Mean, Median and Mode

Three different answers to the question "what is typical?", each useful in different situations.

Primary
Secondary
Updated 14 November 2026

What you will learn

Calculate the mean, median and mode.
Choose the best average for the data.
Find a missing value from a given mean.

Before you start: you should be able to add, divide and put numbers in order. See Frequency Tables and Dot Plots.

The idea

An average is a single number that represents a whole set of data. There are three common ways to choose that number, and they can give quite different answers.

Mean: add up all the values and divide by how many there are. This is what most people call “the average”.
Median: put the values in order and take the middle one. If there is an even number of values, take the mean of the middle two.
Mode: the value that occurs most often. A set can have more than one mode, or none.

Alongside an average we often give the range, the largest value minus the smallest, as a simple measure of how spread out the data is.

The goals data from Example 1. The tallest stack, 2 goals, is the mode. The middle dot is also at 2.

Which average should I use?

Average	Best when…	Weakness
Mean	data is fairly symmetrical with no extreme values	dragged around by outliers
Median	data has outliers or is skewed (e.g. incomes, house prices)	ignores the size of most values
Mode	data is categories (favourite colour, shoe size)	may not exist or may not be central

The median is 2. The mean, about 2.33, sits just to the right of it, so the two are close because the data has no extreme values.

The first eight of the nine ordered scores. The 5th value is the median, 2, and the 9th is 6.

Worked examples

Example 1: All three averages

The number of goals a team scored in nine matches: $2, 0, 3, 1, 2, 4, 2, 1, 6$ .

Order the data: $0, 1, 1, 2, 2, 2, 3, 4, 6$ .
Mean: the sum is $21$ , and there are $9$ values. $21 \div 9 \approx 2.33$ .
Median: with $9$ values the middle one is the $\frac{9 + 1}{2} = 5$ th: $2$ .
Mode: $2$ appears three times, more than any other value.
Range: $6 - 0 = 6$ .

Answer: mean $\approx 2.33$ , median $2$ , mode $2$ , range $6$ .

Example 2: An even number of values

Find the median of $14, 9, 21, 11, 17, 8$ .

Order: $8, 9, 11, 14, 17, 21$ .
Six values, so the middle falls between the 3rd and 4th: $11$ and $14$ .
Median $= \frac{11 + 14}{2} = 12.5$ .

Answer: $12.5$

Example 3: Finding a missing value

Four test scores have a mean of $72$ . What must the fifth score be to raise the mean to $75$ ?

Total of the first four: $4 \times 72 = 288$ .
Required total for five: $5 \times 75 = 375$ .
Fifth score: $375 - 288 = 87$ .

Answer: $87$

An outlier can mislead. If nine people earn £30,000 and one earns £1,000,000, the mean salary is £127,000, which describes nobody. The median, £30,000, is far more honest.

Why it matters

Averages appear constantly in news and everyday life: average house prices (usually medians), batting averages, average speed cameras, mean exam grades and the “most popular size” a shop stocks (the mode). Knowing which average has been used, and why, helps you judge whether a claim is fair.

The mean is also the building block for standard deviation, which measures how far values typically sit from it.

Practice

Your turn. Type or choose an answer, then press Check. Getting one wrong is fine, that is what practice is for. You can try as many times as you like.