1.6 Measure Of Dispersion

A measure of central tendency on its own says very little. Two sets of marks can share the same mean while one is tightly bunched around it and the other is scattered from top to bottom of the scale, and no average will tell them apart. What is missing is a measure of how far the observations lie from the centre – a measure of dispersion, or variability.

For that reason a measure of variability is nearly always reported alongside a measure of central tendency; quoting one without the other gives an incomplete picture. Small variability means the observations cluster closely about the mean, so the mean is a dependable summary of them. Large variability means they are widely spread, and the mean, though still correct, describes any individual observation poorly.

The four common measures of variation are the range, the variance, the standard deviation and the coefficient of variation. They are taken in turn below.

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