📊 Statistics District · Scatter graphs

Correlation

Use plotted paired data to interpret correlation with careful statistical language. In this lesson, focus on a scatter graph shows whether two variables tend to change together.

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Understand Correlation

Use plotted paired data to interpret correlation with careful statistical language. In this lesson, focus on a scatter graph shows whether two variables tend to change together.

A scatter graph shows whether two variables tend to change together. A line of best fit should pass through the middle of the cloud with a balanced spread of points, while an outlier needs separate attention. For correlation, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.

Start here

Correlation: A scatter graph shows whether two variables tend to change together. Check that a best-fit line leaves a sensible balance of points above and below it. Keep the correlation representation visible until the final line.

Picture the idea

Plot paired points, drag a line through the data cloud and compare balanced and biased fits. Use the model to explain one change you notice while working on correlation.

Check as you go

Check that a best-fit line leaves a sensible balance of points above and below it. Write that check beside the final correlation answer.

Key vocabulary

paired datacorrelationoutlierline of best fitinterpolation

Rules and key facts

Given information: Correlation — A scatter graph for study time and test score has points that rise from left to right. Identify the correlation. Method choice: Substitute the x-coordinate into the equation. Compare the calculated y-value with the point's y-coordinate. Calculation or reasoning: The points rise from left to right: as study time increases, test score tends to increase. This overall upward trend is positive correlation. Final answer: positive correlation. Check: Compare the calculated y-value with the point's y-coordinate.

  • Read both variable axes and plot paired points.
  • Describe direction and strength without claiming causation.
  • Notice any outlier.
  • For a line of best fit, balance points above and below before estimating. Record the check explicitly for correlation.

Step-by-step method

  1. Read both variable axes and plot paired points.
  2. Describe direction and strength without claiming causation.
  3. Notice any outlier.
  4. For a line of best fit, balance points above and below before estimating. Record the check explicitly for correlation.

What you need first

  • Recognise the vocabulary: paired data, correlation, outlier.
  • Be able to explain the purpose of correlation before calculating.
  • Keep the relevant values, units and representation visible while you work.

Real-world use

  • Scientific investigations
  • Comparing trends

Visual / interactive

See the idea, then move it around

Skip to Practice

Plot paired points, drag a line through the data cloud and compare balanced and biased fits. Use the model to explain one change you notice while working on correlation.

Scatter graph + correlation + line of best fit tool 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: Correlation — A scatter graph for study time and test score has points that rise from left to right. Identify the correlation. Method choice: use the correlation method and show each step with the stated values. Calculation or reasoning: A scatter graph for study time and test score has points that rise from left to right. Identify the correlation. Final answer: positive correlation. Check: substitute or compare with the original information to confirm the result fits the question.

  1. Read both variable axes and plot paired points.
  2. Describe direction and strength without claiming causation.
  3. Notice any outlier.
Secure example

Use the normal method

Given information: Correlation — The points for temperature and coat sales cluster closely around a downward-sloping line. Describe the relationship fully. Method choice: use the correlation method and show each step with the stated values. Calculation or reasoning: The points fall from left to right and stay close to a line, so the graph shows strong negative correlation. Final answer: strong negative correlation. Check: substitute or compare with the original information to confirm the result fits the question.

Check: Check the correlation result against the original information.

Challenge example

Stretch the idea

Given information: Correlation — Most plotted points are near (2, 5), (3, 7), (4, 9), (5, 11), but one point is (9, 2). Which coordinate is the outlier? Method choice: use the correlation method and show each step with the stated values. Calculation or reasoning: (9, 2) is far away from the overall upward pattern, so it is the outlier. Final answer: (9, 2). 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: Correlation — A line of best fit is modelled by y = 4x + 6. Estimate y when x = 4. Method choice: use the correlation method and show each step with the stated values. Calculation or reasoning: Substitute x = 4: y = 4 × 4 + 6 = 22. Final answer: 22. 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

  • Claiming correlation proves causation. This is a key trap when answering correlation questions.
  • Joining every dot instead of drawing a balanced trend line.

How to check your answer

Check that a best-fit line leaves a sensible balance of points above and below it. Write that check beside the final correlation answer.

