Year 9 Interactive Maths - Second Edition

## Quartiles

If a data set of values is arranged in ascending order of magnitude, then:
• 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 the range as it describes the middle 50% of the data values.

#### Example 8

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

18     20     23     20     23     27     24     23     29

##### Solution:

Arrange the values in ascending order of magnitude:

18     20     20     23     23     23     24     27     29

There are 9 values in the data set.

This means the middle 50% of the data values range from 20 to 25.5.

###### 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.