# Definition:Quartile

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## 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

## Sources

- 2011: Charles Henry Brase and Corrinne Pellillo Brase:
*Understandable Statistics*(10th ed.): $\S 3.3$