The lower quartile (Q_{1}) is the median of
the lower half of the data set.

The upper quartile (Q_{3}) is the median of
the upper half of the data set.

The interquartile range (IQR) is the spread of the
middle 50% of the data values. So:

The interquartile range is a more useful measure ofspread than range as it describes the middle 50% of the data values and thus,
is less affected by outliers.

Example 6

Find the median, lower quartile, upper quartile and interquartile range
of the following data set of scores:

19 21
24 21
24 28
25 24 30

Solution:

Arrange the score values in ascending order of magnitude:

19 21
21 24
24 24
25 28 30

There are 9 values in the data set.

This means the middle 50% of the data values range from 21 to 26.5.

Note:

The quartiles divide the set of measurements into four equal parts. Twenty-five
per cent of the measurements are less than the lower
quartile, fifty
per cent of the measurements are less than the median and seventy-five
per cent of the measurements are less than the upper
quartile. So,
fifty per cent of the measurements are between the lower quartile and
the upper quartile.