Unexplained variance is a term used in analysis of variance (ANOVA). ANOVA is a statistical method of comparing the means of different groups. It compares the variance within the groups to the variance between the groups. The former is also called unexplained variance, because it is not explained by the groups. For example, if you wanted to compare the heights of men and women, there would be variation within the groups because not all people of the same gender are the same height and between groups because men and women differ in average height, as well. The former is unexplained variance.
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Square the values in the first group. In the example, square all the heights of men in your sample.

Sum these squared values.

Sum the original values in the first group. In the example, sum the heights of all men in your sample.

Square the result of Step 3.

Divide the result in Step 4 by the number of subjects in the first group. In the example, this would be the number of men in your sample.

Subtract the result in Step 5 from the result in Step 2.

Repeat Steps 1 through 6 for the other groups. In the example, do this for women in your sample.

Sum the final numbers for each group. This is the unexplained variance.