The lower quartile, median and upper quartile are usually denoted by Q_1, Q_2 and Q_3. To find them you must first arrange the data in order of size.

If n is odd, then Q_2 is the \frac{1}{2}(n+1)th value. If n is even the median is halfway between the \frac{1}{2}nth value and the next.

To find Q_1 find the median of the lower half of the data. To find Q_3, find the median of the upper half of the data.

If n is odd, then Q_2 is the \frac{1}{2}(n+1)th value. If n is even the median is halfway between the \frac{1}{2}nth value and the next.

To find Q_1 find the median of the lower half of the data. To find Q_3, find the median of the upper half of the data.

## Software/Applets used on this page

## Glossary

### median

the middle value of a set of data that has been arranged in order of magnitude; half the data values are above it and half are below.

### quartile

In an ordered set of data 25% are below the first (Q

_{1}), 50% are below the second (Q_{2}), 75% are below the third (Q_{3}).### union

The union of two sets A and B is the set containing all the elements of A and B.