm.pdf(x, mu, sigma)\n",
|
||
"\n",
|
||
"# Nun können wir uns die Verteilung ansehen\n",
|
||
"\n",
|
||
"plt.plot(x, y, label=f'Normalverteilung (μ={mu}, σ={sigma})')\n",
|
||
"plt.title('Normalverteilung')\n",
|
||
"plt.xlabel('x')\n",
|
||
"plt.ylabel('f(x)')\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 13,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1000x600 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Genauso können mehrere Normalverteilungen auf einem Graphen dargestellt werden\n",
|
||
"params = [\n",
|
||
" {'mu': 0, 'sigma': 0.5},\n",
|
||
" {'mu': 0, 'sigma': 1},\n",
|
||
" {'mu': 0, 'sigma': 1.5},\n",
|
||
" {'mu': 1, 'sigma': 1},\n",
|
||
" {'mu': -1, 'sigma': 1}\n",
|
||
"]\n",
|
||
"\n",
|
||
"z = np.linspace(-4,4, 1000)\n",
|
||
"\n",
|
||
"max_mu = max([param['mu'] for param in params])\n",
|
||
"max_sigma = max([param['sigma'] for param in params])\n",
|
||
"\n",
|
||
"x = z * max_sigma + max_mu\n",
|
||
"\n",
|
||
"# Erstellen des Plots\n",
|
||
"plt.figure(figsize=(10, 6))\n",
|
||
"\n",
|
||
"# Für jede Verteilung die PDF berechnen und plotten\n",
|
||
"for param in params:\n",
|
||
" mu = param['mu']\n",
|
||
" sigma = param['sigma']\n",
|
||
" y = norm.pdf(x, mu, sigma)\n",
|
||
" plt.plot(x, y, label=f'μ={mu}, σ={sigma}')\n",
|
||
"\n",
|
||
"plt.title('Vergleich von 5 verschiedenen Normalverteilungen')\n",
|
||
"plt.xlabel('x')\n",
|
||
"plt.ylabel('f(x)')\n",
|
||
"plt.legend()\n",
|
||
"\n",
|
||
"plt.grid(True)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Wiederholung:\n",
|
||
"\n",
|
||
"Was passiert bei der $z$-Normalisierung?"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"---"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Pandas Describe Methode"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Viele statistische Größen können auch berechnet werden, indem die Werte in den Dataframes aggregiert werden.\n",
|
||
"\n",
|
||
"Außerdem gibt es die Methode `describe()`, welche wichtige statistische Maße direkt liefert."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"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>count</th>\n",
|
||
" <td>1309.000000</td>\n",
|
||
" <td>1309.000000</td>\n",
|
||
" <td>1046.000000</td>\n",
|
||
" <td>1309.000000</td>\n",
|
||
" <td>1309.000000</td>\n",
|
||
" <td>1308.000000</td>\n",
|
||
" <td>121.000000</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>mean</th>\n",
|
||
" <td>2.294882</td>\n",
|
||
" <td>0.381971</td>\n",
|
||
" <td>29.881135</td>\n",
|
||
" <td>0.498854</td>\n",
|
||
" <td>0.385027</td>\n",
|
||
" <td>33.295479</td>\n",
|
||
" <td>160.809917</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>std</th>\n",
|
||
" <td>0.837836</td>\n",
|
||
" <td>0.486055</td>\n",
|
||
" <td>14.413500</td>\n",
|
||
" <td>1.041658</td>\n",
|
||
" <td>0.865560</td>\n",
|
||
" <td>51.758668</td>\n",
|
||
" <td>97.696922</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>min</th>\n",
|
||
" <td>1.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>0.166700</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>1.000000</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>25%</th>\n",
|
||
" <td>2.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>21.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>7.895800</td>\n",
|
||
" <td>72.000000</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>50%</th>\n",
|
||
" <td>3.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>28.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>14.454200</td>\n",
|
||
" <td>155.000000</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>75%</th>\n",
|
||
" <td>3.000000</td>\n",
|
||
" <td>1.000000</td>\n",
|
||
" <td>39.000000</td>\n",
|
||
" <td>1.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>31.275000</td>\n",
|
||
