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 in the Wolfram Language
as BoxWhiskerChart[data].

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).