Given a set of data, order the observations by size. Then divide the set into four such that each part contains a quarter of the observations. These are the quartiles.
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Find the difference between the values for quartile 3 and quartile 1.
First Quartile = 43 Third Qaurtile = 61
The interquartile range is the difference between the Lower quartile and the upper quartile. Obviously you need to be able to find these values. Haylock (2006) explains how to do this for difficult size groups in mathematics explained for primary teachers. He explains the position of the lower quartile is a quarter of (n+1) and that of the upper quartile is three-quarters of (n+1). So for a group of 7 numbers, you find a quarter of 8, which is 2. Therefore the number in second place is the lower quartile. Three quarters of 8 is 6 and so the number in 6th position is the upper quartile. Now take the lower quartile from the upper quartile.
The sides of the box are the quartile values: the left is the first quartile and the right is the third quartile. The width, therefore is the interquartile range.
the sum of the upper quartile and lower quartile is 56 and their difference is 24. find upper quartile and lower quartile.