Why is the variance additive? An intuition.

The variance of some data can be defined in rough terms as the mean of the squared deviations from the mean. Let’s repeat that because it is important: Variance: Mean of squared deviations from the mean. An example helps to illustrate. Assume some class of students are forced to write an exam in a statistics class (OMG). Let’s say the grades range fom 1 to 6, 1 being the best and 6 the …