Extension challenge

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

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Correlation challenge

Use trend line controls to solve three checked correlation 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 Correlation Guardian

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Correlation Guardian

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

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Study cards and flashcards · always open

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Study cards

Core idea

Correlation: A scatter graph shows whether two variables tend to change together. Check that a best-fit line leaves a sensible balance of points above and below it. Keep the correlation representation visible until the final line.

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Key vocabulary

paired data · correlation · outlier · line of best fit · interpolation

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Rules

Read both variable axes and plot paired points. Describe direction and strength without claiming causation. Notice any outlier. For a line of best fit, balance points above and below before estimating. Record the check explicitly for correlation.

Tap to mark reviewed
Formula / fact

Given information: Correlation — A scatter graph for study time and test score has points that rise from left to right. Identify the correlation. Method choice: Substitute the x-coordinate into the equation. Compare the calculated y-value with the point's y-coordinate. Calculation or reasoning: The points rise from left to right: as study time increases, test score tends to increase. This overall upward trend is positive correlation. Final answer: positive correlation. Check: Compare the calculated y-value with the point's y-coordinate.

Tap to mark reviewed
Foundation example

Given information: Correlation — A scatter graph for study time and test score has points that rise from left to right. Identify the correlation. Method choice: use the correlation method and show each step with the stated values. Calculation or reasoning: A scatter graph for study time and test score has points that rise from left to right. Identify the correlation. Final answer: positive correlation. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Secure example

Given information: Correlation — The points for temperature and coat sales cluster closely around a downward-sloping line. Describe the relationship fully. Method choice: use the correlation method and show each step with the stated values. Calculation or reasoning: The points fall from left to right and stay close to a line, so the graph shows strong negative correlation. Final answer: strong negative correlation. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Challenge example

Given information: Correlation — Most plotted points are near (2, 5), (3, 7), (4, 9), (5, 11), but one point is (9, 2). Which coordinate is the outlier? Method choice: use the correlation method and show each step with the stated values. Calculation or reasoning: (9, 2) is far away from the overall upward pattern, so it is the outlier. Final answer: (9, 2). Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Exam-style example

Given information: Correlation — A line of best fit is modelled by y = 4x + 6. Estimate y when x = 4. Method choice: use the correlation method and show each step with the stated values. Calculation or reasoning: Substitute x = 4: y = 4 × 4 + 6 = 22. Final answer: 22. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Common mistake

Claiming correlation proves causation. This is a key trap when answering correlation questions.

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Exam tip

For correlation, show the key representation before the final calculation. Use this final check: Check that a best-fit line leaves a sensible balance of points above and below it.

Tap to mark reviewed
Real-world use

Scientific investigations, Comparing trends

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Checklist

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

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Flashcards

I’m Stuck

Help for Correlation

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

Simple explanation

Correlation: A scatter graph shows whether two variables tend to change together. Check that a best-fit line leaves a sensible balance of points above and below it. Keep the correlation representation visible until the final line.

Think of correlation 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. Read both variable axes and plot paired points.
  2. Describe direction and strength without claiming causation.
  3. Notice any outlier.
  4. For a line of best fit, balance points above and below before estimating. Record the check explicitly for correlation.

Hint 1

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

Hint 2

Read both variable axes and plot paired points.

Full worked solution

Given information: Correlation — A scatter graph for study time and test score has points that rise from left to right. Identify the correlation. Method choice: use the correlation method and show each step with the stated values. Calculation or reasoning: A scatter graph for study time and test score has points that rise from left to right. Identify the correlation. Final answer: positive correlation. Check: substitute or compare with the original information to confirm the result fits the question.

Method: Read both variable axes and plot paired points. → Describe direction and strength without claiming causation. → Notice any outlier. → For a line of best fit, balance points above and below before estimating. Record the check explicitly for correlation.

Common mistake warning

Claiming correlation proves causation. This is a key trap when answering correlation questions.

Choose a support button above when you need a nudge.

Mastery milestones

Badges reward learning, not locked clicking

  • I can explain correlation in my own words.
  • I can use these words accurately: paired data, correlation, outlier.
  • I can follow the 4-step method without guessing.
  • I can avoid this mistake: Claiming correlation proves causation.
  • I can apply this check: Check that a best-fit line leaves a sensible balance of points above and below it.
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