How tall is your class?

Suppose someone asks, 'How tall is your class?' What would you say? One number alone will not do it — you need the centre AND the spread.

Take a Grade 5 class. The boys' heights, in centimetres, are 147, 135, 130, 154, 128, 135, 134, 158, 155, 146, 146, 142, 140, 141, 144, 145, 150. The girls' are 143, 136, 150, 144, 154, 140, 145, 148, 156, 150, 150.

Draw a dot plot for the whole class, and one each for boys and girls. Then mark the mean and median on each. For the whole class, mean 144.4 and median 145; for the boys, mean 142.94 and median 144; for the girls, mean 146.9 and median 148.

Now read it. The boys' heights are more spread out, running from 128 to 158. The girls' lie between 136 and 156. So both the tallest and the shortest in the class are boys — a fact about VARIABILITY that no average could tell you.

Yet the boys' average height is less than the whole class average, and less than the girls'. So we can say the girls are taller than the boys in this class. Say that carefully: it does not mean every girl is taller than every boy, and the dot plot shows plenty of overlap.

For the boys, mean (142.94) is slightly below median (144), which indicates a small influence from values on the lower side. For the girls, mean (146.9) is below median (148) too, again a small pull from below.

The same reading works for any comparison. Two groups of children estimate a minute with their eyes shut. Group A: mean 58.21, median 60. Group B: mean 59.28, median 59.5. Group B's mean is closer to 60 seconds and its data is tighter around the centre; Group A's median is exactly 60 but its mean is pulled lower by some short guesses. Describing both the centre and the spread is what actually answers the question.