\section{Box plots and distribution summaries}
Load the optional \key{distribution} library in the preamble:
\begin{source}
\usegradbarslibrary{distribution}
\end{source}
Samples are comma-separated. Empty fields and \key{NA} are missing; zero is
retained. Statistics use unsorted, unrounded observations, then sort internally.
Quartiles use type-7 linear interpolation: for sorted $x_1,\ldots,x_n$, let
$h=1+(n-1)p$, $j=\lfloor h\rfloor$ and $g=h-j$; then
$Q(p)=(1-g)x_j+gx_{j+1}$, taking $x_n$ at $h=n$.
Use $p=0.25,0.5,0.75$ for Q1, median and Q3. Whiskers are the extreme actual
observations inside $[Q1-1.5\,IQR,Q3+1.5\,IQR]$, inclusive. Hollow points are
observations outside this interval, not data automatically excluded from analysis.
\begin{demo}{One record, two input paths}
\gradboxplot[width=52mm,height=5ex,palette=accessible]{0,2,3,4,5,6,7,8,16}
\quad
\gradboxsummary[width=52mm,height=5ex]{n=9,q1=3,median=5,q3=7,
  low=0,high=8,outliers={16}}
\end{demo}
The example keeps the box, whiskers, median and outlier distinguishable,
with \key{height=5ex} for readability. With \key{0,1,2,3,100}, the outlier
at 100 compresses the main 0--3 range to about 3\% of the total width.
Increasing width alone does not resolve this linear-scale effect. Report
extreme outliers separately with an explicit explanation when needed; never
silently remove them or change their positions.
The default \key{box range=auto} includes outliers; a constant range expands
only for drawing. Use \key{box range=fixed,min=...,max=...} or a named scale
for comparisons. n=0 displays missing; n=1 is constant; n=2 follows the same
formula. Coincident outliers overlap but keep their count in alternative text.
Box whiskers are not confidence intervals. Percent formatting is rejected.
\begin{demo}{Readable statistics and native columns}
\gradcomputesummary{0,2,3,4,5,6,7,8,16}{%
  n=\gradstat{n}; median=\gradstat{median};
  outliers=\gradstat{outlier count}}
\par\medskip
\begin{center}
\begin{gradtable}[align=c,header align=c,style=distribution,width=\linewidth,scale=column]
\gradcolumn{name}{Method}
\gradcolumn[type=boxplot,options={height=5ex,palette=accessible}]{samples}{Distribution}
\gradrow{Alpha,{0,2,3,4,5,6,7,8,16}}
\gradrow{Beta,{-3,0,2,5,9,12,14}}
\gradrow{Missing,NA}
\end{gradtable}
\end{center}
\end{demo}
\key{\gradstat} is available within the callback of \key{\gradcomputesummary}.
Fields include n, missing, min, max, mean, q1, median, q3, iqr, low, high,
outliers, outlier count and method. \key{\gradsummarytext} prints the main
statistics. Precomputed records require n, q1, median, q3, low and high;
unknown missing/outlier counts remain unknown. No algorithm can be verified
without the samples. Optional extrema, mean and outliers are checked for
consistency. Raw samples are not silently pooled across rows or groups.