Mean, Median and Mode: Which Average Should You Use?

Three Answers to Three Different Questions

"Average" is not one calculation. It is a loose word covering three, and they answer genuinely different questions about the same numbers:

Mean — add everything up and divide by how many there are. What would everyone get if the total were shared equally?
Median — sort the values and take the middle one. What does the typical, middle-ranked case look like?
Mode — the value that appears most often. What is the most common outcome?

When a figure is quoted as an average without saying which, it is nearly always the mean — and that is frequently the one least suited to the data.

Worked on the Same Data

Take the eight salaries at a small firm, in thousands of pounds:

21, 24, 25, 25, 27, 31, 38, 250

Mean: the total is 441, divided by 8 gives £55,125.

Median: with eight values there is no single middle, so take the two middle ones — the fourth and fifth, 25 and 27 — and average them: £26,000.

Mode: 25 is the only value appearing more than once, so the mode is £25,000.

Three legitimate averages of one data set, and the largest is more than double the smallest. Note also that seven of the eight people earn less than the mean. A figure that almost nobody reaches is a poor description of a typical salary.

Why One Value Breaks the Mean

The mean uses every value, so a single extreme figure — an outlier — pulls it a long way. The director on £250,000 adds roughly £28,000 to the mean on their own.

Remove that one salary and the mean of the remaining seven falls to £27,286, while the median barely moves, from £26,000 to £25,000.

That resistance is the median's defining property. It only cares about the order of the values, so replacing the top salary with £2.5 million would not change it at all.

This is why the Office for National Statistics reports UK earnings using the median, and why house prices and response times are usually quoted the same way. Income and price data are right-skewed — a long tail of high values with a floor at zero — and the mean systematically overstates the typical case for anything shaped that way.

Choosing the Right One

Use the mean when the data is roughly symmetric and free of extremes, and whenever the total matters. The mean is the only one of the three that reconstructs the total: mean × count returns the sum, which is what makes it the right tool for budgets, dosing, and anything you will multiply back up.

Use the median when the data is skewed or contains outliers you do not want to discard — incomes, house prices, waiting times, page load times. It is also the safer default whenever you do not yet know the shape of the data.

Use the mode for categorical data, where it is the only one that works at all. There is no mean shoe size sold or mean favourite colour, but there is certainly a most common one. For numeric data the mode is usually the least informative of the three.

The Mode's Awkward Cases

The mode misbehaves more than the others, and the exceptions are worth recognising.

A data set can have no mode, when every value appears exactly once. It can be bimodal or multimodal, with two or more values tied at the top.

Two clear peaks are usually a signal rather than a nuisance: they often mean two different populations have been mixed together. Heights across a mixed-sex group, or commute times that split between drivers and train users, will show two peaks. In that situation no single average describes the data honestly, and the right move is to separate the groups rather than to average across them.

An Average Alone Tells You Very Little

Two data sets can share a mean and have nothing else in common:

50, 50, 50, 50 — mean 50
10, 30, 70, 90 — mean 50

Identical averages, entirely different behaviour. Describing the second as "averaging 50" hides everything that matters about it, which is why an average is normally reported alongside a measure of spread:

Range: highest minus lowest. Quick, and destroyed by a single outlier — the range of our salary data is £229,000.
Standard deviation: roughly, the typical distance of a value from the mean. The first set above has a standard deviation of 0; the second is near 31.6.

A mean of 50 with a standard deviation of 0 and a mean of 50 with a standard deviation of 31.6 are two very different statements, and only the second pair of numbers tells you which one you are looking at.

Sample or Population: Divide by n or n − 1

Standard deviation calculators offer a sample and a population setting, and the choice changes the answer.

If your numbers are the entire group you care about — every employee at the firm, every item produced — that is a population, and you divide by n. If they are a subset used to estimate something wider — 200 customers standing in for all customers — that is a sample, and you divide by n − 1.

The smaller divisor makes the sample figure slightly larger. This is Bessel's correction, and it exists because a sample's values cluster around the sample's own mean rather than the true one, which makes the raw spread an underestimate. Dividing by n − 1 compensates.

For 10, 30, 70, 90 the population standard deviation is 31.62 and the sample figure is 36.51 — about 15% higher on four values. The gap shrinks as the data set grows and is negligible by a few hundred values, but on small sets it is large enough to matter. When in doubt, ask whether you are describing these numbers or estimating something beyond them.

You Cannot Average Two Averages

This is the most common error in practice, and it is easy to commit without noticing.

Class A has 20 students averaging 60%. Class B has 5 students averaging 90%. The combined average is not (60 + 90) ÷ 2 = 75%.

Work from the totals instead. Class A contributed 20 × 60 = 1,200 marks and class B 5 × 90 = 450, giving 1,650 marks across 25 students — a true average of 66%.

Averaging the averages overstated the result by nine percentage points, because it treated five students as though they carried the same weight as twenty. Averages can only be combined directly when the groups behind them are the same size; otherwise you need a weighted mean, which is what recovering the totals amounts to.

The same trap appears in blended rates, average speeds over legs of different lengths, and any dashboard that averages a column of pre-computed averages.

Conclusion

Mean, median and mode are not competing answers to one question; they answer three. Reach for the median when the data is skewed, the mean when totals matter and the values are well behaved, and the mode when the data is not numeric at all. Then report a measure of spread beside it, because an average without one is a headline with the story removed.

Paste a column of figures into a Statistics Calculator to get all three at once, along with the range, and check the shape of your data before deciding which number to quote.

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