📊 Statistics District · Averages

Range

Calculate and interpret the range as a useful summary of a real data set. In this lesson, focus on the range measures spread by subtracting the minimum from the maximum.

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Understand Range

Calculate and interpret the range as a useful summary of a real data set. In this lesson, focus on the range measures spread by subtracting the minimum from the maximum.

The range measures spread by subtracting the minimum from the maximum. It uses only the two endpoints, so an outlier can change it dramatically. For range, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.

Start here

Range: The range measures spread by subtracting the minimum from the maximum. Add the range to the minimum and confirm that the result is the maximum. Keep the range representation visible until the final line.

Picture the idea

Slide the minimum and maximum gates on a data strip and watch their distance become the range. Use the model to explain one change you notice while working on range.

Check as you go

Add the range to the minimum and confirm that the result is the maximum. Write that check beside the final range answer.

Key vocabulary

rangemaximumminimumspreadoutlier

Rules and key facts

Given information: Range — Find the range of 2, 2, 4, 6. Method choice: Identify the largest and smallest values first. Subtract the smallest value from the largest value to measure the spread. Calculation or reasoning: Maximum − minimum = 6 − 2 = 4. Final answer: 4. Check: Subtract the smallest value from the largest value to measure the spread.

  • Identify the minimum value.
  • Identify the maximum value.
  • Subtract minimum from maximum.
  • State what the spread suggests in context. Record the check explicitly for range.

Step-by-step method

  1. Identify the minimum value.
  2. Identify the maximum value.
  3. Subtract minimum from maximum.
  4. State what the spread suggests in context. Record the check explicitly for range.

What you need first

  • Recognise the vocabulary: range, maximum, minimum.
  • Be able to explain the purpose of range before calculating.
  • Keep the relevant values, units and representation visible while you work.

Real-world use

  • Temperature variation
  • Consistency checks

Visual / interactive

See the idea, then move it around

Skip to Practice

Slide the minimum and maximum gates on a data strip and watch their distance become the range. Use the model to explain one change you notice while working on range.

Mean / median / mode / range calculator Connected to this topic; move controls, check outputs, then earn XP only from verified actions.
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Worked examples

Examples, methods and exam thinking

Level 1 · Foundation

Understand the idea with small numbers, one representation and one clear step.

Level 2 · Secure

Use the standard Year 8 method with mixed examples and normal wording.

Level 3 · Challenge

Handle multi-step or less familiar questions and explain choices.

Level 4 · Exam-style

Solve a worded question, show reasoning, check accuracy and write a final sentence.

Foundation example

Build confidence

Given information: Range — Find the range of 2, 2, 4, 6. Method choice: use the range method and show each step with the stated values. Calculation or reasoning: Maximum − minimum = 6 − 2 = 4. Final answer: 4. Check: substitute or compare with the original information to confirm the result fits the question.

  1. Identify the minimum value.
  2. Identify the maximum value.
  3. Subtract minimum from maximum.
Secure example

Use the normal method

Given information: Range — Find the range of 3, 14, 14, 24. Method choice: use the range method and show each step with the stated values. Calculation or reasoning: Maximum − minimum = 24 − 3 = 21. Final answer: 21. Check: substitute or compare with the original information to confirm the result fits the question.

Check: Check the range result against the original information.

Challenge example

Stretch the idea

Given information: Range — Find the range of 3, 13, 9, 20. Method choice: use the range method and show each step with the stated values. Calculation or reasoning: Maximum − minimum = 20 − 3 = 17. Final answer: 17. Check: substitute or compare with the original information to confirm the result fits the question.

Try explaining why each step works before checking the answer.

Exam-style example

Show your reasoning

Given information: Range — Find the range of 3, 12, 4, 16. Method choice: use the range method and show each step with the stated values. Calculation or reasoning: Maximum − minimum = 16 − 3 = 13. Final answer: 13. Check: substitute or compare with the original information to confirm the result fits the question.

Exam tip: Underline the units and command word. Show the key calculation and write the answer in context.

Common mistakes

  • Subtracting in the wrong order. This is a key trap when answering range questions.
  • Using the number of values instead of the endpoint difference.

How to check your answer

Add the range to the minimum and confirm that the result is the maximum. Write that check beside the final range answer.

Extension challenge

Create a range problem with a tempting incorrect answer. Solve it, apply the check, and explain exactly where the incorrect method breaks down.

