{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "f8f12250", "metadata": { "tags": [ "remove-cell" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "---------------------------------\n", "Working on the host: Joachims-MacBook-Pro.local\n", "\n", "---------------------------------\n", "Python version: 3.10.2 | packaged by conda-forge | (main, Feb 1 2022, 19:30:18) [Clang 11.1.0 ]\n", "\n", "---------------------------------\n", "Python interpreter: /opt/miniconda3/envs/srh/bin/python\n" ] } ], "source": [ "%matplotlib inline\n", "# Load the \"autoreload\" extension\n", "%load_ext autoreload\n", "# always reload modules\n", "%autoreload 2\n", "# black formatter for jupyter notebooks\n", "#%load_ext nb_black\n", "# black formatter for jupyter lab\n", "%load_ext lab_black\n", "\n", "%run ../../src/notebook_env.py" ] }, { "cell_type": "markdown", "id": "68f732f8-3e48-48bd-ba95-a853f66d6db8", "metadata": {}, "source": [ "# Streuungsmaße" ] }, { "cell_type": "code", "execution_count": 2, "id": "9c742b43", "metadata": {}, "outputs": [], "source": [ "import random\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "from scipy.stats import norm, gaussian_kde" ] }, { "cell_type": "markdown", "id": "62b0d2d6-1dde-4e6c-998f-f21dab5bbca3", "metadata": { "tags": [] }, "source": [ "Die Maße der zentralen Tendenz, wie Mittelwert, Median und Modus, geben nicht das ganze Bild der Verteilung eines Datensatzes wieder. Zwei Datensätze mit demselben Mittelwert können völlig unterschiedliche Streuungen aufweisen. Die Streuung der Beobachtungswerte des einen Datensatzes kann viel größer oder kleiner sein als die des anderen Datensatzes. Daher ist der Mittelwert, Median oder Modus allein in der Regel kein ausreichendes Maß, um die Form der Verteilung eines Datensatzes aufzuzeigen. Wir benötigen auch ein Maß, das Informationen über die Variation zwischen den Datenwerten liefert. Diese Maße werden als **Streuungsmaße** bezeichnet. Die Maße der zentralen Tendenz und der Streuung ergeben zusammengenommen ein besseres Bild eines Datensatzes als die Maße der zentralen Tendenz allein ({cite:p}`fahrmeirstatistik` s.65)." ] }, { "cell_type": "markdown", "id": "a8f87905-2c47-4862-9db7-3769afd4f1d1", "metadata": { "tags": [] }, "source": [ "## Varianz und Standardabweichung" ] }, { "cell_type": "markdown", "id": "655228bc-bf5f-4a61-ae31-3933be467e7c", "metadata": { "tags": [] }, "source": [ "Die **Varianz** ist die Summe der quadrierten Abweichungen vom Mittelwert. Die Varianz für Populationsdaten wird mit $\\sigma^2$ bezeichnet (gelesen als Sigma-Quadrat), und die für Stichprobendaten berechnete Varianz wird mit $s^2$ bezeichnet. \n", "\n", "$$ \\sigma^2 = \\frac{\\sum_{i=1}^n (x_i - \\mu)^2}{N} $$\n", "\n", "und\n", "$$ s^2 = \\frac{\\sum_{i=1}^n (x_i - \\bar{x})^2}{n-1} $$\n", "\n", "wobei $\\sigma^2$ die Varianz der Grundgesamtheit und $s^2$ die Stichprobenvarianz ist. Die Größe $x_i-\\mu$ oder $x_i-\\bar{x}$ in den obigen Formeln wird als die Abweichung des $x_i$-Wertes $(x_1,x_2, \\dots ,x_n)$ vom Mittelwert bezeichnet ({cite:p}`fahrmeirstatistik` s.64). \n", "\n", "Die Standardabweichung ist das gebräuchlichste Maß für die Streuung. Der Wert der Standardabweichung gibt an, wie eng die Werte eines Datensatzes um den Mittelwert herum gestreut sind. Im Allgemeinen zeigt ein niedriger Wert der Standardabweichung für einen Datensatz an, dass die Werte dieses Datensatzes über einen relativ kleineren Bereich um den Mittelwert herum verteilt sind. Im Gegensatz dazu zeigt ein größerer Wert der Standardabweichung für einen Datensatz an, dass die Werte dieses Datensatzes über einen relativ größeren Bereich um den Mittelwert herum gestreut sind ({cite:p}`fahrmeirstatistik` s.65).\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "7be5ffaf", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "TITLESIZE = 17\n", "SEED = np.random.seed(42)\n", "SIZE = 100\n", "x = np.linspace(0, 1, SIZE)\n", "\n", "fig, ax = plt.subplots(ncols=2, figsize=(16, 6))\n", "\n", "y = np.random.normal(loc=0.5, scale=1.0, size=SIZE)\n", "ax[0].plot(x, y, \"o\")\n", "ax[0].set_title(\"Geringe Abweichungen um den Mittelwert\", size=TITLESIZE)\n", "\n", "y = np.random.normal(loc=0.5, scale=3.0, size=SIZE)\n", "ax[1].plot(x, y, \"o\")\n", "ax[1].set_title(\"Grosse Abweichungen um den Mittelwert\", size=TITLESIZE)\n", "\n", "for _ax in