How to Calculate the Average (Mean, Median, Mode)

Whenever you summarise a set of numbers, from exam marks to monthly spending, you reach for an average. But average is not one thing: learning how to calculate the average properly means knowing the mean, the median, and the mode, and when each one tells the truth. The mean is what most people call the average, but the median and mode often describe real data better, especially when a few extreme values would otherwise distort the picture. This guide explains all three with a single worked example so you can see how they differ, and shows when to use each. For related calculations, our percentage calculator is a handy companion.

The mean (average)

The mean is what people usually mean by average. You add up all the values, then divide by how many there are.

The mean uses every number in the set, which makes it powerful but also sensitive: a single very large or very small value can pull it up or down.

The median

The median is the middle value when the numbers are arranged in order from smallest to largest. If there is an odd number of values, it is the one in the middle. If there is an even number, it is the average of the two middle values.

Because it only cares about position, the median is not thrown off by extreme values, which makes it ideal for skewed data like incomes or house prices.

The mode

The mode is the value that appears most often. A set can have one mode, more than one, or none at all if every value is unique. The mode is the only average that works for non-numerical data, such as the most common shoe size or favourite colour.

One example, all three

Take the data set 4, 8, 6, 8, 10.

1. Mean: (4 + 8 + 6 + 8 + 10) = 36, divided by 5 = 7.2.
2. Median: sorted, it is 4, 6, 8, 8, 10; the middle value is 8.
3. Mode: 8 appears twice, more than any other value, so the mode is 8.

In plain English: the same five numbers give a mean of 7.2, a median of 8, and a mode of 8. They differ because each measures the centre in a different way.

For grade averages

Averaging comes up constantly in school and work. Our GPA calculator averages your grades, and our percentage calculator handles related percentage maths.

Which average to use

• Mean: best for fairly symmetric data with no extreme outliers, like test scores.
• Median: best for skewed data, such as income or property prices, where a few large values would distort the mean.
• Mode: best for categories or finding the most common value, and the only option for non-numerical data.

When someone quotes an average without saying which, they usually mean the mean, but the median often gives a fairer picture of typical values.

Frequently asked questions

How do I calculate the average?

The most common average is the mean: add all the numbers together, then divide by how many numbers there are. For 4, 8, 6, 8, and 10, the sum is 36 and there are 5 values, so the mean is 36 divided by 5, which is 7.2. This is what people usually mean by the average.

What is the difference between mean, median, and mode?

The mean is the sum of the values divided by how many there are. The median is the middle value when the numbers are sorted. The mode is the value that appears most often. For 4, 6, 8, 8, 10, the mean is 7.2, the median is 8, and the mode is 8. Each measures the centre differently.

How do I find the median?

Sort the numbers from smallest to largest, then find the middle one. With an odd count, it is the single middle value. With an even count, take the average of the two middle values. For 4, 6, 8, 8, 10, the middle value is 8, so the median is 8. The median ignores extreme values.

When should I use the median instead of the mean?

Use the median when your data is skewed or has extreme outliers, such as incomes, house prices, or wait times. A few very high values pull the mean upward, making it misleading, while the median stays near the typical value. For fairly symmetric data with no big outliers, the mean is usually fine.

Can a data set have more than one mode?

Yes. A data set can have one mode, two modes (bimodal), several modes, or no mode at all if every value appears just once. The mode is simply the most frequently occurring value. It is also the only average that works for non-numerical data, like the most common category or choice.

The bottom line

To calculate the average, most often you want the mean: add the values and divide by the count, giving 7.2 for the set 4, 8, 6, 8, 10. The median is the middle value (8) and the mode is the most common value (8). Choose the mean for symmetric data, the median for skewed data, and the mode for categories. For grade averages, try our GPA calculator.

Further reading

For authoritative background on this topic, see Average on Wikipedia.