How to add upper/lower fence + outliers to a box plot?

Question

I'm trying to create a box & whiskers plot that includes the upper & lower fence, and the outliers. My current plot looks like this (minus all the labeling):

\documentclass [12pt, letterpaper] {article}
\usepackage {pgfplots}
\pgfplotsset {compat=1.18}
\usepgfplotslibrary {statistics}
\begin {document}
\begin {center}
\begin {tikzpicture}
\begin {axis} [
    xmin = 15,
    xmax = 35,
    xtick = {15, 20, 25, 30, 35},
    ytick = \empty,
    width = 10cm,
    height = 5cm,
]
\addplot + [
    boxplot prepared = {
        median = 25.5,
        upper quartile = 27,
        lower quartile = 23,
        upper whisker = 31,
        lower whisker = 17,
    },
] coordinates {};
\end {axis}
\end {tikzpicture}
\end {center}
\end {document}

The problem is I can't figure out how to add the upper fence, lower fence, and my outliers; I'd need my graph to look more-so like this:

Answer 1

• I provide a very manual solution because I am not skilled enough for a more automated solution.
• I calculate the position of the fences manually according to Wikipedia (as of 2022-01-30), see citation block below.
• Then I draw a dashed line manually.
• Watch out, the code must be before \end{axis}!
• You can use \draw[dashed, blue] (17, 0.6) -- (17, 1.4); if you want to change the color.
• I commented %ytick = \empty out, in order to see which values I need for the y positions (0.6 and 1.4).

The same data set can also be made into a box-plot through a different approach as shown in Figure 3. This time the boundaries of the whiskers are found within the 1.5 IQR value. From above the upper quartile (Q3), a distance of 1.5 times the IQR is measured out and a whisker is drawn up to the largest observed data point from the dataset that falls within this distance. Similarly, a distance of 1.5 times the IQR is measured out below the lower quartile (Q1) and a whisker is drawn down to the lowest observed data point from the dataset that falls within this distance. All other observed data points outside the boundary of the whiskers are plotted as outliers.

(Source: https://towardsdatascience.com/understanding-boxplots-5e2df7bcbd51)

---

\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\usepgfplotslibrary{statistics}
\begin{document}
\begin{center}
\begin{tikzpicture}
\begin{axis} [
    xmin = 15,
    xmax = 35,
    xtick = {15, 20, 25, 30, 35},
    %ytick = \empty,
    width = 10cm,
    height = 5cm,
]
\addplot+[
    boxplot prepared = {
        median = 25.5,
        upper quartile = 27, % Q3
        lower quartile = 23, % Q1
        upper whisker = 31,
        lower whisker = 17,
    },
] coordinates {};
% https://en.wikipedia.org/wiki/Box_plot
% IQR = 27 - 23 = 4
% 1.5 * IQR = 6
% Lower Fence = Q1 - 1.5 * IQR = 17
% Upper Fence = Q3 + 1.5 * IQR = 33
\draw[dashed] (17, 0.6) -- (17, 1.4);
\draw[dashed] (33, 0.6) -- (33, 1.4);
\end{axis}
\end{tikzpicture}
\end{center}
\end{document}