ax:\n", " _ax.set_xticks([])\n", " _ax.set_yticks([])\n", " _ax.axhline(0.5, color=\"k\")\n", " _ax.set_ylim(-6, 6)\n", " _ax.legend([\"Daten\", \"Mittelwert\"])" ] }, { "cell_type": "markdown", "id": "c2d5168f-537e-4cf4-abd7-6057ce3a58c3", "metadata": {}, "source": [ "Die Standardabweichung erhält man durch Ziehen der Quadratwurzel aus der **Varianz**. Folglich wird die für Grundgesamtheitsdaten berechnete Standardabweichung mit $\\sigma$ und die für Stichprobendaten berechnete Standardabweichung mit $s$ bezeichnet. \n", "\n", "$$ \\sigma = \\sqrt{\\frac{\\sum_{i=1}^n (x_i - \\mu)^2}{N}} $$\n", "\n", "und \n", "\n", "$$ s = \\sqrt{\\frac{\\sum_{i=1}^n (x_i - \\bar{x})^2}{n-1}} $$ \n", "\n", "wobei $\\sigma$ die Standardabweichung der Grundgesamtheit und $s$ die Standardabweichung der Stichprobe ist.\n", "\n", "Als Übung berechnen wir für einige numerische Variablen, die im `students` Datensatz von Interesse sind, den Mittelwert, den Median, die Varianz und die Standardabweichung und stellen sie in einem Dataframe dar." ] }, { "cell_type": "code", "execution_count": 4, "id": "1905437b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
ageheightweightnc.score
11916064.81.91
21917273.01.56
32216870.61.24
41918379.71.37
52117571.41.46
61918985.81.34
72115665.91.11
82116765.72.03
91819594.41.29
101816566.01.19
\n", "
" ], "text/plain": [ " age height weight nc.score\n", "1 19 160 64.8 1.91\n", "2 19 172 73.0 1.56\n", "3 22 168 70.6 1.24\n", "4 19 183 79.7 1.37\n", "5 21 175 71.4 1.46\n", "6 19 189 85.8 1.34\n", "7 21 156 65.9 1.11\n", "8 21 167 65.7 2.03\n", "9 18 195 94.4 1.29\n", "10 18 165 66.0 1.19" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Lesen der Datei students.csv als Dataframe; nur die Spalten \"age\", \"weight\", \"height\" und \"nc.score\" Spalten werden eingelesen\n", "\n", "students = pd.read_csv(\n", " \"../../data/students.csv\",\n", " index_col=0,\n", " usecols=[\"age\", \"height\", \"weight\", \"nc.score\"],\n", ")\n", "# Zeige die ersten 10 Werte\n", "students.head(10)" ] }, { "cell_type": "markdown", "id": "d11a1b68-2a9d-493e-aa55-f236234922b0", "metadata": {}, "source": [ "Pandas verfügt über die Methode `agg`. Diese lässt uns sehr einfach verschiedene deskritptive Statisitken berechnen." ] }, { "cell_type": "code", "execution_count": 5, "id": "7558705f", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
ageheightweightnc.score
mean22.541571171.38075072.9981312.166481
median21.000000171.00000071.8000002.040000
var36.785568122.71165274.5660170.658610
std6.06511111.0775298.6351620.811548
\n", "
" ], "text/plain": [ " age height weight nc.score\n", "mean 22.541571 171.380750 72.998131 2.166481\n", "median 21.000000 171.000000 71.800000 2.040000\n", "var 36.785568 122.711652 74.566017 0.658610\n", "std 6.065111 11.077529 8.635162 0.811548" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "students.agg([\"mean\", \"median\", \"var\", \"std\"])" ] }, { "cell_type": "markdown", "id": "2af403d5-11cc-44d8-81b6-9e40bf0c3534", "metadata": {}, "source": [ "### Verwendung der Standardabweichung\n", "Mit Hilfe des **Mittelwerts** und der **Standardabweichung** lässt sich der Anteil oder Prozentsatz der Gesamtbeobachtungen ermitteln, die in ein bestimmtes Intervall um den Mittelwert fallen." ] }, { "cell_type": "markdown", "id": "0bea95c6-1b5d-4aa0-bcce-43fed2fff83a", "metadata": {}, "source": [ "#### Tschebyscheff-Theorem\n", "Das Tschebyscheff Ungleichung gibt eine untere Schranke für die Fläche unter einer Kurve zwischen zwei Punkten, die auf gegenüberliegenden Seiten des Mittelwerts und im gleichen Abstand vom Mittelwert liegen." ] }, { "cell_type": "markdown", "id": "87f7bca3-66f3-4263-93ae-c62d01931e62", "metadata": {}, "source": [ "> **Für jede Zahl $k$, die größer als $1$ ist, liegen mindestens $1-\\frac{1}{k^2}$ der Datenwerte innerhalb von $k$ Standardabweichungen vom Mittelwert.**" ] }, { "cell_type": "markdown", "id": "6a9cbb89-17c5-48b5-aa21-61a9a9929ae1", "metadata": {}, "source": [ "Lassen Sie uns Python verwenden, um ein Gefühl für den Tschebyscheff-Theorem zu bekommen." ] }, { "cell_type": "code", "execution_count": 6, "id": "80447faf", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
kProzent
01.00.0
11.117.0
21.231.0
31.341.0
41.449.0
51.556.0
61.661.0
71.765.0
81.869.0
91.972.0
102.075.0
112.177.0
122.279.0
132.381.0
142.483.0
152.584.0
162.685.0
172.786.0
182.887.0
192.988.0
203.089.0
