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).

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

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.

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