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Measures Of Dispersion

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We have seen the different ways that you can determine an average value for a set of data, but it is also important to know about the results as a whole. Are they all close to the average value or are they all spread out? This information can be as important as the average, when analysing a set of data.

You can see that these two graphs have the same average value, but have completely different distributions.

The most important measure of dispersion is the standard deviation, which we shall look at on the next page.

The Interquartile Range

The measure of dispersion that is usually quoted with the median, is the interquartile range. This tells you the range of values covered by the middle 50% of data.

To find the interquartile range, you need to know two values, the lower quartile, (the value one quarter of the way through the sample,) and the upper quartile, (the value three quarters of the way through the sample.)

x
f	2	7	10	9	5	3
cf	2	9	19	28	33	36

To estimate the interquartile range, the easiest method is to draw a cumulative frequency polygon. Since there are 36 pieces of data in our sample, the lower quartile will be the 9^th value and the upper quartile will be the 27^th value.

From the graph, it easy to read off the upper and lower quartiles, in the same way that we read off the median.

From our graph we can see that the UQ=39 and the LQ=20.

Therefore the Interquartile Range is given by

Although the Interquartile Range is useful, by far the most common measure of dispersion is the standard deviation.

Go To Standard Deviation

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