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A median is the middle value (or pair of values) when a list is sorted. The quartiles are the values at the quarter and three-quarter points in the list.

If a list is sorted and divided into four, the lower quartile is at the first quarter point. The median is at the second quarter point (which is halfway). The upper quartile is at the third quarter point.

The inter-quartile range is the range of values between the lower quartile and the upper quartile, and is used as a measure of spread when comparing two or more sets of data because it ignores any outliers (data which may be extreme or unusual).

Example 1

A survey of the number of birds in a garden at any one time was taken in a town. The number recorded at 9am for each garden was:

5, 11, 3, 8, 14, 6, 4, 1, 7, 19, 13, 5, 11, 16, 4, 8, 10, 1, 11, 13, 9, 13, 4

Find the interquartile range for the number of birds in gardens at 9am.

Sort the data into order:

1, 1, 3, 4, 4, 4, 5, 5, 6, 7, 8, 8, 9, 10, 11, 11, 11, 13, 13, 13, 14, 16, 19

There are 23 items, the lower quartile is the `frac(23+1)(4)` = 6th value. The upper quartile is the 18th value (3 x 6).

The 6th value = 4. the 18th value is 13.

Interquartile range = 13 - 4 = 9.

Answer: 9

Example 2

The batting performance of two cricket clubs are being compared. The Swifts have a median of 145 and an interquartile range of 22. The Bears have a median of 157 and an interquartile range of 36.

Compare the two clubs.

Compare both medians; and note that the Swifts have a smaller interquartile range and discuss what that means.

Answer: The Swifts are more likely to achieve their median score of 145 as they have a smaller interquartile range than the Bears. However, the Bears have a higher median score.

See also Median and Box plots