Abstract
Letter values were introduced and named by J. W. Tukey in the 1970s as selected quantiles. The idea is to choose a small set of quantiles to characterize an ordered sample of values, quantiles that are each defined as either individual order statistics or the mean of two such statistics. The procedure is to start with the median, to continue with quartiles, and then with first and last octiles, and so on. At each step, approximate medians are identified of successively smaller tail fractions until the extremes, the minimum and maximum, are reached. As a historical aside, the same idea can be identified in work by Francis Galton from 1880.
Letter values are supported by Stata through the official command