213.190.0
223.290.0
233.391.0
243.491.0
253.592.0
263.692.0
273.793.0
283.893.0
293.993.0
304.094.0
\n", "
" ], "text/plain": [ " k Prozent\n", "0 1.0 0.0\n", "1 1.1 17.0\n", "2 1.2 31.0\n", "3 1.3 41.0\n", "4 1.4 49.0\n", "5 1.5 56.0\n", "6 1.6 61.0\n", "7 1.7 65.0\n", "8 1.8 69.0\n", "9 1.9 72.0\n", "10 2.0 75.0\n", "11 2.1 77.0\n", "12 2.2 79.0\n", "13 2.3 81.0\n", "14 2.4 83.0\n", "15 2.5 84.0\n", "16 2.6 85.0\n", "17 2.7 86.0\n", "18 2.8 87.0\n", "19 2.9 88.0\n", "20 3.0 89.0\n", "21 3.1 90.0\n", "22 3.2 90.0\n", "23 3.3 91.0\n", "24 3.4 91.0\n", "25 3.5 92.0\n", "26 3.6 92.0\n", "27 3.7 93.0\n", "28 3.8 93.0\n", "29 3.9 93.0\n", "30 4.0 94.0" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k = np.arange(1, 4.1, 0.1)\n", "value = np.round((1 - (1 / k**2)) * 100)\n", "chebyshev = pd.DataFrame({\"k\": k, \"Prozent\": value})\n", "chebyshev" ] }, { "cell_type": "markdown", "id": "fe4a9575-4dbc-450a-8daf-c3e02e52950c", "metadata": {}, "source": [ "Um es in Worte zu fassen: Für $k=2$ bedeutet das, dass mindestens **$75 \\% $** der Datenwerte innerhalb von **2 Standardabweichungen** vom Mittelwert liegen.\n", "\n", "Stellen wir das Tschebyscheff-Theorem mit Python dar: " ] }, { "cell_type": "code", "execution_count": 7, "id": "75c58dd3", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "chebyshev.plot.scatter(x=\"k\", y=\"Prozent\", ax=ax)\n", "ax.set_title(\"Tschebyscheff-Theorem\")\n", "ax.grid()" ] }, { "cell_type": "markdown", "id": "06a93b1e-58c5-4da9-b062-bc4231271f14", "metadata": {}, "source": [ "Das Theorem gilt sowohl für Stichproben- als auch für Grundgesamtheitsdaten. Das Tschebyscheffsche Ungleichung gilt für Verteilungen beliebiger Form. Es kann jedoch nur für $k > 1$ verwendet werden. Denn wenn $k=1$ ist, ist der Wert von $1-\\frac{1}{k^2}$ Null, und wenn $k < 1$ ist, ist der Wert von $1-\\frac{1}{k^2}$ negativ ({cite:p}`fahrmeirstatistik` s.304). " ] }, { "cell_type": "markdown", "id": "a956ad74-9896-42a4-a214-4a61b5c2aedf", "metadata": {}, "source": [ "#### Empirische Regel\n", "Während das Tschebyscheffsche Ungleichung auf jede Art von Verteilung anwendbar ist, gilt die **empirische Regel** nur für eine bestimmte Art von Verteilung, die so genannte **Gaußverteilung** oder **Normalverteilung**. Es gibt 3 Regeln:

Bei einer Normalverteilung sind \n", "\n", "1. $68 \\%$ der Beobachtungen innerhalb einer Standardabweichung des Mittelwerts.\n", "2. $95 \\%$ der Beobachtungen innerhalb von zwei Standardabweichungen des Mittelwerts.\n", "3. $99,7 \\%$ der Beobachtungen innerhalb von drei Standardabweichungen des Mittelwerts.\n", "\n" ] }, { "cell_type": "markdown", "id": "ff03f162-a97b-4f78-a060-edff11e00408", "metadata": {}, "source": [ "Da wir inzwischen über genügend Hacking-Power verfügen, werden wir versuchen zu testen, ob die drei Regeln gültig sind. \n", "\n", "**(1) Erstens** werden wir die Funktion `random.normal()` in Python erforschen, um normalverteilte Daten zu erzeugen, und \n", "\n", "**(2) Zweitens** werden wir zu unserem `students` Datensatz zurückkehren und diese Regeln an diesem Datensatz zu validieren. \n", "

Die Normalverteilung gehört zur Familie der stetigen Verteilungen. In Python gibt es eine Vielzahl von Wahrscheinlichkeitsverteilungen (hier). Um Daten aus einer Normalverteilung zu erzeugen, kann man die Funktion `random.normal()` verwenden, die ein Zufallsvariablengenerator für die Normalverteilung ist.\n", "\n", "Mit der Funktion `np.random.normal(loc=0.0, scale=1.0)` können wir Zufallsvariablen aus einer Normalverteilung mit einem gegebenen Mittelwert (Standard ist $0$) und einer Standardabweichung (Standard ist $1$) entnehmen. Mit dem Argument `size` können wir die Anzahl der erzeugten Zufallsvariablen bestimmen." ] }, { "cell_type": "code", "execution_count": 8, "id": "bcec69c1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.35778736])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.normal(loc=0.0, scale=1.0, size=1)" ] }, { "cell_type": "code", "execution_count": 9, "id": "6ac44682", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.56078453])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.normal(loc=0.0, scale=1.0, size=1)" ] }, { "cell_type": "code", "execution_count": 10, "id": "88aaaf8e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1.08305124])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.normal(loc=0.0, scale=1.0, size=1)" ] }, { "cell_type": "markdown", "id": "5f35ca74-3235-4c10-804b-881637218c4d", "metadata": {}, "source": [ "Wir können die Funktion ziemlich einfach bitten, Hunderte oder Tausende oder noch mehr (Pseudo-)Zufallszahlen zu ziehen:" ] }, { "cell_type": "code", "execution_count": 11, "id": "9ca81cb7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 1.05380205, -1.37766937, -0.93782504, 0.51503527, 0.51378595,\n", " 0.51504769, 3.85273149, 0.57089051, 1.13556564, 0.95400176])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.normal(loc=0.0, scale=1.0, size=10)" ] }, { "cell_type": "code", "execution_count": 12, "id": "a54cae55", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0.65139125, -0.31526924, 0.75896922, -0.77282521, -0.23681861,\n", " -0.48536355, 0.08187414, 2.31465857, -1.86726519, 0.68626019,\n", " -1.61271587, -0.47193187, 1.0889506 , 0.06428002, -1.07774478,\n", " -0.71530371, 0.67959775, -0.73036663, 0.21645859, 0.04557184,\n", " -0.65160035, 2.14394409, 0.63391902, -2.02514259, 0.18645431,\n", " -0.66178646, 0.85243333, -0.79252074, -0.11473644, 0.50498728,\n", " 0.86575519, -1.20029641, -0.33450124, -0.47494531, -0.65332923,\n", " 1.76545424, 0.40498171, -1.26088395, 0.91786195, 2.1221562 ,\n", " 1.03246526, -1.51936997, -0.48423407, 1.26691115, -0.70766947,\n", " 0.44381943, 0.77463405, -0.92693047, -0.05952536, -3.24126734,\n", " -1.02438764, -0.25256815, -1.24778318, 1.6324113 , -1.43014138,\n", " -0.44004449, 0.13074058, 1.44127329, -1.43586215, 1.16316375,\n", " 0.01023306, -0.98150865, 0.46210347, 0.1990597 , -0.60021688,\n", " 0.06980208, -0.3853136 , 0.11351735, 0.66213067, 1.58601682,\n", " -1.2378155 , 2.13303337, -1.9520878 , -0.1517851 , 0.58831721,\n", " 0.28099187, -0.62269952, -0.20812225, -0.49300093, -0.58936476,\n", " 0.8496021 , 0.35701549, -0.6929096 , 0.89959988, 0.30729952,\n", " 0.81286212, 0.62962884, -0.82899501, -0.56018104, 0.74729361,\n", " 0.61037027, -0.02090159, 0.11732738, 1.2776649 , -0.59157139,\n", " 0.54709738, -0.20219265, -0.2176812 , 1.09877685, 0.82541635])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.normal(loc=0.0, scale=1.0, size=100)" ] }, { "cell_type": "markdown", "id": "b4ee5e96-f3f3-4729-8bba-92e661fbc062", "metadata": {}, "source": [ "Wenn wir ein Histogramm dieser Zahlen erstellen, sehen wir die namensgebende glockenförmige Verteilung." ] }, { "cell_type": "code", "execution_count": 13, "id": "fe957281", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y_norm = np.random.normal(loc=0.0, scale=1.0, size=100000)\n", "bins = int(len(y_norm) / 1000) # bestimmt die Anzahl der Bins\n", "plt.hist(y_norm, bins=bins)\n", "plt.ylabel(\"Absolute Häufigkeit\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "6a650d2c-d02d-4d9e-b12b-ef5002c7fc71", "metadata": {}, "source": [ "Wir kennen bereits den Mittelwert und die Standardabweichung der Werte in `y_norm`, da wir die Funktion `np.random.normal()` explizit mit `mean=0` und `sd=1` aufgerufen haben. Wir müssen also nur die Zahlen in `y_norm` zählen, die größer als $-1$ bzw. kleiner als $1$ und $2$ bzw. $-2$ und $3$ bzw. $-3$ sind, und sie zur Länge von `y_norm`, in unserem Fall $100.000$, in Beziehung setzen, um die drei oben genannten Regeln zu bestätigen." ] }, { "cell_type": "code", "execution_count": 14, "id": "e2e77065", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sd1 : 0.68143\n", "sd2 : 0.95444\n", "sd3 : 0.99737\n" ] } ], "source": [ "# Berechne Anzahl der Werte < 1 - Anzahl der Werte > -1 durch Gesamtanzahl\n", "sd1 = sum((y_norm > -1) & (y_norm < 1)) / len(y_norm)\n", "\n", "# Berechne Anzahl der Werte < 2 - Anzahl der Werte > -2 durch Gesamtanzahl\n", "sd2 = sum((y_norm > -2) & (y_norm < 2)) / len(y_norm)\n", "\n", "# Berechne Anzahl der Werte < 3 - Anzahl der Werte > -3 durch Gesamtanzahl\n", "sd3 = sum((y_norm > -3) & (y_norm < 3)) / len(y_norm)\n", "\n", "print(\"sd1 :\", sd1)\n", "print(\"sd2 :\", sd2)\n", "print(\"sd3 :\", sd3)" ] }, { "cell_type": "markdown", "id": "da2d7460-1771-41de-9e9a-5f610dcb70c1", "metadata": {}, "source": [ "Perfekte Übereinstimmung! Die drei empirischen Regeln sind offensichtlich gültig. Um unsere Ergebnisse zu veranschaulichen, stellen wir das Histogramm erneut dar und fügen einige Anmerkungen hinzu. Bitte beachten Sie, dass wir in der `hist()`-Funktion das Argument `density=True` setzen. Dies hat zur Folge, dass das resultierende