Scatter graphs | AQA GCSE Maths Notes

Visual model

Correlation and line of best fit

positive correlationline of best fittrend, not exact

Look for the overall pattern.

Use the line of best fit for estimates.

Do not extrapolate too far beyond the data.

Gold-standard guide

20 mins

What you will learn

Identify correlation and use lines of best fit.

Use a clear step-by-step method for scatter graphs.

Check your answer and avoid the most common exam mistake.

Useful before you start

Core number skillsEarlier statistics skillsShowing clear working

Core knowledge

Know the rule, then use it

These are the short notes. Read each one, then check you can use it in the worked example below.

Method

Correlation: positive — both increase together

Step 1

Identify the type of correlation

As revision hours increase, exam scores increase → positive correlation

Step 2

Assess the strength

If points lie close to a straight line, the correlation is strong

Step 3

Describe drawing the line of best fit

Draw a straight line with roughly equal numbers of points on each side

Watch out

Students draw the line of best fit from one corner to another rather than balancing points on each side

Correlation

Correlation describes association, not proof of causation.

Line of best fit

Interpolate inside the data range; be careful with extrapolation.

Worked example

Describe the correlation in a scatter graph where higher revision hours are associated with higher exam scores. Draw a line of best fit and explain how to use it.

Identify the type of correlation: As revision hours increase, exam scores increase → positive correlation.

Assess the strength: If points lie close to a straight line, the correlation is strong.

Describe drawing the line of best fit: Draw a straight line with roughly equal numbers of points on each side.It should pass through or near (mean hours, mean score).

Use the line of best fit for prediction: Interpolation: reading off a value within the data range — reliable.Extrapolation: extending beyond the data — unreliable, as the pattern may not continue.

Final answer

Strong positive correlation; line of best fit passes through the mean point

Question ladder

Build up to the hardest questions

Do them in order. If you miss a step, read the solution, then redo the question without looking.

Workedreasoning

Describe the correlation in a scatter graph where higher revision hours are associated with higher exam scores. Draw a line of best fit and explain how to use it.

4 marks4 minsscatter-graphs-worked

Show solution

Worked solution

1.Identify the type of correlation: As revision hours increase, exam scores increase → positive correlation.
2.Assess the strength: If points lie close to a straight line, the correlation is strong.
3.Describe drawing the line of best fit: Draw a straight line with roughly equal numbers of points on each side.It should pass through or near (mean hours, mean score).
4.Use the line of best fit for prediction: Interpolation: reading off a value within the data range — reliable.Extrapolation: extending beyond the data — unreliable, as the pattern may not continue.

Final answer

Strong positive correlation; line of best fit passes through the mean point

Mark points

M1: identify the type of correlation
M1: assess the strength
M1: describe drawing the line of best fit
M1: use the line of best fit for prediction
A1: Strong positive correlation; line of best fit passes through the mean point

Watch out

Students draw the line of best fit from one corner to another rather than balancing points on each side.The line must have roughly equal scatter above and below it — it is not a 'connect-the-dots' line.

Diagnosticrecall

What type of correlation: car age vs value?

1 mark2 minsscatter-graphs-q1

Show solution

Worked solution

1.Spot the skill: Correlation: positive — both increase together.
2.Use the identify the type of correlation stage first, then assess the strength.
3.Keep the final answer visible: Negative correlation.

Final answer

Negative correlation

Mark points

M1: use the correct correlation: positive — both increase together. negative — as one increases the other decreases.no correlation — no pattern. strength: strong (points close to line), weak (spread out).line of best fit: balanced line through the point (x̄, ȳ).
A1: Negative correlation

Watch out

Easyprocedure

A line of best fit passes through (5, 40) and (10, 70). Find the equation.

2 marks3 minsscatter-graphs-q2

Show solution

Worked solution

1.Spot the skill: Correlation: positive — both increase together.
2.Use the assess the strength stage first, then describe drawing the line of best fit.
3.Keep the final answer visible: Gradient = (70−40)/(10−5) = 6; y = 6x + 10.

