Plot paired data, describe the correlation and what it means, draw a line of best fit and use it to estimate values sensibly. It is on Foundation and Higher, aimed at grade 4. Free questions with answers are on this page.
A scatter graph plots two measurements for each item. Positive correlation: as one goes up, so does the other. Negative: one up, the other down. None: a cloud. Strength is how tightly the points hug a straight line. Correlation is not causation — ice cream and drowning both rise in summer.
A line of best fit is a ruler line through the middle of the points, not necessarily through (0,0) and not joining the first to the last. Read off it to estimate (interpolation inside the data). Extrapolation outside the data is unreliable — say so if asked.
Positive correlation: both increase. Negative: one up, the other down. None: a cloud. A line of best fit is used to interpolate (inside the data range). Extrapolation (beyond the range) is unreliable. Correlation is not causation.
Objectives
Each point is one pair of measurements.
Upwards is positive. Downwards is negative. No tilt is none.
A straight line through the middle of the points, following their tilt.
Key points
Plot points accurately from a table of paired data.
Describe correlation as positive, negative or none, and say what it means in the context.
Draw a line of best fit that follows the trend with points balanced either side.
Use the line to estimate one value from the other.
Worked examples
Example 1
A line of best fit passes through (0, 10) and (2, 14). What is its gradient?
2 marks
Change in y = 14 − 10 = 4.
Change in x = 2 − 0 = 2.
Gradient = 4 ÷ 2 = 2.
Answer: 2
Common slips
Slip: Change in y = 16 − 10 = 4. That changes a number from the question, so it answers a different question.
Slip: Change in x = 5 − 0 = 2. That changes a number in the working, so the step no longer follows from the one before.
Slip: Gradient = 8 ÷ 2 = 2. That does not match the working above it.
Example 2
The equation of a line of best fit is y = 5x + 10. Use it to estimate y when x = 16.
2 marks
Put x = 16 into y = 5x + 10.
5 × 16 = 80.
80 + 10 = 90.
Answer: 90
Common slips
Slip: Put x = 18 into y = 5x + 10. That changes a number from the question, so it answers a different question.
Slip: 5 + 16 = 21. That uses addition, but this step needs multiplication.
Slip: 80 − 10 = 70. That uses subtraction, but this step needs addition.
Example 3
A line of best fit passes through (30, 80) and (40, 60). Use the line to estimate y when x = 38.
3 marks
Gradient = (60 − 80) ÷ (40 − 30) = −2.
From x = 30 to x = 38, y changes by −2 × 8 = −16.
y = 80 − 16 = 64.
Answer: 64
Common slips
Slip: Gradient = (62 − 80) ÷ (40 − 30) = −2. That changes a number from the question, so it answers a different question.
Slip: From x = 33 to x = 38, y changes by −2 × 8 = −16. That changes a number in the working, so the step no longer follows from the one before.
Slip: y = 84 − 16 = 64. That does not match the working above it.
Questions and answers
GCSE Maths scatter graphs questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
A line of best fit passes through (2, 55) and (8, 43). What is its gradient?
Show answer
Answer: -2
Change in y = 43 − 55 = −12.
Change in x = 8 − 2 = 6.
M1 — Change in y = 43 − 55 = −12.
A1 — Answer -2
Question 2 Easy2 marks
The equation of a line of best fit is y = 2x + 13. Use it to estimate y when x = 23.
Show answer
Answer: 59
Put x = 23 into y = 2x + 13.
2 × 23 = 46.
M1 — Put x = 23 into y = 2x + 13.
A1 — Answer 59
Question 3 Medium2 marks
The equation of a line of best fit is y = 3x + 16. Use it to estimate y when x = 30.
Show answer
Answer: 106
Put x = 30 into y = 3x + 16.
3 × 30 = 90.
M1 — Put x = 30 into y = 3x + 16.
A1 — Answer 106
Question 4 Medium2 marks
A line of best fit passes through (30, 20) and (40, 40). Use the line to estimate y when x = 35.
Show answer
Answer: 30
Gradient = (40 − 20) ÷ (40 − 30) = 2.
From x = 30 to x = 35, y changes by 2 × 5 = 10.
M1 — Gradient = (40 − 20) ÷ (40 − 30) = 2.
A1 — Answer 30
Question 5 Hard2 marks
A line of best fit passes through (30, 85) and (40, 65). Use the line to estimate y when x = 37.
Show answer
Answer: 71
Gradient = (65 − 85) ÷ (40 − 30) = −2.
From x = 30 to x = 37, y changes by −2 × 7 = −14.
M1 — Gradient = (65 − 85) ÷ (40 − 30) = −2.
A1 — Answer 71
Question 6 Hard2 marks
A line of best fit passes through (0, 10) and (3, 19). What is its gradient?
Show answer
Answer: 3
Change in y = 19 − 10 = 9.
Change in x = 3 − 0 = 3.
M1 — Change in y = 19 − 10 = 9.
A1 — Answer 3
Question 7 Exam-style3 marks
A line of best fit passes through (10, 35) and (20, 75). Use the line to estimate y when x = 15.
Show answer
Answer: 55
Gradient = (75 − 35) ÷ (20 − 10) = 4.
From x = 10 to x = 15, y changes by 4 × 5 = 20.
y = 35 + 20 = 55.
M1 — Gradient = (75 − 35) ÷ (20 − 10) = 4.
M1 — From x = 10 to x = 15, y changes by 4 × 5 = 20.
A1 — Answer 55
Common mistakes
Most lost marks on this topic are one slip.
Joining the points like a frequency polygon.
A scatter graph uses a line of best fit, or no line, not a join-the-dots path.
Forcing the line through the origin.
Only do that if the situation must pass through zero.
Saying the correlation proves a cause.
It shows an association.
Spot the slip
Positive correlation means
as one quantity increases, the other tends to increase
the points form a perfect vertical line
one quantity causes the other
Show the slip
as one quantity increases, the other tends to increase The cloud of points slopes upwards.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Use a ruler for the line of best fit and make sure it extends across the range of the points.
For 'describe the relationship', always mention both variables in context — one word like 'positive' is not enough there.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.