how to calculate variance

Variance is a measure of dispersion. Please visit the variance page for a definition and brief explanation. Here is a description of how to calculate sample variance.

Imagine you are studying happiness, using a 10 point scale. Five people agree to participate in your happiness study, and do your questionnaire. From those five people, you get the following scores:

3,4,5,6,7

The first thing to calculate is the average, or mean. In this case, the mean is 5.

The second thing is to find the "distance from the mean" for each score. (ie score - mean, written mathematically as x-). These numbers are

-2,-1, 0,1,2

The third step involves squaring each of those numbers. This will give us the "squared distance from the mean". We get

4,1,0,1,4

The fourth step involves adding these numbers together.

4 plus 1 plus 0 plus 1 plus 4 equals.... 10

The final step, divide by N-1, where N is the number of scores. In this example, N is 5, so N-1 is 4.