A scatter graph shows two measurements for each observation as one point. Look for a trend, draw an appropriate line of best fit and treat predictions as estimates, not proof of cause.
Foundation & Higher6 worked examples10 original questions
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Start with the meaning
What you need to know about scatter graphs
For each pupil, record two things: hours spent practising and a quiz score. One pupil who practised for two hours and scored four becomes one dot at (2, 4). Repeating this for the other pupils lets you see whether larger values of one measurement tend to go with larger or smaller values of the other.
See the idea first
One dot is one pair of measurements
The horizontal x-axis shows practice time and the vertical y-axis quiz score. A tendency to rise from left to right is positive correlation; a tendency to fall is negative correlation. Correlation describes an association, not a guarantee for every pupil.
Each dot belongs to one pupil. Keep that pupil's two measurements paired; do not join adjacent dots.
The paired observations
Hours
1
2
3
4
5
6
Score
2
4
3
6
5
7
From problem to method
Typical problems you need to be able to solve
These are the main kinds of question in this topic. Each card first states the problem, then explains how to solve it.
Plot paired data
What the problem asks: Add a pupil with 3 hours of practice and score 5 to a scatter graph.
How to solve it: Find 3 on the horizontal axis, then 5 vertically, and place one cross or dot at (3, 5). Do not reorder the hours independently of the scores.
Describe correlation
What the problem asks: The dots generally rise from left to right but are not on one line. Describe the relationship.
How to solve it: There is positive correlation: higher x-values tend to accompany higher y-values. Strength depends on how closely dots follow the trend, not on how steep it is.
Estimate with a line of best fit
What the problem asks: For the displayed data, use a reasonable fitted line to estimate score at 4.5 hours.
How to solve it: A line such as y = x + 1 gives about 5.5. This input lies inside the observed 1–6 hour range, so it is interpolation. It is a prediction, not an exact score.
Judge a claim
What the problem asks: Someone says the graph proves practice time causes higher scores. Is that justified?
How to solve it: No. The relationship could also involve other factors, such as prior understanding. Correlation alone does not establish causation.
A reliable routine
Use a line of best fit for an estimate
A straight line is useful when the plotted data has an approximately linear trend. It summarises the centre of the scatter rather than connecting successive observations. With no useful trend, a straight-line prediction may be unjustified.
Plot paired values on labelled axes with suitable scales.
Describe direction and how closely points follow the trend; inspect unusual points.
Draw a line through the middle of the pattern, balancing scatter above and below. It need not pass through the origin.
Read an estimate from the line and state whether it is inside or outside the observed range.
Check: An outlier should be checked, not automatically deleted. Extrapolation extends beyond the evidence and may predict impossible values.
Fully worked
Scatter graphs GCSE worked examples
Each solution explains the clue, why the method fits and how to check the result.
Example 1
Plot one pair
2 marks
Question
On axes showing hours horizontally and score vertically, plot a pupil with 5 hours and score 5.
The required point is (5, 5). Move to five hours across, then five marks up. The dot's two values must refer to the same pupil.
This one dot is the pupil at (5, 5): five hours across and five marks up.
Example 2
Describe a trend
2 marks
Question
Describe the correlation in this scatter graph.
Each dot belongs to one pupil. Keep that pupil's two measurements paired; do not join adjacent dots.
There is positive correlation: quiz scores generally increase as practice hours increase. Not every pupil follows the trend exactly; the points show scatter.
Example 3
Interpolate
2 marks
Question
Use the shown line of best fit to estimate score after 4.5 hours of practice.
One reasonable straight line of best fit is y = x + 1 over the observed range. It balances the vertical scatter; it does not have to pass through every point.
The fitted line is y = x + 1.
y=4.5+1=5.5
The estimate is about 5.5 marks. It lies within the observed practice-time range.
Example 4
Read backwards
2 marks
Question
Use the same fitted line to estimate practice time associated with a score of 6.
One reasonable straight line of best fit is y = x + 1 over the observed range. It balances the vertical scatter; it does not have to pass through every point.
Read horizontally from score 6 to the fitted line, then down to the time axis. Since 6 = x + 1, the estimate is 5 hours. It is not a promise that five hours produces exactly six marks.
