What Is an Average? Three Different Answers

A single number standing in for many

The answer to what is an average is a purpose rather than a formula: it is one number chosen to represent a whole set of them.

The formal name is a measure of central tendency — a value near the middle of the data that a single figure can stand for. There are three in common use because there are three defensible ways to decide what 'the middle' means.

The mean balances

Add everything and divide by how many. The result is the value each item would have if the total were shared out equally.

Physically it is a balance point: if the numbers were weights on a ruler, the mean is where it would balance. That is exactly why one extreme value drags it so far — a heavy weight far out shifts the balance point a long way.

The median splits

Sort the data and take the middle value. With an even count, take the mean of the two in the middle.

It ignores how far away the extreme values are and only cares about their position, which makes it immune to outliers. Change 11 to 1100 in the set above and the mean leaps to 280 while the median moves not at all.

The mode counts

Whichever value occurs most often. It is the only average that works on data which is not numeric — the most common shoe size, the best-selling colour, the most frequent survey response.

It is also the only one that must be a value actually present in the data. A mean of 8.5 may match nothing in the set; a mode always does.

A set can have two modes, or more, or none at all if every value appears once. All three outcomes are valid results.

Why 'average' on its own is ambiguous

In everyday speech average nearly always means the mean, and that assumption is occasionally exploited.

Average income reported as a mean can be far above what most people earn, because a small number of very high incomes pull it up. Reported as a median it describes the typical case. Both are honest calculations of different things, and the choice of which to publish is a choice about what story to tell.

That is the practical reason to know all three: not to compute them, which is easy, but to notice which one you are being shown.

The weighted mean, when items do not count equally

Sometimes the values being averaged do not deserve equal weight. A course grade where the exam counts for 60% and coursework for 40% is not the mean of the two marks.

The unweighted mean would have been 60, which overstates the result by two marks. Whenever an average is described with percentages attached to its parts, it is a weighted mean and the ordinary formula does not apply.

An average alone is half a description

Two sets can share a mean and look nothing alike. 49, 50, 51 and 0, 50, 100 both average 50, but one is tightly grouped and the other is spread across the whole range.

That is what the range and the standard deviation are for. A central value says where the data sits; a measure of spread says how tightly it clusters there, and you need both before you have described anything.

Questions about what is an average