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.


  2. 2.



  • The most common percentiles of a distribution function are the median ( (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.

Title percentile
Canonical name Percentile
Date of creation 2013-03-22 16:17:13
Last modified on 2013-03-22 16:17:13
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 17
Author CWoo (3771)
Entry type Definition
Classification msc 62-07
Synonym first quartile
Synonym third quartile
Synonym IQR
Defines quartile
Defines upper quartile
Defines lower quartile
Defines interquartile range