Definition:Quartile

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

Let $D$ be divided into precisely $4$ classes.

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:


 * The second quartile, $Q_2$, is defined as the median of $D$


 * The first quartile, $Q_1$, is defined as the median of the data values below and not including $Q_2$


 * The third quartile, $Q_3$, is defined as the median of the data values above and not including $Q_2$

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.


 * As mentioned above, the second quartile is often referred to as the median.

Also see

 * Definition:Interquartile Range
 * Definition:Percentile
 * Definition:Quantile