Why is the variance of the difference the sum of the variances?
The means of variables behave very intuitively, but not so the variances, and many pupils find this very difficult to really come to terms with. Even if they can say the right words when asked it explicitly, they will often subtract the variances when in the middle of a problem which involves a difference of variables. Research indicates that confronting a misconception explicitly can help to resolve the cognitive conflict which lies behind it.