Sample Quantiles in Statistical Packages

Rob J. Hyndman, Yanan Fan

Research output: Contribution to journalArticleResearchpeer-review

628 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)361-365
Number of pages5
JournalThe American Statistician
Issue number4
Publication statusPublished - 1 Jan 1996


  • Percentiles
  • Quartiles
  • Sample quantiles
  • Statistical computer packages

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