Year 10 Interactive Maths - Second Edition

Quartiles

• The median is the middle value of the data set.

• The lower quartile (Q₁) is the median of the lower half of the data set.

• The upper quartile (Q₃) 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 of spread 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.
• The lower quartile, median and upper quartile are often denoted by Q₁, Q₂ and Q₃ respectively.
• The median is also denoted by m.

Key Terms

quartiles, median, lower quartile, upper quartile, interquartile range, outliers