" <td>256.000000</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>max</th>\n",
|
||
" <td>3.000000</td>\n",
|
||
" <td>1.000000</td>\n",
|
||
" <td>80.000000</td>\n",
|
||
" <td>8.000000</td>\n",
|
||
" <td>9.000000</td>\n",
|
||
" <td>512.329200</td>\n",
|
||
" <td>328.000000</td>\n",
|
||
" </tr>\n",
|
||
" </tbody>\n",
|
||
"</table>\n",
|
||
"</div>"
|
||
],
|
||
"text/plain": [
|
||
" pclass survived age sibsp parch \\\n",
|
||
"count 1309.000000 1309.000000 1046.000000 1309.000000 1309.000000 \n",
|
||
"mean 2.294882 0.381971 29.881135 0.498854 0.385027 \n",
|
||
"std 0.837836 0.486055 14.413500 1.041658 0.865560 \n",
|
||
"min 1.000000 0.000000 0.166700 0.000000 0.000000 \n",
|
||
"25% 2.000000 0.000000 21.000000 0.000000 0.000000 \n",
|
||
"50% 3.000000 0.000000 28.000000 0.000000 0.000000 \n",
|
||
"75% 3.000000 1.000000 39.000000 1.000000 0.000000 \n",
|
||
"max 3.000000 1.000000 80.000000 8.000000 9.000000 \n",
|
||
"\n",
|
||
" fare body \n",
|
||
"count 1308.000000 121.000000 \n",
|
||
"mean 33.295479 160.809917 \n",
|
||
"std 51.758668 97.696922 \n",
|
||
"min 0.000000 1.000000 \n",
|
||
"25% 7.895800 72.000000 \n",
|
||
"50% 14.454200 155.000000 \n",
|
||
"75% 31.275000 256.000000 \n",
|
||
"max 512.329200 328.000000 "
|
||
]
|
||
},
|
||
"execution_count": 14,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Deskriptive Statistiken für alle (numerischen) Spalten\n",
|
||
"df.describe()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 15,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/html": [
|
||
"<div>\n",
|
||
"<style scoped>\n",
|
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|
||
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|
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|
||
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|
||
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|
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
" <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>count</th>\n",
|
||
" <td>1309.000000</td>\n",
|
||
" <td>1309.000000</td>\n",
|
||
" <td>1309</td>\n",
|
||
" <td>1309</td>\n",
|
||
" <td>1046.000000</td>\n",
|
||
" <td>1309.000000</td>\n",
|
||
" <td>1309.000000</td>\n",
|
||
" <td>1309</td>\n",
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
" <td>745</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>unique</th>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>1307</td>\n",
|
||
" <td>2</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>929</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>186</td>\n",
|
||
" <td>3</td>\n",
|
||
" <td>27</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>369</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>top</th>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>Kelly, Mr. James</td>\n",
|
||
" <td>male</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>CA. 2343</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>C23 C25 C27</td>\n",
|
||
" <td>S</td>\n",
|
||
" <td>13</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>New York, NY</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>freq</th>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>2</td>\n",
|
||
" <td>843</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>11</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>6</td>\n",
|
||
" <td>914</td>\n",
|
||
" <td>39</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>64</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>mean</th>\n",
|
||
" <td>2.294882</td>\n",
|
||
" <td>0.381971</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>29.881135</td>\n",
|
||
" <td>0.498854</td>\n",
|
||
" <td>0.385027</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>33.295479</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>160.809917</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>std</th>\n",
|
||
