What is a scatter graph?
A scatter graph plots pairs of data as points, to show whether there is a relationship (correlation) between two variables.
Key vocabulary:
- Positive correlation — as one variable increases, the other tends to increase too
- Negative correlation — as one variable increases, the other tends to decrease
- No correlation — there is no clear relationship between the two variables
- Line of best fit — a single straight line, drawn by eye, that best represents the trend, with roughly equal points above and below it
- Outlier — a point that doesn't fit the general pattern of the rest of the data
Plotting data from a table
Worked Example 1
The table shows revision time and test score for 9 students. Describe the correlation shown, and identify any outlier.
| Revision (hours) | 1 | 2 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| Test score (%) | 20 | 35 | 85 | 40 | 55 | 58 | 68 | 75 | 82 | 88 |
1
As revision time increases, test score generally increases too — this is positive correlation
2
The student who revised for 2 hours but scored 85% doesn't fit the pattern — this is an outlier
AnswerPositive correlation; outlier at (2, 85)
Positive correlation: as revision time increases, test score tends to increase. The line of best fit ignores the outlier at (2, 85).
Interpolation — reading within the data
Worked Example 2
Using the line of best fit above, estimate the test score for a student who revised for 6 hours.
1
Find 6 hours on the horizontal axis, and go straight up to the line of best fit
2
Read across to the vertical axis: approximately 68%
3
Since 6 hours is within the range of the data (1 to 9 hours), this is interpolation — a reasonably reliable estimate
Answer≈ 68%
Extrapolation — reading beyond the data
Worked Example 3
Using the same line of best fit, estimate the test score for a student who revised for 15 hours. Comment on the reliability of this estimate.
1
Extending the line of best fit to x = 15 gives a score of roughly 150%
2
This is impossible — test scores cannot exceed 100%
3
15 hours is far outside the data range (1–9 hours), so this is extrapolation — the trend may not continue in the same way, making the estimate unreliable
AnswerUnreliable — this is extrapolation, well outside the range of the data
Finding the equation of the line of best fit
Worked Example 4 — Equation of the line
A line of best fit passes through the points (2, 20) and (8, 80). Find its equation in the form y = mx + c, then use it to estimate y when x = 5.
1
Find the gradient: m = (80 − 20) ÷ (8 − 2) = 60 ÷ 6 = 10
2
Substitute (2, 20) into y = 10x + c: 20 = 10(2) + c → c = 0
3
Equation: y = 10x. When x = 5: y = 10(5) = 50
Answery = 10x; y = 50 when x = 5
Practice questions
Work through each question before checking the answers.
Foundation (Grade 3–5)
Q1A scatter graph shows hours of TV watched vs exam score, with points trending downward from left to right. What type of correlation is this?Foundation
Q2A scatter graph plots shoe size against favourite colour. What type of correlation would you expect, and why?Foundation
Q3Define the term "outlier" in the context of a scatter graph.Foundation
Q4A scatter graph shows car engine size against fuel used per 100km, with a clear upward trend. Explain what this positive correlation means in context.Foundation
Q5True or false: joining the points on a scatter graph with a dot-to-dot line correctly shows the trend. Explain your answer.Foundation
Higher (Grade 5–7)
Q6
The table shows the height and weight of 6 people. State the type of correlation shown.
