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.
Vocabulary in this text
- average /ˈævɚɪdʒ/ — the result of adding values and dividing by their number
- describe /dɪskɹˈaɪb/ — to say what someone or something is like
- reduce /ɹəˈdus/ — to make something smaller or less
- recover /ɹɪˈkʌvɚ/ — to become well again
- minutes /ˈmɪnəts/ — the written record of what a meeting decided
- tally /ˈtæli/ — to count things one by one and record them
- result /ɹɪˈzʌlt/ — what happens because of something