" <td>0.837836</td>\n",
|
||
" <td>0.486055</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>14.413500</td>\n",
|
||
" <td>1.041658</td>\n",
|
||
" <td>0.865560</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>51.758668</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>97.696922</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>min</th>\n",
|
||
" <td>1.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>0.166700</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>1.000000</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>25%</th>\n",
|
||
" <td>2.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>21.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>7.895800</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>72.000000</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>50%</th>\n",
|
||
" <td>3.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>28.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>14.454200</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>155.000000</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>75%</th>\n",
|
||
" <td>3.000000</td>\n",
|
||
" <td>1.000000</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>39.000000</td>\n",
|
||
" <td>1.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>31.275000</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>256.000000</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>max</th>\n",
|
||
" <td>3.000000</td>\n",
|
||
" <td>1.000000</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>80.000000</td>\n",
|
||
" <td>8.000000</td>\n",
|
||
" <td>9.000000</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>512.329200</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>328.000000</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" </tr>\n",
|
||
" </tbody>\n",
|
||
"</table>\n",
|
||
"</div>"
|
||
],
|
||
"text/plain": [
|
||
" pclass survived name sex age \\\n",
|
||
"count 1309.000000 1309.000000 1309 1309 1046.000000 \n",
|
||
"unique NaN NaN 1307 2 NaN \n",
|
||
"top NaN NaN Kelly, Mr. James male NaN \n",
|
||
"freq NaN NaN 2 843 NaN \n",
|
||
"mean 2.294882 0.381971 NaN NaN 29.881135 \n",
|
||
"std 0.837836 0.486055 NaN NaN 14.413500 \n",
|
||
"min 1.000000 0.000000 NaN NaN 0.166700 \n",
|
||
"25% 2.000000 0.000000 NaN NaN 21.000000 \n",
|
||
"50% 3.000000 0.000000 NaN NaN 28.000000 \n",
|
||
"75% 3.000000 1.000000 NaN NaN 39.000000 \n",
|
||
"max 3.000000 1.000000 NaN NaN 80.000000 \n",
|
||
"\n",
|
||
" sibsp parch ticket fare cabin embarked \\\n",
|
||
"count 1309.000000 1309.000000 1309 1308.000000 295 1307 \n",
|
||
"unique NaN NaN 929 NaN 186 3 \n",
|
||
"top NaN NaN CA. 2343 NaN C23 C25 C27 S \n",
|
||
"freq NaN NaN 11 NaN 6 914 \n",
|
||
"mean 0.498854 0.385027 NaN 33.295479 NaN NaN \n",
|
||
"std 1.041658 0.865560 NaN 51.758668 NaN NaN \n",
|
||
"min 0.000000 0.000000 NaN 0.000000 NaN NaN \n",
|
||
"25% 0.000000 0.000000 NaN 7.895800 NaN NaN \n",
|
||
"50% 0.000000 0.000000 NaN 14.454200 NaN NaN \n",
|
||
"75% 1.000000 0.000000 NaN 31.275000 NaN NaN \n",
|
||
"max 8.000000 9.000000 NaN 512.329200 NaN NaN \n",
|
||
"\n",
|
||
" boat body home.dest \n",
|
||
"count 486 121.000000 745 \n",
|
||
"unique 27 NaN 369 \n",
|
||
"top 13 NaN New York, NY \n",
|
||
"freq 39 NaN 64 \n",
|
||
"mean NaN 160.809917 NaN \n",
|
||
"std NaN 97.696922 NaN \n",
|
||
"min NaN 1.000000 NaN \n",
|
||
"25% NaN 72.000000 NaN \n",
|
||
"50% NaN 155.000000 NaN \n",
|
||
"75% NaN 256.000000 NaN \n",
|
||
"max NaN 328.000000 NaN "
|
||
]
|
||
},
|
||
"execution_count": 15,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Sollen alle Spalten verwendet werden (i.e. auch die nicht numerischen), so verwenden wir folgendes.\n",
|
||
"df.describe(include='all')"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 16,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Wir können natürlich auch die deskriptiven Statistiken mit der Aggregationsfunktion berechnen\n",
