How to Draw and Interpret Scatter Graphs — KS3 Maths

A scatter graph plots pairs of measurements as points to show whether two variables are related. The pattern of points reveals the correlation: positive, negative, or none. A line of best fit drawn through the middle of the points lets you make predictions.

What is a scatter graph?

A scatter graph (also called a scatter diagram or scatter plot) shows bivariate data — two measurements taken from the same subject. Each pair of measurements becomes a single point plotted at coordinates (x, y).

Example: measuring the shoe size and height of each pupil in a Year 9 class gives 30 coordinate pairs. Plotting them as a scatter graph reveals whether taller pupils tend to have larger feet.

Types of correlation

Type | Pattern of points | Meaning
Strong positive correlation | Points rise steeply from bottom-left to top-right | As one variable increases, the other increases strongly
Weak positive correlation | Points rise loosely from bottom-left to top-right | As one increases, the other tends to increase, but with spread
Strong negative correlation | Points fall steeply from top-left to bottom-right | As one increases, the other decreases strongly
Weak negative correlation | Points fall loosely | Tendency to decrease, but with spread
No correlation | Points scattered randomly | No relationship between the two variables

Important: correlation does not prove causation. Just because two things are correlated does not mean one causes the other.

How to draw a scatter graph — step by step

Step 1 — label the axes

Draw two perpendicular axes. Label the horizontal (x) axis with one variable and the vertical (y) axis with the other. Include units.

Step 2 — choose appropriate scales

Read the data range and choose scales that fit all points neatly within the graph area. The scale does not have to start at 0, but it must be consistent.

Step 3 — plot each data point

For each pair of values (x, y), find x on the horizontal axis and y on the vertical axis, then mark the point with a small cross (×) or dot.

Step 4 — draw a line of best fit (if required)

Draw a single straight line that passes through the middle of the cloud of points, with roughly equal numbers of points on either side. The line does not need to pass through any specific point or through the origin.

Step 5 — title the graph

Add a clear title that describes both variables and the context (e.g. "Shoe size against height for Year 9 pupils").

Worked example — drawing and using a scatter graph

Ten pupils sat a revision test and then an exam. Their scores (out of 50) are below.

Pupil | Revision test | Exam
A | 12 | 18
B | 20 | 24
C | 25 | 30
D | 30 | 35
E | 35 | 38
F | 38 | 42
G | 40 | 44
H | 42 | 45
I | 45 | 47
J | 48 | 49

Plotting: Label the x-axis "Revision test score (out of 50)" and the y-axis "Exam score (out of 50)." Plot the ten points.

Correlation: The points rise from bottom-left to top-right with little scatter — this is strong positive correlation. Pupils with higher revision test scores tended to score higher on the exam.

Line of best fit: Draw a straight line running through the middle of the data, passing approximately through (12, 18) and (48, 49).

Prediction: Estimate the exam score for a pupil with a revision test score of 32.

Draw a vertical line from 32 on the x-axis to the line of best fit, then read across horizontally to the y-axis. The predicted exam score is approximately 37.

Interpreting lines of best fit

Task | Method
Predict y from a given x | Draw vertical line from x to the line, then horizontal to y-axis
Predict x from a given y | Draw horizontal line from y to the line, then vertical to x-axis
Describe the relationship | State the type of correlation (positive/negative, strong/weak) and what it means in context

Outliers

An outlier is a point that lies far away from the rest of the data and from the line of best fit. Outliers can be caused by a measurement error or by a genuinely unusual case. In KS3 exams, you may be asked to identify an outlier and suggest a reason for it.

Interpolation and extrapolation

Interpolation — predicting within the range of the data. This is reasonably reliable.

Extrapolation — predicting outside the data range. This is less reliable because the relationship may not continue beyond the observed values.

Example: If the revision scores in the example above only go up to 48, predicting the exam score for a revision score of 60 would be extrapolation — and potentially unreliable.

Scatter graphs in the national curriculum

The DfE's KS3 mathematics programme of study requires pupils to use scatter graphs to recognise correlation and make predictions, and to understand that correlation does not indicate causation. The statutory national curriculum for Key Stage 3 and 4 confirms that drawing, interpreting, and using lines of best fit are assessed in the statistics strand of both KS3 and GCSE maths.

Frequently asked questions

What is the difference between correlation and causation?

Correlation means two variables tend to change together. Causation means one variable directly causes the change in the other. A classic example: ice cream sales and drowning rates both rise in summer, but ice cream does not cause drowning — hot weather increases both independently. Always describe a scatter graph using the word "correlation," not "causation."

Does the line of best fit have to go through the origin?

No. The line of best fit should go through the middle of the data cloud, which may not be at the origin at all. In exam questions, do not force the line through (0, 0) unless the data genuinely supports this. Forcing it through the origin when the data does not justify it will give inaccurate predictions.

How many points should be on each side of the line of best fit?

Aim for roughly equal numbers — about half above and half below. A few points will sit exactly on the line, which is fine. If you find that many more points are above the line than below (or vice versa), adjust the position of the line before drawing it in.

Can I draw a curved line of best fit?

At KS3, the line of best fit is always straight. Curved lines of best fit (polynomial or non-linear models) are beyond the KS3 scope. If the data appears to curve, still draw the best straight line through the centre of the data and note that a linear model may not perfectly describe the relationship.

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