Find the range of: 3, 7, 10, 15
Range = max − min.
15 − 3 = 12.
Range
Range measures how spread out data is by finding the difference between the highest and lowest values. It gives a simple indication of variation.
Overview
The range tells you how spread out a set of data is.
It is found by subtracting the smallest value from the largest value.
Range = largest value - smallest value
A small range means the data values are closer together.
A large range means the data values are more spread out.
What you should understand after this topic
- Calculate the range
- Identify the largest and smallest values correctly
- Understand what the range tells you about spread
- Compare two sets of data using range
- Avoid common exam mistakes
Small range
Values are close together.
Large range
Values are spread out more.
Key Definitions
Range
The difference between the largest and smallest values.
Largest Value
The highest number in the data set.
Smallest Value
The lowest number in the data set.
Spread
How far apart the data values are.
Key Rules
Main rule
\( \text{range} = \text{largest} - \text{smallest} \)
Check carefully
Do not subtract the first and last numbers unless you know the list is correct.
Order can help
Putting the data in order makes the smallest and largest easier to see.
Range is about spread
It does not tell you the middle. It tells you how wide the data is.
How to Solve
Step 1: Understand the range
The range is a measure of spread. It shows how far apart the data values are.
\( \text{Range} = \text{largest value} - \text{smallest value} \)
Exam tip: Always subtract smallest from largest (not the other way around).
Step 2: Find the values
Look for the smallest and largest numbers in the data.
Order the data if needed.
Identify the smallest value.
Identify the largest value.
Step 3: Calculate the range
Subtract the smallest value from the largest value.
Include units if given in the question.
Step 4: Compare data sets
Large range
Data is more spread out.
Small range
Data is more consistent.
Step 5: Limitations of the range
Affected by outliers
One extreme value can change the range a lot.
Uses only two values
Ignores the rest of the data.
Not always reliable
May not represent the full spread.
Step 6: Exam method summary
See averages for other measures of data.
- Find the smallest value.
- Find the largest value.
- Subtract smallest from largest.
- Compare ranges if required.
- Comment on spread or consistency.
Example Questions
Edexcel
Exam-style questions inspired by Edexcel GCSE Mathematics, focusing on calculating the range of data.
Edexcel
Find the range of \( 4,\ 8,\ 6,\ 10 \).
Edexcel
Find the range of \( 12,\ 15,\ 11,\ 18,\ 14 \).
Edexcel
The heights of five plants, in cm, are 32, 35, 30, 38 and 34.
Find the range of the heights.
AQA
Exam-style questions based on the AQA GCSE Mathematics specification, focusing on comparing ranges and interpreting spread.
AQA
Which data set has the greater range?
\( 5,\ 6,\ 7,\ 8 \quad \text{or} \quad 2,\ 6,\ 10,\ 14 \)
AQA
The times, in seconds, for two runners are shown below.
| Runner A | Runner B |
|---|---|
| 12 | 11 |
| 13 | 15 |
| 14 | 12 |
| 12 | 16 |
Which runner has the greater range?
AQA
A student says, "A smaller range means the data is more consistent."
Tick one box. True ☐ False ☐
Give a reason for your answer.
OCR
Exam-style questions aligned with OCR GCSE Mathematics, emphasising reasoning and working backwards with range.
OCR
A data set has a smallest value of 9 and a range of 13.
Find the largest value.
OCR
The range of a data set is 18. The largest value is 42.
Find the smallest value.
OCR
Explain what a large range tells you about a data set.
Exam Checklist
Step 1
Find the smallest value in the data.
Step 2
Find the largest value in the data.
Step 3
Subtract smallest from largest.
Step 4
Check that the answer is positive and makes sense.
Most common exam mistakes
Wrong subtraction
Subtracting in the wrong order.
Wrong values
Choosing values that are not actually the smallest or largest.
Not reading carefully
Missing that the question is about range, not mean or median.
Comparison mistake
Forgetting that a larger range means more spread.
Common Mistakes
These are common mistakes students make when calculating and interpreting range in GCSE Maths.
Subtracting in the wrong order
Incorrect
A student subtracts the largest value from the smallest value.
Correct
Range is found by subtracting the smallest value from the largest value: \(\text{range} = \text{maximum} - \text{minimum}\).
Choosing the wrong maximum or minimum
Incorrect
A student does not correctly identify the highest or lowest value.
Correct
Check all the data carefully to find the true maximum and minimum before calculating the range.
Not checking all data values
Incorrect
A student calculates the range without reviewing the full dataset.
Correct
Always scan the entire dataset to ensure no values are missed when identifying the extremes.
Ignoring units
Incorrect
A student gives the range without units.
Correct
Include the same units as the data in your final answer, such as cm, seconds, or kg.
Confusing range with average
Incorrect
A student thinks the range represents a typical value.
Correct
Range measures spread, not the centre of the data. It shows how far apart the values are, not an average.
Ignoring the effect of outliers
Incorrect
A student assumes the range always represents the spread accurately.
Correct
Outliers can greatly affect the range. Be aware that one extreme value can make the range misleading.
Try It Yourself
Practise calculating and interpreting the range of data sets.
Foundation
Foundation Practice
Calculate the range and understand what it represents.
Find the range of: 5, 8, 12, 20
Subtract smallest from largest.
20 − 5 = 15.
What does the range measure?
Think variation.
Range measures spread.
Find the range of: 10, 10, 10, 10
All values are the same.
10 − 10 = 0.
Find the range of: 2, 6, 9, 13, 18
Largest − smallest.
18 − 2 = 16.
Find the range of: 25, 30, 35, 40
Max − min.
40 − 25 = 15.
A student subtracts smallest − largest. What is wrong?
Largest first.
Range = largest − smallest.
Find the range of: 6, 14, 21, 27
Subtract smallest from largest.
27 − 6 = 21.
Which data set has the smallest range?
Look at spread.
8 − 5 = 3 (smallest range).
Find the range of: 100, 120, 140, 180
Largest − smallest.
180 − 100 = 80.
Higher
Higher Practice
Interpret and compare ranges, including the effect of outliers.
Which data set has the largest range?
Look at spread.
100 − 1 = 99 (largest range).
Find the range of: 12, 18, 25, 60
Max − min.
60 − 12 = 48.
What effect does an outlier have on the range?
Outliers are extreme values.
Outliers increase the range.
A data set is: 5, 7, 8, 9, 50. Find the range.
Look at extreme values.
50 − 5 = 45.
Two data sets have the same mean but different ranges. What does this show?
Range measures spread.
Different range → different spread.
Find the range of: 200, 210, 220, 250
Max − min.
250 − 200 = 50.
Which data set is more consistent?
Small range = consistent.
13 − 10 = 3 → most consistent.
A data set has minimum 15 and range 25. Find the maximum value.
Max = min + range.
15 + 25 = 40.
If the range is 0, what does this mean?
Max = min.
All values are the same.
A data set has maximum 90 and range 30. Find the minimum value.
Min = max − range.
90 − 30 = 60.
Games
Practise this topic with interactive games.
Games coming soon.
Frequently Asked Questions
What is range?
Highest minus lowest value.
What does range show?
Spread of data.
What is a limitation?
It uses only two values.