Mean, median or mode: how do I justify which average a question wants?

Look at the distribution, not the data type. The decision turns almost entirely on whether there are extreme values, and a question giving you a skewed data set is telling you the answer.

The decision

Median when the data are skewed or contain outliers. The median is the middle value, so one enormous figure moves it hardly at all.

Mean when the data are roughly symmetrical and you want every value to count. It uses all the data, which is its strength and its weakness.

Mode when the data are categorical, or when the question is about what is most common rather than what is typical. The only average available for non-numerical data.

Why outliers decide it

Take six salaries: 22,000, 24,000, 25,000, 26,000, 28,000 and 310,000.

The mean is about 72,500. No one earns anything near that — five of the six earn under 30,000. The mean has been dragged upward by a single value and now describes nobody.

The median is 25,500, which genuinely represents a typical salary here.

That is the whole argument, and a question about income, house prices or waiting times is usually built on exactly this shape. Naming the outlier and saying which direction it pulls the mean is where the marks are.

What examiners ask

Rarely "calculate the mean". Usually something requiring judgement:

"Which average best represents the data? Justify." Name the average, identify the feature of the data that makes it appropriate, and say why the others are worse. Three parts, three marks.

"Explain why the mean is misleading here." Point at the specific extreme value and say it inflates or deflates the mean away from the bulk of the data.

"A company quotes its mean salary in an advert. Comment." This is asking you to notice that the mean has been chosen because it flatters. Saying so is the answer.

The spread matters too

An average alone describes very little, and higher-mark questions want you to say so.

Two data sets can share a mean of 50 while one ranges from 48 to 52 and the other from 5 to 95. Those are completely different situations and the average hides it.

So pair your average with a measure of spread, and pair it consistently:

• Median goes with the interquartile range — both resist outliers
• Mean goes with the standard deviation — both use every value

Mixing them, such as quoting a median with a standard deviation, is not wrong exactly but it is inconsistent, and examiners notice.

A small trap worth knowing

With grouped data you can only estimate the mean, because you no longer have the individual values — you are assuming everything sits at the midpoint of its class.

Questions often ask why your answer is an estimate, and that is the reason. Saying it in one sentence is a free mark that most candidates leave.