\begin{definition}[Definition:Quartile]
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 $Q_2$
\end{definition}