Measures of Variability: Variance and Standard Deviation

The most commonly used measure of variability to describe scores in a distribution is the standard deviation. It is an index that indicates how spread out scores are in a distribution relative to the average score. In effect, the index reflects something like the average dispersion or deviation of the scores (X) about their mean; the greater the spread of scores, the greater the standard deviation.

For example, in the figure below, both distributions have the same mean, but scores in distribution A cluster more tightly about the mean than the scores in distribution B. If only the mean is used to represent how subjects in the respective distributions performed, it would seem reasonable to conclude that both groups were about the same.

Comparison of
variability in two distributions

As is apparent, however, subjects in group A had much less variability in performance than those in group B. Group B subjects were more heavily represented in the tails of the distribution than were those in group A. This might indicate that there was some interaction between subject aptitudes or abilities and the specific treatment resulting in less uniform performance for subjects in group B.

What is important to note is that in the absence of context, the mean alone is not a good indicator of how people, in general, performed. The mean becomes more interpretable when accompanied by an index of variability describing how scores in the distribution deviate from the average.