Sample Quantiles in Statistical Packages
The American Statistician, 50 (4):
361--365 (November 1996)ArticleType: research-article / Full publication date:
Nov., 1996 / Copyright © 1996 American Statistical
Association.DOI: 10.2307/2684934
Abstract
There are a large number of different definitions used for
sample quantiles in statistical computer packages. Often
within the same package one definition will be used to
compute a quantile explicitly, while other definitions may
be used when producing a boxplot, a probability plot, or a
QQ plot. We compare the most commonly implemented sample
quantile definitions by writing them in a common notation
and investigating their motivation and some of their
properties. We argue that there is a need to adopt a
standard definition for sample quantiles so that the same
answers are produced by different packages and within each
package. We conclude by recommending that the
median-unbiased estimator be used because it has most of
the desirable properties of a quantile estimator and can be
defined independently of the underlying distribution.