Histogramm nicht mehr die Zählungen auf der y-Achse anzeigt, sondern die **Dichtewerte** (normalisierte Zählung geteilt durch Bin-Breite), was bedeutet, dass sich die Balkenbereiche zu $1$ summieren." ] }, { "cell_type": "code", "execution_count": 15, "id": "de2f1f5e", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.hist(y_norm, bins=bins)\n", "ax.set_ylabel(\"Absolute Häufigkeit\")\n", "for e, std in enumerate([(-1, 1), (-2, 2), (-3, 3)]):\n", " plt.axvline(std[0], color=f\"C{e+1}\")\n", " plt.axvline(std[1], color=f\"C{e+1}\")" ] }, { "cell_type": "markdown", "id": "049ce592-42b5-4b46-b396-15491b14ce9c", "metadata": {}, "source": [ "Nun, lassen Sie uns an der **zweiten** Aufgabe arbeiten: Überprüfen Sie die drei empirischen Regeln anhand des `students` Datensatzes. Dazu müssen wir überprüfen, ob eine der numerischen Variablen im Studentendatensatz normalverteilt ist. Wir beginnen mit der Extraktion numerischer Variablen von Interesse aus dem `students` Datensatz. Dann zeichnen wir Histogramme und beurteilen, ob die Variable normalverteilt ist oder nicht. Zunächst überprüfen wir jedoch den Datensatz, indem wir die Funktion `head()` aufrufen." ] }, { "cell_type": "code", "execution_count": 16, "id": "eb51e94e", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
ageheightweightscore1score2salary
11916064.8NaNNaNNaN
21917273.0NaNNaNNaN
32216870.645.046.0NaN
41918379.7NaNNaNNaN
52117571.4NaNNaNNaN
61918985.8NaNNaNNaN
72115665.9NaNNaNNaN
82116765.758.062.0NaN
91819594.457.067.0NaN
101816566.0NaNNaNNaN
\n", "
" ], "text/plain": [ " age height weight score1 score2 salary\n", "1 19 160 64.8 NaN NaN NaN\n", "2 19 172 73.0 NaN NaN NaN\n", "3 22 168 70.6 45.0 46.0 NaN\n", "4 19 183 79.7 NaN NaN NaN\n", "5 21 175 71.4 NaN NaN NaN\n", "6 19 189 85.8 NaN NaN NaN\n", "7 21 156 65.9 NaN NaN NaN\n", "8 21 167 65.7 58.0 62.0 NaN\n", "9 18 195 94.4 57.0 67.0 NaN\n", "10 18 165 66.0 NaN NaN NaN" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Lesen der Datei students.csv als Dataframe;\n", "students = pd.read_csv(\n", " \"../../data/students.csv\",\n", " usecols=[\"age\", \"height\", \"weight\", \"score1\", \"score2\", \"salary\"],\n", ")\n", "students.head(10)" ] }, { "cell_type": "markdown", "id": "8c769aaf-3a90-4547-9297-e757c941b9a5", "metadata": {}, "source": [ "Um einen Überblick über die Form der Verteilung der einzelnen Variablen zu erhalten, verwenden wir die Methode `hist()`." ] }, { "cell_type": "code", "execution_count": 17, "id": "9b61c3d4", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "cols = students.columns\n", "fig, ax = plt.subplots(ncols=int(len(cols) / 2), nrows=2)\n", "ax = np.ravel(ax) # vereinfacht das iterieren durch die axes Objekte\n", "titles = {\n", " \"age\": \"Alter\",\n", " \"height\": \"Grösse\",\n", " \"weight\": \"Gewicht\",\n", " \"score1\": \"Punkte1\",\n", " \"score2\": \"Punkte2\",\n", " \"salary\": \"Gehalt\",\n", "}\n", "\n", "for e, col in enumerate(cols):\n", " bins = int(students[col].nunique() / 2)\n", " ax[e].hist(students[col], bins=bins, density=True)\n", " ax[e].set_title(titles[col])\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "id": "7ec26b78-5e38-42f5-a15e-7f99848c2f7b", "metadata": {}, "source": [ "Wir stellen sofort fest, dass einige Variablen positiv verzerrt sind, also schließen wir sie aus und behalten diejenigen, die normal verteilt zu sein scheinen." ] }, { "cell_type": "code", "execution_count": 18, "id": "487c2a2c", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "cols = [\"height\", \"salary\"]\n", "fig, ax = plt.subplots(ncols=2)\n", "ax = np.ravel(ax) # vereinfacht das iterieren durch die axes Objekte\n", "bins_fact = {\"height\": 2, \"salary\": 40}\n", "\n", "for e, col in enumerate(cols):\n", " bins = int(students[col].nunique() / bins_fact[col])\n", " ax[e].hist(students[col], bins=bins)\n", " ax[e].set_title(titles[col])\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "id": "a3e9441d-caf1-47b5-a249-486e24a4b5e3", "metadata": {}, "source": [ "Nun, sowohl die Variable `height` als auch die Variable `salary` scheinen mehr oder weniger normalverteilt zu sein. Es ist also eine Frage des Geschmacks, welche Variable man für die weitere Analyse auswählt. Für den Moment bleiben wir bei der Gehaltsvariable und überprüfen, ob die drei oben genannten empirischen Regeln gültig sind. Wir wechseln zu Python und validieren diese