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. See descriptive statistics for the formulae used. StatsDirect enables you to choose one of these two parametric schemes or the nonparametric scheme for each plot. 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. The upper hinge is the 3(n+1)/4th value whereas the upper quartile is the (3n+1)/4th value.
Note that some software plots the upper and lower hinge and not the upper and lower quartile in box and whisker plots.
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'. Box and Whisker plots, described by Tukey (1977), give a pictorial representation of nonparametric descriptive statistics.