Higher| Height (cm) | 150 | 155 | 160 | 165 | 170 | 175 |
|---|---|---|---|---|---|---|
| Weight (kg) | 50 | 54 | 58 | 62 | 65 | 70 |
Q7Using the data from Q6, and assuming a straight-line trend between 160cm (58kg) and 170cm (65kg), estimate the weight of someone 168cm tall.Higher
Q8Using the data from Q6, explain why estimating the weight of someone 220cm tall using the line of best fit would be unreliable.Higher
Q9A line of best fit has equation y = 2.5x + 10, valid for x between 0 and 10. Estimate y when x = 6.Higher
Q10A scatter graph plots temperature against ice cream sales. Most points near 30°C show around 80 sales, but one point at 30°C shows only 5 sales. Identify this point and explain why it is usually ignored when drawing the line of best fit.Higher
Higher — Hard (Grade 8–9)
Q11A line of best fit passes through (2, 20) and (8, 80). Find its equation in the form y = mx + c.Grade 8–9
Q12Using the equation from Q11, estimate y when x = 5, and state whether this is interpolation or extrapolation, given the data ranges from x = 1 to x = 9.Grade 8–9
Q13Using the equation from Q11, estimate y when x = 15, and explain why this estimate is unreliable.Grade 8–9
Q14A line of best fit relating hours studied (x) to test score (y) has gradient 3.2. Explain what this gradient represents in context.Grade 8–9
Q15A student says: "There is positive correlation between ice cream sales and shark attacks, so buying less ice cream would reduce shark attacks." Explain why this reasoning is flawed.Grade 8–9
Answers
Foundation (Q1–Q5)
Q1Negative correlation(as TV hours increase, exam score decreases)
Q2No correlation(shoe size and favourite colour are unrelated)
Q3A point that does not fit the general pattern shown by the rest of the data
Q4As engine size increases, fuel used per 100km also tends to increase
Q5False(a single straight line of best fit should be drawn, not a dot-to-dot line joining every point)
Higher (Q6–Q10)
Q6Positive correlation(as height increases, weight increases)
Q763.6 kg(gradient 0.7 kg/cm; 58 + 0.7 × 8)
Q8220cm is far outside the data range (150–175cm), so this is extrapolation — the trend may not continue in the same way, making the estimate unreliable
Q925(2.5 × 6 + 10)
Q10The point at (30°C, 5 sales) is an outlier — it doesn't fit the overall trend and is likely due to an unusual circumstance, so it is generally ignored when drawing the line of best fit
Higher — Hard (Q11–Q15)
Q11y = 10x(gradient = 60 ÷ 6 = 10; c = 0)
Q12y = 50; interpolation(x = 5 is within the data range 1–9)
Q13y = 150; unreliable(x = 15 is far outside the data range — extrapolation, and the trend may not continue linearly that far)
Q14For every extra hour studied, the test score increases by about 3.2 marks on average, based on the trend in the data
Q15Correlation does not imply causation. Both variables are likely linked to a third factor — hot weather increases both ice cream sales and the number of people swimming in the sea, which increases the risk of shark attacks. Buying less ice cream would not affect shark attacks.
Common mistakes
Common Mistake 1
Joining the points instead of drawing a line of best fit
A scatter graph should have one straight line that best represents the overall trend — not a jagged dot-to-dot line connecting every point. The line does not need to pass through any of the actual points.
Common Mistake 2
Including outliers when drawing the line of best fit
An outlier can pull a line of best fit away from the true trend if it's accidentally used to help position the line. Identify outliers first, and draw the line to fit the rest of the data.
Common Mistake 3
Treating extrapolated estimates as reliable
Estimating a value outside the range of the original data assumes the trend continues in exactly the same way — which often isn't true. Always flag extrapolated answers as less reliable than interpolated ones.
Common Mistake 4
Assuming correlation means one variable causes the other
Two variables can be strongly correlated without either one causing the other — both might be influenced by a third factor. Never conclude "A causes B" from a scatter graph alone.
Exam tips
💡 Exam Tip 1
Use a ruler and go through the middle of the data
When drawing a line of best fit by eye, aim for roughly equal numbers of points above and below the line, spread evenly along its length — not just clustered near one end.
💡 Exam Tip 2
Always name the type of correlation precisely
Say "positive correlation" or "negative correlation" rather than just "correlated" — and if there's no clear pattern, say "no correlation" rather than leaving the answer blank.
💡 Exam Tip 3
State interpolation or extrapolation explicitly
When asked to comment on the reliability of an estimate, name the specific reason: whether the x-value used is inside or outside the range of the given data, and what that means for how much you can trust the answer.
💡 Exam Tip 4
Give context in your interpretation
When describing what a correlation means, refer back to the actual variables in the question (e.g. "as revision time increases, test score tends to increase") rather than a generic answer like "the two variables are linked".
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