Skip to story
ELI5 Yahaaa

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.

Average Pulled by the biggestnumberMiddle value Stands where mostpeople are
Two honest summaries of the same nine people.
  1. Step 1 of 5

    An average shares everything out equally.

    1 Add them all up2 Divide by howmany3 Everyone getsthe same

    Add every value and divide by how many there are. It answers: if everyone had the same, how much would that be?

  2. Step 2 of 5

    One extreme value drags it far.

    What nine people earn£20,000What the average saysover £1,000,000

    Nine people earning twenty thousand and one earning ten million have an average income of over a million. Nobody in the room has it.

  3. Step 3 of 5

    The middle value ignores the extreme.

    Average Leaps when one valueleapsMiddle value Does not move

    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.

  4. Step 4 of 5

    Which one is honest depends on the question.

    Sharing a total The average is theanswerDescribing a typical case The middle value is

    For a total shared out — a bill, a rainfall — the average is exactly right. For a typical person, the middle value is far better.

  5. Step 5 of 5

    Reports pick whichever suits.

    1 The same data2?Two honestsummaries3 One headline

    '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.

Topics