Final answer

Gradient = (70−40)/(10−5) = 6; y = 6x + 10

Mark points

M1: use the correct correlation: positive — both increase together. negative — as one increases the other decreases.no correlation — no pattern. strength: strong (points close to line), weak (spread out).line of best fit: balanced line through the point (x̄, ȳ).
A1: Gradient = (70−40)/(10−5) = 6; y = 6x + 10

Watch out

Mediumreasoning

Explain why extrapolation is unreliable.

3 marks4 minsscatter-graphs-q3

Show solution

Worked solution

1.Spot the skill: Correlation: positive — both increase together.
2.Use the describe drawing the line of best fit stage first, then use the line of best fit for prediction.
3.Keep the final answer visible: The relationship shown by the data may not continue beyond the observed range.

Final answer

The relationship shown by the data may not continue beyond the observed range

Mark points

M1: use the correct correlation: positive — both increase together. negative — as one increases the other decreases.no correlation — no pattern. strength: strong (points close to line), weak (spread out).line of best fit: balanced line through the point (x̄, ȳ).
A1: The relationship shown by the data may not continue beyond the observed range

Watch out

Hardproblem solving

The mean hours studied = 7, mean score = 62. Must the line of best fit pass through (7, 62)?

3 marks5 minsscatter-graphs-q4

Show solution

Worked solution

1.Spot the skill: Correlation: positive — both increase together.
2.Use the use the line of best fit for prediction stage first, then identify the type of correlation.
3.Keep the final answer visible: Yes — the mean point lies on the line of best fit.

Final answer

Yes — the mean point lies on the line of best fit

Mark points

M1: use the correct correlation: positive — both increase together. negative — as one increases the other decreases.no correlation — no pattern. strength: strong (points close to line), weak (spread out).line of best fit: balanced line through the point (x̄, ȳ).
A1: Yes — the mean point lies on the line of best fit

Watch out

Exam-stylemulti-step

Distinguish between correlation and causation.

4 marks6 minsscatter-graphs-q5

Show solution

Worked solution

1.Spot the skill: Correlation: positive — both increase together.
2.Use the identify the type of correlation stage first, then assess the strength.
3.Keep the final answer visible: Correlation means two variables change together; causation means one directly causes the change in the other.

Final answer

Correlation means two variables change together; causation means one directly causes the change in the other

Mark points

M1: use the correct correlation: positive — both increase together. negative — as one increases the other decreases.no correlation — no pattern. strength: strong (points close to line), weak (spread out).line of best fit: balanced line through the point (x̄, ȳ).
A1: Correlation means two variables change together; causation means one directly causes the change in the other

Watch out

Grade 9 stretchproblem solving

Explain why using a line of best fit to predict far outside the data range may be unreliable.

4 marks7 minsscatter-g9

Show solution

Worked solution

1.Identify that the prediction is an extrapolation.
2.Explain that the observed relationship may not continue.

Final answer

It is an extrapolation, so the pattern may change beyond the observed data.

Mark points

C1: identify extrapolation
C1: explain unreliability

Watch out

Do not rush straight into arithmetic. Select the relevant method and show a complete chain of working.

Timed checkpoint

12 mins - 9 marks

Switch between skills

Set a timer and attempt all four questions before opening any answers. This is closer to the way skills appear in a real paper.

1Scatter graphs - 2 marksWhat type of correlation: car age vs value?Mark answer

Answer

Negative correlation

2Collecting and sampling data - 2 marksWhy might a questionnaire question be biased?Mark answer

Answer

Leading wording, only offering responses that agree, or not including a 'no' option

3Averages and range - 2 marksThe mean of 5 numbers is 12. Four of them are 8, 14, 10, 15. Find the fifth.Mark answer

Answer

4Grouped data and estimated mean - 3 marksA survey records [10,20): 5 responses and [20,30): 15. Estimate total mean across both groups.Mark answer

Answer

Use midpoints 15 and 25: (5×15 + 15×25)/20 = $45\frac{0}{2}0$ = 22.5

Mastery check

I can explain the method for scatter graphs.
I can show clear working without skipping key steps.
I can avoid this mistake: Students draw the line of best fit from one corner to another rather than balancing points on each side.The line must have roughly equal scatter above and below it — it is not a 'connect-the-dots' line.

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