Levelling everyone off
What Does an Average Actually Tell You?
An average is the height everyone would have if the total were shared out evenly.
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Step 1 of 4
An average answers a sharing question.
Pour everyone's amount into one pile, then share it back out equally. Whatever each person ends up with is the average.
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Step 2 of 4
Adding and dividing does exactly that.
Adding makes the single pile and dividing by how many people shares it back. The familiar recipe is just that story in symbols.
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Step 3 of 4
Nobody has to actually have it.
The average family has 2.4 children, and no family anywhere has 2.4 children. An average is a fact about a group, and it is allowed to be a number no single member could possibly be.
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Step 4 of 4
It is one number standing in for many.
That is the whole bargain. You get something short enough to say out loud, and in exchange you give up everything about how the amounts differed — which sometimes matters enormously.
When the difference between the amounts is the interesting part, the middle value is usually the better summary — `median-vs-average` is about exactly when.
The short version
An average is what everyone would get if the total were shared out evenly — a fact about a group rather than any member, and one number standing in for all the ways they differed.
Try it yourself
Work out the average height of your family, then check how many people are actually that height. Often nobody is.