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:

The second quartile of $D$ is defined as the median of $D$.

It is commonly denoted $Q_2$.

The first quartile of $D$ is defined as the median of the data values in $D$ below and not including the second quartile $Q_2$.

It is commonly denoted $Q_1$.

The third quartile of $D$ is defined as the median of the data values in $D$ above and not including the second quartile $Q_2$.

It is commonly denoted $Q_3$.

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