|
||
"summary_statistics = df.select_dtypes(include='number').agg(['mean', 'std', 'min', 'max', 'median'])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 17,
|
||
"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>mean</th>\n",
|
||
" <td>2.294882</td>\n",
|
||
" <td>0.381971</td>\n",
|
||
" <td>29.881135</td>\n",
|
||
" <td>0.498854</td>\n",
|
||
" <td>0.385027</td>\n",
|
||
" <td>33.295479</td>\n",
|
||
" <td>160.809917</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>std</th>\n",
|
||
" <td>0.837836</td>\n",
|
||
" <td>0.486055</td>\n",
|
||
" <td>14.413500</td>\n",
|
||
" <td>1.041658</td>\n",
|
||
" <td>0.865560</td>\n",
|
||
" <td>51.758668</td>\n",
|
||
" <td>97.696922</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>min</th>\n",
|
||
" <td>1.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>0.166700</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>1.000000</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>max</th>\n",
|
||
" <td>3.000000</td>\n",
|
||
" <td>1.000000</td>\n",
|
||
" <td>80.000000</td>\n",
|
||
" <td>8.000000</td>\n",
|
||
" <td>9.000000</td>\n",
|
||
" <td>512.329200</td>\n",
|
||
" <td>328.000000</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>median</th>\n",
|
||
" <td>3.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>28.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>0.000000</td>\n",
|
||
" <td>14.454200</td>\n",
|
||
" <td>155.000000</td>\n",
|
||
" </tr>\n",
|
||
" </tbody>\n",
|
||
"</table>\n",
|
||
"</div>"
|
||
],
|
||
"text/plain": [
|
||
" pclass survived age sibsp parch fare \\\n",
|
||
"mean 2.294882 0.381971 29.881135 0.498854 0.385027 33.295479 \n",
|
||
"std 0.837836 0.486055 14.413500 1.041658 0.865560 51.758668 \n",
|
||
"min 1.000000 0.000000 0.166700 0.000000 0.000000 0.000000 \n",
|
||
"max 3.000000 1.000000 80.000000 8.000000 9.000000 512.329200 \n",
|
||
"median 3.000000 0.000000 28.000000 0.000000 0.000000 14.454200 \n",
|
||
"\n",
|
||
" body \n",
|
||
"mean 160.809917 \n",
|
||
"std 97.696922 \n",
|
||
"min 1.000000 \n",
|
||
"max 328.000000 \n",
|
||
"median 155.000000 "
|
||
]
|
||
},
|
||
"execution_count": 17,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"summary_statistics"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 18,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Des weiteren können viele Statistiken auch mit dem stats Modul von scipy erstellt werden\n",
|
||
"\n",
|
||
"from scipy import stats\n",
|
||
"\n",
|
||
"# Berechnen der Summary Statistics für das Dataframe df mit scipy stats\n",
|
||
"summary_statistics_scipy = df.select_dtypes(include='number').apply(stats.describe, axis=0)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 19,
|
||
"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</th>\n",
|
||
" <td>1309</td>\n",
|
||
" <td>1309</td>\n",
|
||
" <td>1309</td>\n",
|
||
" <td>1309</td>\n",
|
||
" <td>1309</td>\n",
|
||
" <td>1309</td>\n",
|
||
" <td>1309</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>1</th>\n",
|
||
" <td>(1, 3)</td>\n",
|
||
" <td>(0, 1)</td>\n",
|
||
" <td>(nan, nan)</td>\n",
|
||
" <td>(0, 8)</td>\n",
|
||
" <td>(0, 9)</td>\n",
|
||
" <td>(nan, nan)</td>\n",
|
||
" <td>(nan, nan)</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>2</th>\n",
|
||
" <td>2.294882</td>\n",
|
||
" <td>0.381971</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>0.498854</td>\n",
|
||
" <td>0.385027</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>3</th>\n",
|
||
" <td>0.701969</td>\n",
|
||
" <td>0.23625</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>1.085052</td>\n",
|
||
" <td>0.749195</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>4</th>\n",
|
||
" <td>-0.597961</td>\n",
|
||
