## 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.

Original language | English |
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Pages (from-to) | 361-365 |

Number of pages | 5 |

Journal | The American Statistician |

Volume | 50 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Jan 1996 |

## Keywords

- Percentiles
- Quartiles
- Sample quantiles
- Statistical computer packages