Mean, Median, Mode and Range: The Complete GCSE Guide to Averages

Averages are one of the most reliable sources of marks on the GCSE Maths Statistics papers. Almost every exam series asks you to find the mean, median, mode and range in some form — and once you know the routine, these are marks you can pick up quickly and confidently. The trick is knowing exactly what each one means and following the same steps every single time.

In this guide we’ll work through a single data set and calculate all four measures, just like you’d be expected to do in the exam.

Step 1: Always order your data first

Before you calculate anything, put your data in order from smallest to largest. This one habit prevents the most common mistakes — especially when finding the median, where an out-of-order list will give you the wrong middle value.

For our worked example, we’ll use this data set (already ordered):

72, 73, 79, 84, 84, 84, 90, 90, 97

That’s nine values. Keep that count in mind — it matters for the median.

The mean (the “average”)

The mean is what most people picture when they hear the word “average”. You find it in two steps:

1. Add up all the values to get the sum.
2. Divide the sum by how many values there are.

For our data:

• Sum = 72 + 73 + 79 + 84 + 84 + 84 + 90 + 90 + 97 = 753
• Number of values = 9
• Mean = 753 ÷ 9 = 83.666…

That’s a recurring decimal, so we round it. Rounding to the nearest hundredth (two decimal places):

Mean = 83.67

Tip: When your answer is a recurring decimal, check whether the question tells you how to round. If it doesn’t, two decimal places (the nearest hundredth) is almost always a safe choice — but always show your full working before you round, as method marks are awarded for it.

The median (the middle value)

A handy way to remember this one: median sounds like medium, and medium is the middle size. The median is the middle value once the data is in order.

With nine values, the middle one is the 5th value — there are four numbers on each side of it:

72, 73, 79, 84, 84, 84, 90, 90, 97

Median = 84

What if there’s an even number of values?

When you have an even number of values, there’s no single middle number — there are two. In that case:

1. Identify the two middle values.
2. Add them together and divide by 2 (find their mean).

For example, if your two middle values were 84 and 90, the median would be (84 + 90) ÷ 2 = 87.

Number of values	Where the median sits
Odd	One middle value
Even	Mean of the two middle values

The mode (the most common value)

Remember: mode = most. The mode is the value that appears most often.

Looking at our data:

• 84 appears three times
• 90 appears two times
• Every other value appears once

So the value that occurs most is 84:

Mode = 84

A data set can have more than one mode. If, say, both 84 and 90 had appeared three times, we’d have two modes (84 and 90) and the data would be bimodal. If no value repeats, there’s no mode at all.

The range (how spread out the data is)

The range is the odd one out — it isn’t an average. It tells you how stretched out your data is, from one extreme to the other. You find it by subtracting the smallest value from the largest:

Range = largest − smallest

For our data:

• Largest value = 97
• Smallest value = 72
• Range = 97 − 72 = 25

A small range means the values are tightly clustered; a large range means they’re widely spread. The range is quick to calculate, but be careful — a single unusually high or low value (an outlier) can stretch it dramatically.

Quick reference summary

Here’s everything from our worked example in one place:

Measure	What it tells you	Method	Our answer
Mean	The overall average	Sum ÷ number of values	83.67
Median	The middle value	Order, then find the centre	84
Mode	The most common value	Find the value that repeats most	84
Range	The spread of the data	Largest − smallest	25

Remember: The mean, median and mode are all measures of average, while the range is a measure of spread. Examiners love to test whether you know the difference — read the command word carefully.

Where these averages turn up next

Averages are the foundation for a huge amount of GCSE Statistics. Once you’re comfortable here, you’ll meet them again in frequency tables, grouped data (where you estimate the mean) and probability work. If probability is your next stop, our guide to Probability Tree Diagrams: Step-by-Step for GCSE is a natural follow-on.

For students chasing the top grades, knowing which average to choose — and being able to justify it — is exactly the kind of detail covered in How to Get a Grade 9 in GCSE Maths: The Tricks They Don’t Tell You. And when the big day arrives, make sure you’ve worked through our GCSE Maths Exam Day Checklist so nothing catches you out.

Practise averages until they’re automatic

Averages reward repetition. The more data sets you work through, the faster and more accurate you become — and these are marks you simply shouldn’t drop on exam day.

Our GCSE Statistics app is built exactly for this. It covers surveys, sampling, charts, averages, spread and probability theory, with question after question to drill the mean, median, mode and range until the method is second nature — for both Foundation and Higher tier.

If you’d rather revise every area of the course in one place, the GCSE Maths all-in-one app bundles Number, Algebra, Geometry and Statistics together, so you can move between averages and the rest of the syllabus without switching apps. Altogether our specialist apps offer 2900+ questions across the four subject apps, giving you more than enough practice to walk into the exam with confidence.

Master the four steps above, practise them regularly, and averages will become some of the easiest marks you earn all paper. You’ve got this.