The mean average — Mathematics, 11–13 years
One number that represents a set of values by sharing their total equally. Mathematics, 11–13 years.
Sharing a total evenly
The mean is found by combining all the values and then sharing the total equally between them. It gives a central number that represents the group, even though no original value may equal it. The word average is often used for this kind of mean.
Why compress the data?
A list of many measurements can be hard to compare with another list. One fair summary makes the overall level easier to see, such as the typical number of points in several matches. The mean is useful when every value should contribute to the result, rather than choosing just the biggest or smallest one.
Calculating a mean
Find the mean of 6, 8, 10 and 12. Add the values: 6 + 8 + 10 + 12 = 36. There are four values, so divide 36 by 4: 36 ÷ 4 = 9. The mean is 9; four scores of 9 would have the same total of 36.
Dividing by the wrong count
A common mistake is adding correctly but dividing by a number that is not the number of values, perhaps because the total or the largest value stands out. This is understandable: the same list contains several numbers to use. Count the entries, not their sum, and divide the total by that count.
A number for comparison
Teams can compare mean points across matches, or a weather station can report a mean temperature for a week. The mean is only a summary, so it can hide important differences: two groups may have the same mean but very different individual results. Check the original values when that detail matters.
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