Box-and-Whisker Plot
A box-and-whisker plot (sometimes called simply a box plot) is a histogram-like method of displaying data, invented by J. Tukey. To create a box-and-whisker
plot, draw a box with ends at the quartiles 
and 
. Draw the statistical median 
as a horizontal
line in the box. Now extend the "whiskers" to the farthest points that
are not outliers (i.e., that are within 3/2 times the interquartile
range of 
and 
). Then, for
every point more than 3/2 times the interquartile
range from the end of a box, draw a dot. If two dots have the same value, draw
them side by side (Gonick and Smith 1993, p. 21). Box-and-whisker plots are
implemented as BoxWhiskerPlot[data]
in the Wolfram Language package StatisticalPlots`
.
A number of other slightly different conventions are sometimes used. In Tukey's original definition, the closely-related and lesser known hinges 
and 
were used instead
of 
and 
(Tukey 1977,
p. 39). In addition, Tukey's original formulation lacked horizontal crossbars,
extended the whiskers all the way to the extreme data points, and drew an unfilled
dot at the maximum and a hatched horizontal strip at the minimum, as illustrated
above (left figure; Tukey 1977, p. 40). A variation extended the whiskers only
out to some arbitrary minimum and maximum values and identifying the outliers with
explicit labels (Tukey 1977, p. 41). Tukey also considered an additional variation
in which the outliers are indicated separately and whiskers are dashed, ending with
dashed crossbars at "adjacent values"
(values closest to but still inside the inner fences).
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