The problem with averages in class

A class average of six out of ten can describe two completely different classes.

In the first, almost every student scored between five and seven. The teaching reached most people, and a small adjustment would help nearly everyone. In the second, half the class scored nine and half scored three. The average is identical and the situation is not remotely the same: one group needs harder work and the other needs a different starting point entirely.

The average cannot tell these apart, because an average throws away the spread by design. That is what it is for — reducing many numbers to one — and the cost is exactly the information a teacher most needs.

Two cheap additions recover most of it. The first is the range: the lowest and highest score. The second is counting how many students fall into each band of two marks, which takes about three minutes with a tally and produces a shape you can see.

Students can use the same idea on their own results. A set of marks averaging seven that runs from four to nine is telling you something different from a set that sits between six and eight, and the first one usually means there is a particular topic missing rather than a general weakness. Looking at the spread of your own results is a three-minute exercise that most people never do.