Box and Whisker Plot (Text-based)

Menu location: Graphics_Box and Whisker (Text).

Box and Whisker plots, described by Tukey (1977), give a pictorial representation of nonparametric descriptive statistics.

In nonparametric terms, the central "box" represents the distance between the first and third quartiles with the median between them marked with a diamond, with the minimum as the origin of the leading "whisker" and with the maximum as the limit of the trailing "whisker".

Note that some software plots the upper and lower hinge and not the upper and lower quartile in box and whisker plots. The upper hinge is the 3(n+1)/4th value whereas the upper quartile is the (3n+1)/4th value.

This convention can also be extended to parametric representation of data using the arithmetic mean bounded by one standard deviation or by its confidence interval. StatsDirect enables you to choose one of these two parametric schemes or the nonparametric scheme for each plot. See descriptive statistics for the formulae used.

This is a useful way to present data to an audience; it is often easier to convey the central location and spread of values pictorially than by quoting a list of descriptive statistics.

Box and whisker plot from Test workbook

Town Boys | >----------[........*.............]-----------------<

Farm Boys | >-------[............*........]--------<

/+--------------+--------------+--------------+--------------+

0 5 10 15 20

min -[ lower quartile - median - upper quartile ]- max

See also the graphical box and whisker plot.