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单词 Percentile
释义

percentile


Given a distribution functionMathworldPlanetmath FX of a random variableMathworldPlanetmath X, on a probability spaceMathworldPlanetmath (Ω,B,P) a p𝑡ℎ-percentile of FX for a given real number p, is a real number r such that

  1. 1.

    P(Xr)p100,

  2. 2.

    P(Xr)1-p100.

Remarks.

  • The most common percentiles of a distribution function are the median (http://planetmath.org/MedianOfADistribution) (the 50th-percentile or the second quartile), the lower quartile (the 25th-percentile or the first quartile), and the upper quartile (the 75th-percentile or the third quartile).

  • In practice, the quartiles are calculated as follows: calculate the median m first, then the median of the data points below m is the first quartile, and the median of the data points above m is the third quartile.

  • The interval between the first quartile and the third quartile is called the interquartile range, or IQR for short. Sometimes, the difference between the first and third quartiles is also called the IQR. Like standard deviationMathworldPlanetmath, IQR is a measure of dispersion. However, IQR is a more robust statistic.

Titlepercentile
Canonical namePercentile
Date of creation2013-03-22 16:17:13
Last modified on2013-03-22 16:17:13
OwnerCWoo (3771)
Last modified byCWoo (3771)
Numerical id17
AuthorCWoo (3771)
Entry typeDefinition
Classificationmsc 62-07
Synonymfirst quartile
Synonymthird quartile
SynonymIQR
Definesquartile
Definesupper quartile
Defineslower quartile
Definesinterquartile range

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更新时间:2025/5/3 15:17:29