Example 5
Extrapolation
3 marks
Question
Use the fitted line y = x + 1 to predict the score at 12 hours, then explain a limitation.
The line predicts 13 marks. But the quiz has only 10 marks and the data covers only 1–6 hours. The extrapolated prediction is impossible, showing that the straight-line model cannot be extended indefinitely.
Example 6
An unusual point
3 marks
Question
Most car age–price points show prices falling as age rises. One old car has an unusually high price. Explain how to handle it.
It is an outlier relative to the trend. Check that the age and price were recorded correctly. It may be a valid special case, such as a rare car; explain its effect on a fitted line rather than deleting it automatically.
10 original questions · total 18 marks
Scatter graphs GCSE exam-style questions
Try each question before opening its fully worked answer. The difficulty rises through the set.
Before you startAllow about 23 minutes · Show your working. Give exact answers unless a question asks you to round, and include units where needed. · answers start collapsed
1
Coordinates
1 mark
Temperature is on x and ice-cream sales on y. A day has 18°C and 42 sales. State its coordinate.
Show worked answer
The point is (18, 42). Horizontal measurement comes first.
2
Pairing
2 marks
Why must you not sort the x-values and y-values independently before plotting?
Show worked answer
It would combine measurements from different observations and invent pairs that were never recorded. That can create a false trend.
3
Negative correlation
1 mark
As a car's age increases, its resale price tends to decrease. Name the correlation.
Show worked answer
Negative correlation: higher values of age tend to go with lower prices.
4
No correlation
1 mark
Dots form a scattered cloud with no clear upward or downward pattern. What does that suggest?
Show worked answer
No clear linear correlation. A straight line is unlikely to give useful predictions from this pattern.
5
Strength versus steepness
2 marks
Does a steeper fitted line necessarily mean stronger correlation?
Show worked answer
No. Strength concerns how closely points follow the trend. A shallow line with points tightly clustered around it can have strong correlation.
6
A supplied fit
2 marks
A line of best fit is y = 2x + 3. Observed x-values run from 1 to 9. Estimate y when x = 5.
Show worked answer
y=2(5)+3=13
This is interpolation because 5 is within 1–9. It is an estimate of an observation, even though evaluation of the line is exact.
7
Extrapolation risk
2 marks
A line of best fit was drawn from data with x-values from 1 to 9. Why is a prediction at x = 20 less reliable?
Show worked answer
It is extrapolation, far beyond recorded inputs. There is no evidence that the same linear trend continues to 20.
8
Causation
2 marks
Children with larger shoes tend to read more difficult books. Does this prove bigger shoes improve reading?
Show worked answer
No. Age may affect both shoe size and reading ability. The association alone does not establish a causal effect.
9
Line placement
2 marks
A student joins every dot in order from left to right. Is that a line of best fit?
Show worked answer
No. A best-fit line summarises the overall trend; joining every dot creates a zigzag that follows individual deviations.
10
Choose a useful estimate
3 marks
A scatter graph covers heights from 140 to 180 cm. A fitted line is m = 0.6h − 50, where h is height in cm and m is mass in kg. Estimate mass at 160 cm and state one limitation.
Show worked answer
m=0.6(160)−50=96−50=46 kg
It is interpolation, but people of the same height can have different masses. The estimate is not an exact individual value.
Examiner-style feedback
Common scatter graphs mistakes
Joining all the dots
Use a fitted trend line when appropriate; the points are separate observations.
Forcing the origin
A best-fit line need not pass through (0, 0). Follow the observed pattern.
Correlation proves cause
Other variables may explain the relationship, and the graph alone cannot decide causation.
30-second recap
Choose, carry out, check
Translate the wording before you reach for a rule.
Keep measurements paired.
Read direction and strength separately.
Fit a trend, not a zigzag.
State limits on predictions.
Quick answers
Scatter graphs FAQ
Must the line pass through every dot?
No. It balances the overall scatter and may pass through few or none of the actual observations.
Is interpolation always accurate?
No. It is generally safer than extrapolation, but scatter, biased data or a poor model can still make an estimate unreliable.
S6 scatter diagrams, correlation, best fit and interpolation/extrapolation across tiers. No regression algorithm or correlation coefficient required. Questions, suggested marks, solutions and diagrams are original practice material, not official past-paper questions.
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