Range

GCSE MATHS • HIGHER TIER

Range Made Simple

Learn how to identify the highest and lowest values, calculate range and compare the spread of datasets.

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Range in Four Moves

1

Identify

Find the highest value in the dataset .

2

Locate

Find the lowest value in the dataset .

3

Subtract

Calculate highest value − lowest value .

4

Interpret

Use the range to describe or compare how spread out the data is .

What You’ll Learn

Understand Range

Know that range is a measure of spread .

Use the Formula

Apply Range = Highest Value − Lowest Value .

Work with Different Data

Calculate ranges involving repeated values, decimals and negatives.

Compare Datasets

Use range to compare variation.

Understand Limitations

Recognise how outliers can affect the range.

The Range Formula

Range = Highest Value − Lowest Value

This formula is one of the easiest formulas in GCSE Statistics, but students must be careful to identify the correct highest and lowest values.

Worked Proof: Range

Step-by-Step Method

  • 1. Identify the largest value.
  • 2. Identify the smallest value.
  • 3. Subtract the smallest value from the largest value.
  • 4. Write the answer clearly.

More Worked Examples

1

Question: Find the range of 3, 7, 9, 12, 15

Highest value = 15

Lowest value = 3
Range = 15 − 3 = 12
Answer: 12

2

Question: Find the range of 20, 25, 18, 30, 12

Highest value = 30

Lowest value = 12
Range = 30 − 12 = 18
Answer: 18

3

Question: Find the range of 5, 5, 5, 5.

Highest value = 5

Lowest value = 5
Range = 5 − 5 = 0
Answer: 0

4

Question: Find the range of 8, 14, 22, 17, 10

Highest value = 22

Lowest value = 8
Range = 14
Answer: 14
  • Common GCSE Mistakes
  • Values: Identify the correct highest and lowest values first.
  • Order: Subtract lowest from highest, not the other way around.
  • Negative numbers: Take care when subtracting a negative value.
  • Decimals: Check decimal subtraction carefully.
  • Meaning: Do not confuse range with an average.
  • Exam Tips
  • Write down the highest and lowest values before calculating.
  • Use Range = Highest Value − Lowest Value.
  • A larger range means the data is more spread out.
  • Check signs carefully when negative numbers are included.
  • Remember that frequencies do not change the highest and lowest data values.
  • Consider the effect of outliers when interpreting range.

Skills Used in Range

Measures of Spread

Highest and Lowest Values

Subtraction

Negative Numbers

Decimals

Comparing Datasets

Frequency Tables

Statistics and Data Handling

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Exam-Style Questions

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Frequently Asked Questions

The range is the difference between the highest and lowest values in a dataset .

Range = Highest Value − Lowest Value .

It means the data values are spread out over a wider interval .

It means the highest and lowest values are the same, so there is no variation .

No. Use the highest and lowest values, regardless of their frequencies .

An unusually high or low value can significantly increase the range .