The mean is the total divided by the number of values: for 2, 3, 4 and 11, the mean is 5. The median is the middle value once you sort them: for the same set, it is 3.5. Both are averages, but extreme values drag the mean and leave the median almost untouched.
The core difference
Both answer "what's typical here?", and they answer it differently. The mean takes every value into account, so one enormous number changes it. The median only cares about position in the sorted list, so it ignores how extreme the extremes are.
Take five salaries: £24,000, £26,000, £28,000, £31,000 and £310,000.
- Mean: £83,800 — a figure nobody in the room earns.
- Median: £28,000 — the middle person's actual pay.
This is why housing and income statistics are almost always reported as medians. A handful of very large values would make the mean describe a world nobody lives in.
How to calculate each
Mean: add all the values, divide by how many there are.
Median: sort the values low to high. With an odd count, the median is the middle one. With an even count, it is the mean of the two middle values — which is why the median of 2, 3, 4, 11 is 3.5, a number not in the set at all.
The test to run
Look at your data and ask: does it contain outliers, or is it skewed?
- If a few values sit far from the rest — incomes, house prices, response times, donation sizes — report the median.
- If the values cluster fairly symmetrically around a centre — heights, exam marks, daily temperatures — the mean is fine, and it is the more informative of the two because it uses every data point.
A quick diagnostic: calculate both. If they are close, either will do. If they diverge sharply, the data is skewed and the median is the honest summary — and the gap between them is itself worth reporting.
The third one people forget
The mode is the most frequently occurring value. It is the only average that works on non-numeric data — you can have a modal shoe size or a modal answer on a survey, but not a mean one.
The mistakes that matter
The first is linguistic: "average" in everyday English usually means the mean, but strictly it covers all three. If precision matters, name which one you used rather than writing "the average".
The second is presentational, and it is how statistics mislead honestly-written reports. Quoting a mean for skewed data is not false, but it invites the wrong conclusion — "average household wealth" figures routinely sit above what most households have. If you are choosing between them because one number looks better, that is the moment to publish both.
Finally, the mean of a set of averages is not the average of the underlying data unless the groups are the same size. Averaging three class averages only works if the classes are equally full.
Frequently Asked Questions
Is the average the mean or the median?
In everyday use, "average" almost always means the mean. Technically it is an umbrella term covering the mean, median and mode, so in reports it is clearer to name the one you used.
When should I use the median instead of the mean?
Whenever the data is skewed or contains outliers — incomes, house prices, waiting times. The median describes the typical case, while one extreme value can pull the mean far away from it.
How do you find the median of an even number of values?
Sort them, take the two middle values and average those. For 4, 6, 9 and 15, the middle pair is 6 and 9, so the median is 7.5.