GCSE Maths • Foundation & Higher
GCSE Mean, Median, Mode and Range Revision Guide
Learn how to calculate and interpret the main averages and range from lists, frequency tables and grouped data.
Foundation
Exam practice
Worked examples
What You'll Learn
Understand the Mean
Calculate the mean from a list of values and from a frequency table.
Round and Estimate
Round whole numbers and decimals, use significant figures and estimate calculations efficiently.
Understand Bounds
Find lower and upper bounds and write them correctly using inequalities.
Work with Factors, Multiples and Primes
Identify factors, multiples and prime numbers and use prime factor decomposition.
Find HCF and LCM
Use factors, multiples and prime factors to calculate highest common factors and lowest common multiples.
Work with Recurring Decimals
Recognise recurring decimals and convert between recurring decimals and fractions.
Key Rules and Formulas
Number Lessons
BIDMAS
Use the correct order of operations in calculations involving brackets, powers and mixed operations.
Bounds
Find lower and upper bounds for rounded values and apply them to measurement problems.
Estimation
Round values to make quick approximate calculations and check exact answers.
Factors, Multiples and Prime Numbers
Identify factors, multiples and primes and use prime factor decomposition.
HCF and LCM
Find highest common factors and lowest common multiples using lists and prime factors.
Recurring Decimals
Recognise recurring decimals and convert recurring decimals into exact fractions.
Rounding
Round whole numbers and decimals to place values, decimal places and significant figures.
CORE SUBTOPICS
Order of Operations
Use brackets first, then indices, then division/multiplication, followed by addition/subtraction.
Rounding Whole Numbers and Decimals
Round to the nearest 10, 100, 1000, decimal places and significant figures.
Estimation and Checking
Use rounded values to calculate approximate answers and judge whether exact results are reasonable.
Lower and Upper Bounds
Use half the rounding interval to find the possible range of an original value.
Factors, Multiples and Prime Numbers
Know the difference between factors and multiples, identify primes and construct factor trees.
Prime Factor Decomposition
Write a number as a product of prime factors, often using index notation.
HCF and LCM
Use shared factors or multiples, or prime factor decomposition, to calculate HCF and LCM.
Recurring Decimals and Fractions
Recognise repeating decimal patterns and use algebra to convert recurring decimals into fractions.
Worked Example
Using BIDMAS
QUESTION
Calculate 3 + 4 × (10 − 6).
Given information: The calculation contains brackets, multiplication and addition.
Method: Follow BIDMAS in the correct order.
✓ Brackets first: 10 − 6 = 4.
✓ Multiply: 4 × 4 = 16.
✓ Add: 3 + 16 = 19.
- Answer: 19
- Key idea: Complete higher-priority operations before addition and subtraction.
- Common mistake: Do not add 3 + 4 before dealing with the brackets and multiplication.
Finding Bounds
QUESTION
A length is 30 cm correct to the nearest centimetre. Give its bounds.
Given information: There are four values, so there will be two middle values.
Method: Order the data first, then average the two middle values.
✓ Ordered data: 2, 6, 8, 10.
✓ Middle values: 6 and 8.
✓ Median = (6 + 8) ÷ 2 = 7.
- Answer: 29.5 ≤ x < 30.5.
- Key idea: The lower bound is included, but the upper bound is not.
- Common mistake: Do not use 30 itself as one of the bounds.
Converting a Recurring Decimal to a Fraction
QUESTION
Convert 0.333... into a fraction.
Method: Use algebra to eliminate the recurring part.
✓ Let x = 0.333…
✓ Then 10x = 3.333…
✓ Subtract: 10x − x = 3.
✓ 9x = 3, so x = 1/3.
- Answer: 1/3
- Key idea: Multiply by a power of 10 so the recurring digits line up, then subtract.
- Common mistake: Do not forget to simplify the final fraction.
- Common GCSE Mistakes
- Ignoring the correct BIDMAS order.
- Confusing decimal places and significant figures.
- Using the rounded value as a bound.
- Confusing factors with multiples.
- Mixing up HCF and LCM.
- Using the wrong power of 10 for recurring decimals.
- Exam Tips
- Show the order of operations clearly.
- Check the digit immediately to the right when rounding.
- Use half the rounding interval for bounds.
- Remember: 1 is not prime.
- Use lowest prime powers for HCF and highest for LCM.
- Simplify recurring-decimal fractions fully.
Ready to Practice?
Printable Worksheet
Practise BIDMAS, rounding, estimation, bounds, factors, HCF, LCM and recurring decimals.
Interactive Quiz
Test your knowledge of key GCSE Number rules and calculations.
Exam-Style Questions
Apply Number skills to mixed Foundation and Higher Tier problems.
Watch the Mean, Median, Mode and Range Tutorial
A step-by-step tutorial covering essential GCSE Number skills.
- Apply BIDMAS correctly
- Round and estimate calculations
- Find lower and upper bounds
- Work with factors, multiples and primes
- Find HCF and LCM
- Convert recurring decimals and fractions
Continue Your GCSE Maths Revision
Continue Your GCSE Maths Revision
Frequently Asked Questions
The mean is found by adding all the values and dividing by the number of values. The median is the middle value when the data is ordered. The mode is the value that appears most often, while the range is the difference between the highest and lowest values.
Add all the values together, then divide the total by the number of values. For example, the mean of 4, 6 and 8 is 18÷3=618 \div 3 = 6.
Yes. The values must be arranged from smallest to largest before finding the median. If there are two middle values, add them together and divide by 2.
Yes. A data set can have two or more modes if several values occur with the same highest frequency. It can also have no mode if every value appears the same number of times.
