Variance

When describing a distribution of scores, one should use at least three indices: the shape of the distribution (e.g., unimodal, normal, and skewed), a measure of central tendency (e.g., mean and median), and a measure of the spread of scores. The variance is an example of the latter measure. The importance of a measure for the spread of scores can be seen in the following example:

• Distribution X: 93 95 97 99 100 101 103 105 107
• Distribution Y: 75 80 90 95 100 105 110 120 125

Both distributions have the same mean ( = = 100), but the scores in distribution X cluster closer to the mean than those in distribution Y.

Several measures can be used to describe the spread of scores. The range ...