Regeln, indem wir zunächst den Mittelwert und die Standardabweichungen berechnen. Bitte beachten Sie, dass die Gehaltsvariable Fehlwerte enthält, die mit `NA` gekennzeichnet sind. Daher schließen wir zunächst alle `NA`-Werte aus, indem wir die Funktion `dropna()` anwenden." ] }, { "cell_type": "code", "execution_count": 19, "id": "32a240f0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "11 45254.108021\n", "13 40552.790243\n", "14 27007.030294\n", "17 33969.159268\n", "28 50617.641870\n", " ... \n", "8229 33259.703079\n", "8234 41028.241341\n", "8235 36750.087135\n", "8238 40112.041834\n", "8239 45900.134459\n", "Name: salary, Length: 1753, dtype: float64" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "salary = students[\"salary\"].dropna()\n", "salary" ] }, { "cell_type": "code", "execution_count": 20, "id": "51a71567", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mittelwert des Gehalts: 42522.112364224806\n", "1 Standardabweichung des Gehalts: 10333.139905546619\n", "2 Standardabweichungen des Gehalts: 20666.279811093238\n", "3 Standardabweichungen des Gehalts: 30999.41971663986\n" ] } ], "source": [ "print(f\"Mittelwert des Gehalts: {salary.mean()}\")\n", "print(f\"1 Standardabweichung des Gehalts: {salary.std()}\")\n", "print(f\"2 Standardabweichungen des Gehalts: {2 * salary.std()}\")\n", "print(f\"3 Standardabweichungen des Gehalts: {3 * salary.std()}\")" ] }, { "cell_type": "markdown", "id": "bff9c75e-a17b-4409-81d4-2756d1c8c3d4", "metadata": {}, "source": [ "Wie in der obigen allgemeinen Beispielform zählen wir die Anzahl der Werte, die größer als $+1$ s.d. bzw. kleiner als $-1$ s.d. und $+2$ s.d. bzw. $-2$ s.d. und $+3$ s.d. bzw. $-3$ s.d. sind, und setzen sie in Beziehung zur Länge des Vektors, in unserem Fall $1753$." ] }, { "cell_type": "code", "execution_count": 21, "id": "222b5dbd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sd1 : 0.6708499714774672\n", "sd2 : 0.9560752994865944\n", "sd3 : 0.9977181973759269\n" ] } ], "source": [ "salary_mean = salary.mean()\n", "salary_std = salary.std()\n", "\n", "sd1 = (\n", " sum((salary > (salary_mean - salary_std)) & (salary < (salary_mean + salary_std)))\n", " / salary.shape[0]\n", ")\n", "\n", "sd2 = (\n", " sum(\n", " (salary > (salary_mean - 2 * salary_std))\n", " & (salary < (salary_mean + 2 * salary_std))\n", " )\n", " / salary.shape[0]\n", ")\n", "\n", "\n", "sd3 = (\n", " sum(\n", " (salary > (salary_mean - 3 * salary_std))\n", " & (salary < (salary_mean + 3 * salary_std))\n", " )\n", " / salary.shape[0]\n", ")\n", "\n", "\n", "print(\"sd1 :\", sd1)\n", "print(\"sd2 :\", sd2)\n", "print(\"sd3 :\", sd3)" ] }, { "cell_type": "markdown", "id": "2241a7b8-8efa-417c-94fd-55cb7572bd25", "metadata": {}, "source": [ "Wow, ziemlich nah dran! Offensichtlich zeigt die Gehaltsvariable eine starke Tendenz zur Unterstützung der so genannten empirischen Regel. Wir stellen das Histogramm für die Variable `salary` dar, um unseren Eindruck zu bestätigen. " ] }, { "cell_type": "code", "execution_count": 22, "id": "2c5f953a", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "bins = int(salary.nunique() / 40)\n", "ax.hist(salary, bins=bins)\n", "ax.set_ylabel(\"Absolute Häufigkeit\")\n", "ax.set_xlabel(\"Gehalt\")\n", "for e in range(3):\n", " ax.axvline(salary_mean + (e + 1) * salary_std, color=f\"C{e+1}\")\n", " ax.axvline(salary_mean - (e + 1) * salary_std, color=f\"C{e+1}\")" ] }, { "cell_type": "markdown", "id": "ac739f07-87dc-4809-9e98-5912be13ffb3", "metadata": {}, "source": [ "Wir können nun unseren Visualisierungsansatz erweitern, indem wir die **empirische Dichteschätzung** mit der Funktion `scipy_kernel.evaluate()` grafisch darstellen und ihre Form überprüfen. Wir stellen die empirische Dichteschätzung als gestrichelte Linie dar, indem wir das (Linientyp-Argument) `'-.'