Practice · always open

Question practice with hints and full solutions

Choose a difficulty, answer questions, ask for hints, see the method, retry, or generate a similar question. XP rewards accurate work and improved scores.

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Year 8 practice studio

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Foundation, secure, challenge and exam-style questions are available immediately with instant feedback.

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Games · always open

Range challenge

Use range gates controls to solve three checked range rounds. Solve at least two of three marked rounds and use feedback to correct any error.

Press Start Game to enter a topic-specific maths arena.

Boss challenge

Challenge Range Guardian

The boss is available when you feel ready. Boss victory badges and legendary status still require a strong pass.

Range Guardian

Timed mixed-difficulty battle. Practice first if you want, or jump in and learn from feedback.

12 mixed questions5:00 timer×2 XP multiplier
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Study cards and flashcards · always open

Study the essentials quickly

Study cards

Core idea

Range: The range measures spread by subtracting the minimum from the maximum. Add the range to the minimum and confirm that the result is the maximum. Keep the range representation visible until the final line.

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Key vocabulary

range · maximum · minimum · spread · outlier

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Rules

Identify the minimum value. Identify the maximum value. Subtract minimum from maximum. State what the spread suggests in context. Record the check explicitly for range.

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Formula / fact

Given information: Range — Find the range of 2, 2, 4, 6. Method choice: Identify the largest and smallest values first. Subtract the smallest value from the largest value to measure the spread. Calculation or reasoning: Maximum − minimum = 6 − 2 = 4. Final answer: 4. Check: Subtract the smallest value from the largest value to measure the spread.

Tap to mark reviewed
Foundation example

Given information: Range — Find the range of 2, 2, 4, 6. Method choice: use the range method and show each step with the stated values. Calculation or reasoning: Maximum − minimum = 6 − 2 = 4. Final answer: 4. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Secure example

Given information: Range — Find the range of 3, 14, 14, 24. Method choice: use the range method and show each step with the stated values. Calculation or reasoning: Maximum − minimum = 24 − 3 = 21. Final answer: 21. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Challenge example

Given information: Range — Find the range of 3, 13, 9, 20. Method choice: use the range method and show each step with the stated values. Calculation or reasoning: Maximum − minimum = 20 − 3 = 17. Final answer: 17. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Exam-style example

Given information: Range — Find the range of 3, 12, 4, 16. Method choice: use the range method and show each step with the stated values. Calculation or reasoning: Maximum − minimum = 16 − 3 = 13. Final answer: 13. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Common mistake

Subtracting in the wrong order. This is a key trap when answering range questions.

Tap to mark reviewed
Exam tip

For range, show the key representation before the final calculation. Use this final check: Add the range to the minimum and confirm that the result is the maximum.

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Real-world use

Temperature variation, Consistency checks

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Checklist

I can explain range, use the method, check for mistakes, and answer an exam-style question.

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Flashcards

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Help for Range

Use this whenever a question feels confusing. Nothing here is locked.

Simple explanation

Range: The range measures spread by subtracting the minimum from the maximum. Add the range to the minimum and confirm that the result is the maximum. Keep the range representation visible until the final line.

Think of range as a careful model: make the important values visible, change one thing at a time, and use the check to prove the answer fits.

Step-by-step breakdown

  1. Identify the minimum value.
  2. Identify the maximum value.
  3. Subtract minimum from maximum.
  4. State what the spread suggests in context. Record the check explicitly for range.

Hint 1

Start by naming the given information and the exact result required for range.

Hint 2

Identify the minimum value.

Full worked solution

Given information: Range — Find the range of 2, 2, 4, 6. Method choice: use the range method and show each step with the stated values. Calculation or reasoning: Maximum − minimum = 6 − 2 = 4. Final answer: 4. Check: substitute or compare with the original information to confirm the result fits the question.

Method: Identify the minimum value. → Identify the maximum value. → Subtract minimum from maximum. → State what the spread suggests in context. Record the check explicitly for range.

Common mistake warning

Subtracting in the wrong order. This is a key trap when answering range questions.

Choose a support button above when you need a nudge.

Mastery milestones

Badges reward learning, not locked clicking

  • I can explain range in my own words.
  • I can use these words accurately: range, maximum, minimum.
  • I can follow the 4-step method without guessing.
  • I can avoid this mistake: Subtracting in the wrong order.
  • I can apply this check: Add the range to the minimum and confirm that the result is the maximum.
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