Median vs Mean: When Averages Lie
Median vs mean explained: why income and house prices always use the median, how one outlier distorts the mean, and which average to use for skewed data.
When a news story reports average income, the choice of average is doing more work than any other decision in the article. Mean and median describe the same dataset and can differ by a factor of two.
Definitions
Mean — add every value, divide by the count. Uses all the data; every observation pulls on the result.
Median — sort the values, take the middle one (or the average of the two middle values for an even count). Uses only position, so extreme values have no more influence than any other.
Mode — the most frequent value. The only one that works for categories, and the only one that can have several answers or none.
The salary example
A ten-person startup:
$42,000 · $45,000 · $48,000 · $52,000 · $55,000 · $58,000 · $61,000 · $67,000 · $74,000 · $520,000
Mean = $1,022,000 ÷ 10 = $102,200 Median = (55,000 + 58,000) ÷ 2 = $56,500
The mean says a typical employee earns six figures. Nine of the ten earn less than three-quarters of it. The founder's compensation moved the mean by $46,000 and the median not at all.
Remove that one salary and the mean drops to $55,778 — almost exactly the median. That collapse is the signature of a single outlier doing all the distortion.
Three datasets compared
| Dataset | Mean | Median | Mode | Best summary |
|---|---|---|---|---|
| Test scores: 72, 75, 78, 78, 81, 84 | 78.0 | 78.0 | 78 | Mean (symmetric) |
| Salaries above | $102,200 | $56,500 | none | Median (right-skewed) |
| House prices: 280k, 310k, 325k, 340k, 2.4m | $731,000 | $325,000 | none | Median (outlier) |
| Shirt sizes sold: S, M, M, L, M, XL | n/a | n/a | M | Mode (categorical) |
Why skew decides it
Income, house prices, wealth, and web-session durations all share a shape: bounded at zero on the left, with a long tail stretching right. Nothing earns negative income, but a few people earn a hundred times the typical amount. In any right-skewed distribution, mean > median, and the gap widens with the tail.
That is why every statistical agency reports median household income and median home price. The mean is not wrong — it is a correct statement about a total divided by a count — but it does not describe a typical case, which is what readers assume an average means.
For roughly symmetric data — heights, test scores, measurement errors — mean and median converge and the mean is preferable, because it uses all the information and feeds directly into standard deviation, confidence intervals, and most inferential statistics.
Which to use
- Mean: symmetric data, no significant outliers, and any time you need a total (mean × count = sum).
- Median: skewed data, known outliers, ordinal data, or whenever you want to describe a typical case.
- Mode: categorical data, or finding the most common outcome in a discrete distribution.
- Report both: when they differ substantially, that gap is itself the story.
FAQ
Why do house prices use median instead of average? A handful of very expensive sales pull the mean far above what a typical buyer pays. The median is not affected by how extreme the top of the market is.
Is the median always better than the mean? No. On symmetric data the mean is more efficient and underpins most statistical methods. The median wins specifically where skew or outliers are present.
What does it mean if the mean is much higher than the median? The distribution is right-skewed — a small number of large values are pulling the mean up. Income and wealth data almost always show this pattern.
Compute all three at once with the Mean, Median, Mode Calculator, then measure the spread using the Standard Deviation Calculator. For what that spread actually tells you, read standard deviation explained.
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*Check both on your own data: use the Mean, Median, Mode Calculator.*