Average Calculator — Mean, Median, Mode & More

Mean, median and mode — what's the difference?

All three are types of average, but they measure different things. Understanding which one to use — and when — is one of the most practically useful bits of maths you'll ever learn.

The mean (also called the arithmetic average) is what most people picture when they hear the word "average". Add all the numbers together and divide by how many there are. Simple and widely understood, but easily skewed by extreme values.

The median is the middle value when all numbers are sorted in order. If there's an even count of numbers, it's the average of the two middle values. The median ignores outliers entirely — it only cares about position, not magnitude.

The mode is the value that appears most often. It's the only average that makes sense for non-numerical data (like the most popular shoe size in a shop), and it's particularly useful when you need to know what's most common rather than what's typical.

Why median is often more useful than mean

Consider UK house prices. The Office for National Statistics reports a mean average that is significantly higher than what most buyers actually pay — because a small number of multi-million-pound London properties drag the mean upward. The median gives a fairer picture of what a typical buyer pays, because half the transactions are above it and half are below.

The same logic applies to salaries. When the ONS reports "average salary" in its Annual Survey of Hours and Earnings (ASHE), they use the median — not the mean — precisely because a small number of very high earners would inflate the mean far beyond what most workers actually take home.

The mode matters most when you're looking at categories or frequencies. A shoe retailer doesn't need to know the mean shoe size of their customers — they need to know the most popular size so they know what stock to order.

Worked example — 8 students' test scores

Notice how the mean (74.125) and median (74.5) are close in this fairly symmetric dataset. In a dataset with extreme outliers, they would be much further apart — which is exactly when the choice between them matters most.

How outliers affect your results

The most important thing to understand about averages is that the mean is sensitive to outliers and the median is not. Imagine you have the salaries of five colleagues: £25,000, £27,000, £28,000, £30,000, and £32,000. The mean is £28,400 and the median is £28,000 — very close. Now a sixth person joins the team on £500,000. The mean jumps to £107,000, which is wildly unrepresentative of what anyone actually earns. The median barely moves — it shifts to £29,000.

This is why the ONS always reports median pay when describing UK earnings. A handful of hedge fund managers and FTSE 100 chief executives would otherwise push the national mean far above what the typical worker takes home.

Choosing the right average

Use the mean when your data is reasonably symmetric and has no extreme outliers — for example, the heights of a group of adults, or the time it takes to complete a task. The mean uses every data point and is the most statistically powerful when used appropriately.

Use the median when your data has outliers or is skewed — house prices, salaries, wealth, waiting times. It gives a better sense of what's "typical" in the dataset.

Use the mode when you need to know the most common value — most popular product size, most frequent response in a survey, most common number of items in an order.

Standard deviation explained simply

The standard deviation tells you how spread out the numbers are from the mean. A low standard deviation means the values cluster tightly around the mean — they're similar to each other. A high standard deviation means the values are widely scattered. This calculator uses the population standard deviation (σ), which is appropriate when your numbers represent the complete dataset rather than a sample from a larger population.

For example, in the test scores dataset (45–95), the standard deviation is around 15.7. This means most scores fall within about 15–16 marks of the mean of 74.125. If the standard deviation were 2, you'd know the scores were all clustered very closely together — a much more consistent class.

What range tells you

The range is simply the highest value minus the lowest value. It's the quickest way to describe how spread out the extreme values are. However, range is very sensitive to outliers — a single unusually high or low value will change it dramatically, even if all the other values are clustered together. For a more robust measure of spread, standard deviation is usually more informative.

Real-world data from the ONS

The ONS Annual Survey of Hours and Earnings (ASHE) consistently shows a meaningful gap between median and mean pay in the UK. In 2024, full-time employees earned a median of around £37,500 per year, but the mean was noticeably higher — because high earners pull the mean upward. The spread between these two figures tells you something important about income inequality: the wider the gap between median and mean, the more skewed the distribution is toward the top.