One giant number spoils it
Why Is the Average Sometimes a Lie?
The average moves when one value is extreme. The middle value does not.
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Step 1 of 5
An average shares everything out equally.
Add every value and divide by how many there are. It answers: if everyone had the same, how much would that be?
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Step 2 of 5
One extreme value drags it far.
Nine people earning twenty thousand and one earning ten million have an average income of over a million. Nobody in the room has it.
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Step 3 of 5
The middle value ignores the extreme.
Line everyone up in order and point at the person in the middle. Making the top person a billionaire does not move that finger at all.
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Step 4 of 5
Which one is honest depends on the question.
For a total shared out — a bill, a rainfall — the average is exactly right. For a typical person, the middle value is far better.
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Step 5 of 5
Reports pick whichever suits.
'Average house price' and 'typical house price' are different numbers, and which one appears in a headline is a choice, not a fact.
A third summary, the commonest value, is different again — useful for shoe sizes, useless for incomes.
The short version
An average is pulled by extreme values while the middle value is not, so which is honest depends on the question asked.
Try it yourself
Write down what nine friends earn, then add one billionaire. Watch the average move and the middle value stay put.
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