# 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.