` und eine Linienbreite von $3$ (Argument `linewidth=3.0`) setzen." ] }, { "cell_type": "code", "execution_count": 23, "id": "b948b12d", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "bins = int(salary.nunique() / 40)\n", "ax.hist(salary, bins=bins, density=True)\n", "ax.set_ylabel(\"Dichte\")\n", "ax.set_xlabel(\"Gehalt\")\n", "\n", "# empirische Dichteschätzung\n", "x_salary = np.linspace(salary.min(), salary.max(), 100)\n", "scipy_kernel = gaussian_kde(salary)\n", "dens_emp = scipy_kernel.evaluate(x_salary)\n", "ax.plot(x_salary, dens_emp, color=\"k\", linestyle=\"dashed\", linewidth=3.0)\n", "\n", "# Standardabweichungen\n", "for e in range(3):\n", " ax.axvline(salary_mean + (e + 1) * salary_std, color=f\"C{e+1}\")\n", " ax.axvline(salary_mean - (e + 1) * salary_std, color=f\"C{e+1}\")" ] }, { "cell_type": "markdown", "id": "3c8353f1-d2b6-4b04-90c0-16bd5ac82f49", "metadata": {}, "source": [ "Schließlich vergleichen wir unsere **empirische Dichteschätzung** mit der theoretischen **Wahrscheinlichkeitsdichtefunktion**, die auf dem tatsächlichen Mittelwert und der Standardabweichung der Daten `salary` basiert. Für einen besseren visuellen Vergleich wechseln wir zurück zu einer nicht eingefärbten Histogramm-Darstellung." ] }, { "cell_type": "code", "execution_count": 24, "id": "bad8ba8e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "bins = int(salary.nunique() / 40)\n", "ax.hist(salary, bins=bins, density=True)\n", "ax.set_ylabel(\"Dichte\")\n", "ax.set_xlabel(\"Gehalt\")\n", "\n", "# empirische Dichteschätzung\n", "x_salary = np.linspace(salary.min(), salary.max(), 100)\n", "scipy_kernel = gaussian_kde(salary)\n", "dens_emp = scipy_kernel.evaluate(x_salary)\n", "ax.plot(\n", " x_salary,\n", " dens_emp,\n", " color=\"k\",\n", " linestyle=\"dashed\",\n", " linewidth=3.0,\n", " label=\"Empirische Dichteschätzung\",\n", ")\n", "\n", "# Wahrscheinlichkeitsdichtefunktion\n", "pdf = norm.pdf(x_salary, loc=salary.mean(), scale=salary.std())\n", "ax.plot(\n", " x_salary, pdf, color=\"k\", linewidth=3.0, label=\"Wahrscheinlichkeitsdichtefunktion\"\n", ")\n", "\n", "# Standardabweichungen\n", "for e in range(3):\n", " ax.axvline(salary_mean + (e + 1) * salary_std, color=f\"C{e+1}\")\n", " ax.axvline(salary_mean - (e + 1) * salary_std, color=f\"C{e+1}\")\n", "ax.legend()" ] }, { "cell_type": "markdown", "id": "e42dfecb-b8a2-456f-a6bd-d8fcea7b0e5d", "metadata": {}, "source": [ "Wir können daraus schließen, dass `salary` im Datensatz der `students` ungefähr normalverteilt ist. Die Grafik zeigt jedoch, dass die Verteilung der Gehaltsvariablen leicht nach linksschief ist. Dies ist an der Abweichung zwischen der **empirischen Dichteschätzung** und der **Wahrscheinlichkeitsdichtefunktion** zu erkennen." ] }, { "cell_type": "markdown", "id": "c639393d-dd23-4c01-8ed9-8a990dbe332c", "metadata": {}, "source": [ "## Die Spannweite" ] }, { "cell_type": "markdown", "id": "c021afb3-9819-4d2b-97c7-43d31b50c2f8", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "Die **Spannweite** als Maß für die Streuung ist einfach zu berechnen. Sie ergibt sich aus der Differenz zwischen dem größten und dem kleinsten Wert in einem Datensatz.\n", "\n", "$$\\text{Range} = \\text{kleinster Wert} - \\text{größter Wert}$$" ] }, { "cell_type": "markdown", "id": "065a6914-92ae-4c7c-abda-0c5427ba7305", "metadata": {}, "source": [ "Betrachten wir unseren `students` Datensatz. Wir unterteilen den Datensatz so, dass er nur numerische Daten enthält." ] }, { "cell_type": "code", "execution_count": 25, "id": "e6f1b4f8-41ef-48c6-a8fa-9096ab16866e", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
stud.idnamegenderageheightweightreligionnc.scoresemestermajorminorscore1score2online_tutorialgraduatedsalary
3600255883Morrison-Cook, AustinMale2017272.6Other1.674thMathematics and StatisticsEconomics and Finance91.087.000NaN
2082686345Lenahan, KyleMale2118178.0Other1.382ndSocial SciencesEconomics and FinanceNaNNaN00NaN
522346731Lee, NicholasMale2219293.1Catholic1.275thEnvironmental SciencesSocial Sciences78.065.01149068.502177
5604963305Kramer, DavidMale5617072.6Orthodox2.145thEnvironmental SciencesMathematics and Statistics72.071.01142606.347228
3671124687Than, JonathanMale2217272.4Protestant1.794thEnvironmental SciencesMathematics and Statistics62.069.00149004.727119
5376696262Macasinag, PauloMale2019794.3Catholic3.416thPolitical ScienceEnvironmental Sciences51.047.01139442.803935
2318452190Briseno, AlishaFemale6316268.0Catholic2.192ndMathematics and StatisticsEnvironmental SciencesNaNNaN00NaN
4840955228Thapa, RichardMale2317576.0Other2.481stMathematics and StatisticsEnvironmental SciencesNaNNaN00NaN
1286854649Duling, Joshua IanMale6117070.3Protestant1.54>6thEconomics and FinanceMathematics and Statistics64.069.010NaN
118582922Valenciano-Poffenbarger, QuincieFemale1917576.8Catholic2.191stSocial SciencesMathematics and StatisticsNaNNaN00NaN
\n", "
