The mean: sharing the total equally — Mathematics, 11–13
The mean is what each value would be if the total were shared out equally, and it reacts to every single value.
The mean is a fair share
The mean of some values is the value each one would have if the total were shared out equally. If five friends have 6, 2, 9, 4 and 4 stickers and they share everything so that all end up with the same number, that number is the mean. It is also the balance point of the data: the value where the small ones and the big ones cancel each other out. Saying “the mean is 5” means “on average, each one has 5”.
One number to describe a group
A long list of numbers is hard to compare with another list. The mean sums a group up in a single value with a meaning: if the mean of the books read in a reading club is 5, you know how many each member would have read if everyone had made the same effort. That lets you compare two groups, or check whether a group is getting close to a goal, such as reading 7 books each.
The mean of 6, 2, 9, 4 and 4
Five friends have 6, 2, 9, 4 and 4 stickers. Step 1: add them all: 6 + 2 + 9 + 4 + 4 = 25. Step 2: share among 5 friends: 25 ÷ 5 = 5. The mean is 5 stickers. Check by sharing: the one with 6 gives 1 and the one with 9 gives 4 (5 to hand out); the one with 2 needs 3 and each of the two with 4 needs 1 (5 to receive). Everyone ends up with 5.
One odd value moves the mean
Four friends score 10, 12, 11 and 11 points: the sum is 44 and the mean is 44 ÷ 4 = 11. If the last score is 51 instead of 11, many people think the mean stays near 11 because “only one changed”. But the sum becomes 84 and the mean 84 ÷ 4 = 21: the extra 40 is shared among all four (40 ÷ 4 = 10). The mean is sensitive to every value, and an atypical value pulls it towards itself. If a mean looks odd, look for an outlier.
Averages all around you
You meet means everywhere: the mean of goals per match of a team, the mean number of minutes you read per day, the mean temperature of a month. When a group has a goal, such as a reading club aiming at 7 books each, the mean tells you whether the group is getting there. It does not tell you who is behind, though, so it is worth looking at all the data too, not only at the mean.
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