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The aggregation illusions · Mean vs median

Most people earn below average.

That sentence sounds wrong, and it is true. When a few values are enormous, the average stops describing anyone — and the question that saves you is which average they mean.

A room of thirty people Each bar is one person’s income, sorted poorest to richest. Watch the two “averages” pull apart.
£20k £500M

An ordinary earner The newcomer The average (mean) The typical person (median)

The average (mean)
what a headline reports
The typical person (median)
the middle of the room
Earn below the average

Fig. 1 — One value, two stories. Nothing here is fudged: every bar is a real income and both lines are computed correctly. The average is a balance point, so a single huge value hauls it away from the crowd; the median only cares who is in the middle, so it barely flinches. Drag the slider down and watch the two lines fall back together.

The short answer

What is the difference between the mean and the median?

The mean is what most people call the average: add up every value and divide by how many there are. The median is the middle value — line everyone up from smallest to largest and take the one in the centre. For symmetric data the two nearly agree; for skewed data, like income or wealth, the mean is pulled toward the extreme values while the median stays with the typical case.

The question that saves you

When they say “average”, do they mean the typical person?

Usually not. “Average” almost always means the mean — add everything up and divide. For money-shaped things (income, wealth, house prices, investment returns), a handful of very large values drag the mean far above what an ordinary person has. The median — the person in the exact middle — is the honest “typical”. When the two disagree, the gap between them measures how lopsided the data are, and the median is the one to trust.

AskMean or median — and how skewed is the thing it is summarising?

01 · The two averages

What is the difference between the mean and the median?

There are two everyday “averages” and they answer different questions. The mean is the one you were taught at school: add up every value and divide by how many there are. The median is simpler than it sounds — line everyone up from smallest to largest and point at the person in the exact middle. Half are below them, half above.

For a tidy, symmetric set of numbers — the heights of a class, say — the mean and the median land in almost the same place, and it does not matter which you quote. Money is not tidy or symmetric, and that is where the trouble starts.

Half of everyone sits below the median — that is what “middle” means. It only sounds alarming when we expect “average” to mean “typical”, and it doesn’t.

02 · Why money breaks the average

Why one billionaire makes everyone look poor

Incomes, wealth, house prices and returns are right-skewed: most people are bunched together at modest amounts, with a long, thin tail of the very rich stretching far out to one side. The mean is a balance point, so it is exquisitely sensitive to that tail. Move one person in our room of thirty from £50,000 to £50 million and the mean leaps by well over a million pounds — while the median does not budge a penny. You watched it happen above.

The famous version: when Bill Gates walks into a small bar, the average wealth of the drinkers rockets into the billions, and on paper everyone is a millionaire. Nobody’s actual wallet has changed. The average has simply stopped describing anyone in the room.

This is why “the average UK salary is about £35,000” and “average household wealth is in the hundreds of thousands” can be true and still mislead: the median salary and the median wealth are noticeably lower, because the means are inflated by the top few per cent. “Most people earn below average” is not a riddle — for skewed data it is simply how things are.

03 · Where it bites

The same trick, in real headlines

Once you can see it, the swap is everywhere a few big values hide in the data:

Pay and wealth. Statistics agencies report both the mean and the median; a headline can pick whichever flatters its story. “Average pay rose to £X” sounds like everyone’s pay rose, even when the median — the typical worker — barely moved and the mean was lifted by bonuses at the top.

House prices. A handful of mansions pull the average price well above the median, so the “average home” can cost far more than the home a typical buyer actually faces.

Investment returns. A fund’s quoted average annual return can sit comfortably above what its typical investor earned, because a few extreme years — and the order they come in — distort the simple average. That is its own illusion, the volatility drag.

“The average customer.” When a few “whales” spend enormously, the mean spend per customer describes none of them, and a business that plans for the average plans for a person who does not exist.

04 · How not to be fooled

How to read an “average” safely

Ask which average it is. If a figure is only ever called “the average”, assume it is the mean, and ask for the median. Reputable sources give both.

For anything money-shaped, prefer the median. Income, wealth, prices, returns, waiting times and durations are all skewed; the median is the trustworthy “typical” for every one of them.

Treat a large mean–median gap as a skew alarm. The further apart they are, the harder a few extreme values are pulling the mean — and the more misleading the word “average” becomes.

Be wary of “X% are above average”. For skewed data, far fewer than half can be above the mean, so “most are below average” is ordinary, not a scandal — and “above average” is a lower bar than it sounds.

When you can, look at the shape of the whole distribution, not a single number. One number can only ever tell one story, and a skewed world has at least two.

Continue the field guide

More ways an average can betray you