" <td>0.485847</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>3.839814</td>\n",
|
||
" <td>3.664872</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>5</th>\n",
|
||
" <td>-1.314641</td>\n",
|
||
" <td>-1.763953</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>19.962194</td>\n",
|
||
" <td>21.454306</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" <td>NaN</td>\n",
|
||
" </tr>\n",
|
||
" </tbody>\n",
|
||
"</table>\n",
|
||
"</div>"
|
||
],
|
||
"text/plain": [
|
||
" pclass survived age sibsp parch fare \\\n",
|
||
"0 1309 1309 1309 1309 1309 1309 \n",
|
||
"1 (1, 3) (0, 1) (nan, nan) (0, 8) (0, 9) (nan, nan) \n",
|
||
"2 2.294882 0.381971 NaN 0.498854 0.385027 NaN \n",
|
||
"3 0.701969 0.23625 NaN 1.085052 0.749195 NaN \n",
|
||
"4 -0.597961 0.485847 NaN 3.839814 3.664872 NaN \n",
|
||
"5 -1.314641 -1.763953 NaN 19.962194 21.454306 NaN \n",
|
||
"\n",
|
||
" body \n",
|
||
"0 1309 \n",
|
||
"1 (nan, nan) \n",
|
||
"2 NaN \n",
|
||
"3 NaN \n",
|
||
"4 NaN \n",
|
||
"5 NaN "
|
||
]
|
||
},
|
||
"execution_count": 19,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"summary_statistics_scipy"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Wir sehen, dass hier der Output etwas anders ist. Die genaue Output Beschreibung findet man in der Dokumentation."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"---"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Anscombe's Quartett"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Ist Statistik wirklich ausreichend, um die Daten gut zu beschreiben?\n",
|
||
"\n",
|
||
"**Nein**"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 20,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 600x600 with 4 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# from https://matplotlib.org/stable/gallery/specialty_plots/anscombe.html\n",
|
||
"\n",
|
||
"x = [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5]\n",
|
||
"y1 = [8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68]\n",
|
||
"y2 = [9.14, 8.14, 8.74, 8.77, 9.26, 8.10, 6.13, 3.10, 9.13, 7.26, 4.74]\n",
|
||
"y3 = [7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73]\n",
|
||
"x4 = [8, 8, 8, 8, 8, 8, 8, 19, 8, 8, 8]\n",
|
||
"y4 = [6.58, 5.76, 7.71, 8.84, 8.47, 7.04, 5.25, 12.50, 5.56, 7.91, 6.89]\n",
|
||
"\n",
|
||
"datasets = {\n",
|
||
" 'I': (x, y1),\n",
|
||
" 'II': (x, y2),\n",
|
||
" 'III': (x, y3),\n",
|
||
" 'IV': (x4, y4)\n",
|
||
"}\n",
|
||
"\n",
|
||
"fig, axs = plt.subplots(2, 2, sharex=True, sharey=True, figsize=(6, 6),\n",
|
||
" gridspec_kw={'wspace': 0.08, 'hspace': 0.08})\n",
|
||
"axs[0, 0].set(xlim=(0, 20), ylim=(2, 14))\n",
|
||
"axs[0, 0].set(xticks=(0, 10, 20), yticks=(4, 8, 12))\n",
|
||
"\n",
|
||
"for ax, (label, (x, y)) in zip(axs.flat, datasets.items()):\n",
|
||
" ax.text(0.1, 0.9, label, fontsize=20, transform=ax.transAxes, va='top')\n",
|
||
" ax.tick_params(direction='in', top=True, right=True)\n",
|
||
" ax.plot(x, y, 'o')\n",
|
||
"\n",
|
||
" # linear regression\n",
|
||
" p1, p0 = np.polyfit(x, y, deg=1) # slope, intercept\n",
|
||
" ax.axline(xy1=(0, p0), slope=p1, color='r', lw=2)\n",
|
||
"\n",
|
||
" # add text box for the statistics\n",
|
||
" stats = (f'$\\\\mu$ = {np.mean(y):.2f}\\n'\n",
|
||
" f'$\\\\sigma$ = {np.std(y):.2f}\\n')\n",
|
||
" # f'$r$ = {np.corrcoef(x, y)[0][1]:.2f}')\n",
|
||
" bbox = dict(boxstyle='round', fc='blanchedalmond', ec='orange', alpha=0.5)\n",
|
||
" ax.text(0.95, 0.07, stats, fontsize=9, bbox=bbox,\n",
|
||
" transform=ax.transAxes, horizontalalignment='right')\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Wie wir sehen können, geben uns die Grafiken viel mehr Einblick in die gegebenen Daten, weswegen wir nun Visualisierungen besprechen werden."
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "dsai",
|
||
"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
|
||
}
|