diff --git a/src/2026-02-13/presentation.tex b/src/2026-02-13/presentation.tex index 5cc6d51..372b211 100644 --- a/src/2026-02-13/presentation.tex +++ b/src/2026-02-13/presentation.tex @@ -39,6 +39,7 @@ \pgfplotsset{compat=newest} \usepgfplotslibrary{fillbetween} \usepgfplotslibrary{groupplots} +\usepgfplotslibrary{statistics} \usepackage{enumerate} \usepackage{listings} @@ -568,7 +569,7 @@ \pause \item Konsistenz \begin{gather*} - \lim_{N\rightarrow \infty} P_\vartheta \big( \lvert + \lim_{N\rightarrow \infty} P \big( \lvert \hat{\vartheta} - \vartheta \rvert \ge \varepsilon \big) = 0 \end{gather*} @@ -980,6 +981,7 @@ + x_{\left( Np + 1 \right)} \right), & Np \in \mathbb{N} \end{cases} \end{align*} + \pause \item Quartilsabstand \begin{align*} x_{3/4} - x_{1/4} @@ -990,7 +992,169 @@ \begin{frame} \frametitle{Boxplots} - % TODO: Create slide + \vspace*{-10mm} + + \begin{figure}[H] + \centering + \begin{tikzpicture} + \begin{axis}[ + width=24cm, + height=6cm, + clip=false, + xticklabel=\empty, + yticklabel=\empty, + ] + \addplot+ [ + mark=*, + kit-red, + boxplot prepared={ + lower whisker=5, + lower quartile=7, + median=8.5, + upper quartile=9.5, + upper whisker=10, + }, + boxplot/every median/.style={draw=kit-blue,line width=2pt}, + boxplot/every whisker/.style={draw=kit-green,line + width=1pt}, + boxplot/every box/.style={black,line width=1pt}, + ] table [row sep=\\,y index=0] { + data\\ 1\\ 3\\ + }; + + \node at (7.5,0) (median) + {\textcolor{kit-blue}{Median: $x_{1/2}$}}; + + \node[below right=0cm and 0cm of median,align=center] + (uw) { + \textcolor{kit-green}{Größte normale Beobachtung:}\\ + $\textcolor{kit-green}{x_{3/4} + \frac{3}{2} + \left( x_{3/4} - x_{1/4} \right)}$ + }; + \node[below left=0cm and 0cm of median,align=center] (lw) + { + \textcolor{kit-green}{Kleinste normale Beobachtung:}\\ + $\textcolor{kit-green}{x_{1/4} - \frac{3}{2} \left( + x_{3/4} - x_{1/4} \right)}$ + }; + + \node at (9.78, 2) (uq) + {Oberes Quartil: $x_{3/4}$}; + \node[left=of uq] (lq) + {Unteres Quartil: $x_{1/4}$}; + + \node[above left=0cm and 0cm of lw] (out) + {\textcolor{kit-red}{Ausreißer}}; + + \draw[kit-blue, line width=1pt] (axis cs: 8.4,0.65) -- (median); + \draw[kit-green, line width=1pt] (axis cs: 5,0.65) -- (lw); + \draw[kit-green, line width=1pt] (axis cs: 10,0.65) -- (uw); + + \draw[kit-red, line width=1pt] (axis cs: 1.08,0.9) -- (out); + \draw[kit-red, line width=1pt] (axis cs: 2.9,0.9) -- (out); + + \draw[line width=1pt] (axis cs: 7,1.42) -- (lq); + \draw[line width=1pt] (axis cs: 9.5,1.42) -- (uq); + \end{axis} + \end{tikzpicture} + \end{figure} +\end{frame} + +\begin{frame} + \frametitle{Zusammenfassung} + + \vspace*{-10mm} + + \begin{columns} + \column{\kitfourcolumns} + \begin{greenblock}{Empirische Kenngrößen} + \vspace*{-8mm} + \begin{align*} + \text{Empirischer Erwartungswert: } & \overline{x} = \frac{1}{N} + \nsum_{i=1}^{N} x_i \\[3mm] + \text{Empirische Varianz: } & s^2 = \frac{1}{N-1} + \nsum_{i=1}^{N} \left( x_i - \overline{x} \right)^2 \\[3mm] + p\text{-Quantil: } + & x_p = + \begin{cases} + x_{\left( \lfloor Np + 1 \rfloor \right)}, & Np + \notin \mathbb{N} \\[3mm] + \frac{1}{2} \left( x_{\left( Np \right)} + + x_{\left( Np + 1 \right)} \right), & Np \in \mathbb{N} + \end{cases} \\[3mm] + \text{Median: } & x_{1/2} \\[3mm] + \text{Quartilsabstand: } & x_{3/4} - x_{1/4} + \end{align*} + \vspace*{-4mm} + \end{greenblock} + \column{\kittwocolumns} + \begin{greenblock}{Boxplot} + \begin{figure}[H] + \centering + \begin{tikzpicture} + \begin{axis}[ + width=3cm, + height=12cm, + boxplot/draw direction=y, + clip=false, + xtick=\empty, + ytick=\empty, + axis lines=none, + ] + \addplot+ [ + mark=*, + kit-red, + boxplot prepared={ + lower whisker=5, + lower quartile=7, + median=8.5, + upper quartile=9.5, + upper whisker=10, + }, + boxplot/every + median/.style={draw=kit-blue,line width=2pt}, + boxplot/every + whisker/.style={draw=kit-green,line width=1pt}, + boxplot/every box/.style={black,line width=1pt}, + ] table [row sep=\\,y index=0] { + data\\ 1\\ 3\\ + }; + + \node[right] (median) at (2.5,8.5) + {$\textcolor{kit-blue}{x_{1/2}}$}; + \node[right] (lq) at (2.5,7) {$x_{1/4}$}; + \node[right] (uq) at (2.5,9.5) {$x_{3/4}$}; + \node[right] (lw) at (2.5,5) + { + $\textcolor{kit-green}{ + x_{1/4} - \frac{3}{2} \left( x_{3/4} - + x_{1/4} \right) + }$ + }; + \node[right] (uw) at (2.5,10.6) + { + $\textcolor{kit-green}{ + x_{1/4} + \frac{3}{2} \left( x_{3/4} - + x_{1/4} \right) + }$ + }; + \node[right] (out) at (2.5,2) + { + \textcolor{kit-red}{Ausreißer} + }; + + \draw[kit-blue,line width=1pt] (1.6,8.5) -- (median); + \draw[line width=1pt] (1.6,9.5) -- (uq); + \draw[line width=1pt] (1.6,7) -- (lq); + \draw[kit-green,line width=1pt] (1.6,5) -- (lw); + \draw[kit-green,line width=1pt] (1.6,10) -- (uw); + \draw[kit-red,line width=1pt] (1.3,1) -- (out); + \draw[kit-red,line width=1pt] (1.3,3) -- (out); + \end{axis} + \end{tikzpicture} + \end{figure} + \end{greenblock} + \end{columns} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -1125,7 +1289,6 @@ \end{align*} \end{frame} -% TODO: p-Quantil einer Stichprobe [p. 113] \begin{frame} \frametitle{Aufgabe 2: Deskriptive Statistik}