The mean as fair sharing — Data, 7–10
The mean tells us what each result would be if the total were shared equally. Data, 7–10 years.
Make the amounts equal
The mean, often called the average, is found by combining all the values and sharing the total equally between them. Imagine moving counters from taller piles to shorter piles until every pile has the same height. That equal height is the mean.
Why use a mean?
A list of many results is difficult to describe with every number. The mean gives one fair-share value that summarises the whole group, while still using every result in the calculation. It is useful when we want the group’s overall level, not the most common result.
Sharing points fairly
Three games give scores of 4, 6 and 8. First add them: 4 + 6 + 8 = 18 points. Then share 18 equally between the three games: 18 ÷ 3 = 6. The mean score is 6, which is also what each game would have if the points were levelled out.
The mean need not be a result
People often expect the mean to be one of the original numbers. That feels natural because the mean describes the same group, but it represents a fair share, not a selected result. For 2, 3 and 4, the mean is 3; for 1, 2 and 4, it is 2⅓.
Mean in real life
A family can find its mean weekly water use, or a coach can summarise scores across several matches. The mean is useful for a broad picture when every measurement matters. It can be misleading if one unusual result is much larger or smaller than the others, so the original data still matter.
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