Law of total variance

The law of total variance states that the total variation or variation in any one thing can be broken down into two parts: the variation that is explained by different groups and the variation that is not explained.

Think of an experiment you might do at school with five different groups of kids. You want to measure how tall each group is. The law of total variance states that the variation or difference in the heights of the groups can be broken down into two parts: the variation that is because some groups have taller kids than other groups and the variation that is because within each group, the kids are not all the same height.

So, using the law of total variance, you can look at the different heights of the groups and say that some of the differences in height are due to the different groups and some of the differences are just because the kids within each group are different heights.