" ], "text/plain": [ " stud.id name gender age height weight \\\n", "3600 255883 Morrison-Cook, Austin Male 20 172 72.6 \n", "2082 686345 Lenahan, Kyle Male 21 181 78.0 \n", "522 346731 Lee, Nicholas Male 22 192 93.1 \n", "5604 963305 Kramer, David Male 56 170 72.6 \n", "3671 124687 Than, Jonathan Male 22 172 72.4 \n", "5376 696262 Macasinag, Paulo Male 20 197 94.3 \n", "2318 452190 Briseno, Alisha Female 63 162 68.0 \n", "4840 955228 Thapa, Richard Male 23 175 76.0 \n", "1286 854649 Duling, Joshua Ian Male 61 170 70.3 \n", "118 582922 Valenciano-Poffenbarger, Quincie Female 19 175 76.8 \n", "\n", " religion nc.score semester major \\\n", "3600 Other 1.67 4th Mathematics and Statistics \n", "2082 Other 1.38 2nd Social Sciences \n", "522 Catholic 1.27 5th Environmental Sciences \n", "5604 Orthodox 2.14 5th Environmental Sciences \n", "3671 Protestant 1.79 4th Environmental Sciences \n", "5376 Catholic 3.41 6th Political Science \n", "2318 Catholic 2.19 2nd Mathematics and Statistics \n", "4840 Other 2.48 1st Mathematics and Statistics \n", "1286 Protestant 1.54 >6th Economics and Finance \n", "118 Catholic 2.19 1st Social Sciences \n", "\n", " minor score1 score2 online_tutorial graduated \\\n", "3600 Economics and Finance 91.0 87.0 0 0 \n", "2082 Economics and Finance NaN NaN 0 0 \n", "522 Social Sciences 78.0 65.0 1 1 \n", "5604 Mathematics and Statistics 72.0 71.0 1 1 \n", "3671 Mathematics and Statistics 62.0 69.0 0 1 \n", "5376 Environmental Sciences 51.0 47.0 1 1 \n", "2318 Environmental Sciences NaN NaN 0 0 \n", "4840 Environmental Sciences NaN NaN 0 0 \n", "1286 Mathematics and Statistics 64.0 69.0 1 0 \n", "118 Mathematics and Statistics NaN NaN 0 0 \n", "\n", " salary \n", "3600 NaN \n", "2082 NaN \n", "522 49068.502177 \n", "5604 42606.347228 \n", "3671 49004.727119 \n", "5376 39442.803935 \n", "2318 NaN \n", "4840 NaN \n", "1286 NaN \n", "118 NaN " ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.read_csv(\"../../data/students.csv\")\n", "df.sample(10)" ] }, { "cell_type": "markdown", "id": "05d42c01-93be-4d4a-8c52-b41581da5567", "metadata": {}, "source": [ "Wir sind also an den Kategorien `age`, `height`, `weight` und `nc.score` interessiert. Wir verwenden die Methoden `min()` und `max()`, um das Minimum und Maximum der ausgewählten Variablen zu berechnen. Erneut greifen wir auf die `agg`-Methode zurück." ] }, { "cell_type": "code", "execution_count": 26, "id": "9d288dea-faf2-452a-92f2-845bc93f31ac", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
ageheightweightnc.score
min1813551.41.0
max64206116.04.0
\n", "
" ], "text/plain": [ " age height weight nc.score\n", "min 18 135 51.4 1.0\n", "max 64 206 116.0 4.0" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "summary = df[[\"age\", \"height\", \"weight\", \"nc.score\"]].agg([\"min\", \"max\"])\n", "summary" ] }, { "cell_type": "markdown", "id": "9e07e95e-91bf-4eaa-b04b-1e882f86ac4f", "metadata": {}, "source": [ "Um nun die Spannweite für jede Variable zu berechnen, müssen wir nur eine Zeile von der anderen abziehen." ] }, { "cell_type": "code", "execution_count": 27, "id": "83170f12-caf0-49bf-a84e-b091de5139b1", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
ageheightweightnc.score
min18.0135.051.41.0
max64.0206.0116.04.0
Spannweite46.071.064.63.0
\n", "
" ], "text/plain": [ " age height weight nc.score\n", "min 18.0 135.0 51.4 1.0\n", "max 64.0 206.0 116.0 4.0\n", "Spannweite 46.0 71.0 64.6 3.0" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "summary.loc[\"Spannweite\"] = summary.loc[\"max\"] - summary.loc[\"min\"]\n", "summary" ] }, { "cell_type": "markdown", "id": "d9633733-a493-488b-aeff-16abd7cf8166", "metadata": {}, "source": [ "Die Spannweite hat wie der Mittelwert den Nachteil, dass sie durch Ausreißer beeinflusst wird. Daher ist die Spannweite kein gutes Streuungsmaß für einen Datensatz, der Ausreißer enthält. Ein weiterer Nachteil der Verwendung der Spannweite als Streuungsmaß ist, dass ihre Berechnung nur auf zwei Werten basiert: dem größten und dem kleinsten. Alle anderen Werte in einem Datensatz werden bei der Berechnung der Spanne ignoriert. Daher ist die Spannweite oftmals kein sehr zufriedenstellendes Maß für die Streuung ({cite:p}`fahrmeirstatistik` s.62)." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.2" }, "vscode": { "interpreter": { "hash": "31f2aee4e71d21fbe5cf8b01ff0e069b9275f58929596ceb00d14d90e3e16cd6" } } }, "nbformat": 4, "nbformat_minor": 5 }