Definition:Quartile

Definition
Let $D$ be a finite collection of data regarding some quantitative variable.

Let $D$ be divided into precisely $4$ class intervals.

A $Q$th quartile is a value in the interval defined by the $Q$th class such that:


 * $\dfrac Q 4$ of the data in $D$ fall at or below the value chosen


 * $1 - \dfrac Q 4$ of the data in $D$ fall at or above the value chosen.

Arbitrarily more precise definitions may be contrived as necessary to define a unique quartile for a given study.

A common convention is:

Also known as

 * The first quartile is often referred to as the lower quartile.


 * The third quartile is often referred to as the upper quartile.


 * The term second quartile is often not used, and instead the median is referred to exclusively.

Also see

 * Definition:Interquartile Range
 * Definition:Percentile
 * Definition:Quantile
 * Definition:Five-Number Summary