Range and standard deviation

An average on its own hides as much as it shows. Two sets of marks can share a mean of 60 while one class is clustered around it and the other is split between people who understood and people who did not.

The range, the largest minus the smallest, is the crude measure, and it is decided entirely by the two most extreme values. Standard deviation is the careful one: roughly, the typical distance of a value from the mean. A small standard deviation means everyone is near the average; a large one means the average describes almost nobody.