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Scatter Graphs

FoundationHigherAQAEdexcelOCR

Get to grips with scatter graphs using these Foundation and Higher GCSE Maths practice questions. The worksheet focuses on scatter graphs, correlation and lines of best fit, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. A line of best fit shows the trend; correlation may be positive, negative or none.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

A scatter graph plots two variables against each other so you can see whether a relationship exists between them. Each point represents one item with two measurements, such as a student's revision hours and their test score.

Correlation describes the pattern. Positive correlation means both variables increase together, negative correlation means one falls as the other rises, and no correlation means the points show no clear trend.

Once a relationship is visible you can draw a line of best fit and use it to estimate a missing value. The important judgement is how much to trust that estimate, which depends on how strong the correlation is and whether you are predicting inside or outside the range of the data.

Revision notes

Describing correlation

Give both the direction and the strength. Direction is positive, negative or none; strength is strong or weak depending on how closely the points cluster.

A full answer also refers to the context: rather than writing positive correlation, write that students who revise for longer tend to score higher marks. Exam mark schemes usually require that interpretation.

Drawing and using a line of best fit

Draw a single straight line following the trend, with roughly equal numbers of points above and below it. It does not have to pass through the origin, and it should not join the points.

To estimate a value, read up from the axis to the line and across, showing your reading lines on the diagram. Examiners award marks for those construction lines.

Reliability and outliers

Interpolation means estimating inside the range of the data, and it is reasonably reliable. Extrapolation means going beyond the data, and it is unreliable because the trend may not continue.

An outlier is a point lying well away from the trend. Identify it, but do not include it when drawing the line of best fit, and mention it if the question asks you to comment.

Key points

  • Each point represents two measurements for one item.
  • Positive correlation: both variables increase together.
  • Negative correlation: one increases as the other decreases.
  • Describe direction, strength and the meaning in context.
  • A line of best fit follows the trend with points balanced either side.
  • Correlation does not prove that one variable causes the other.

Worked examples

Example 1

A scatter graph of revision hours against test score shows points rising from left to right in a tight band. Describe the correlation.

Working

\[\text{Strong positive correlation}\]the points rise together and cluster closely around a line
\[\text{Students who revise longer tend to score higher}\]interpret the relationship in the context of the question

Example 2

Using a line of best fit, a student who revises for 6 hours is estimated to score 72 marks. Explain why this estimate is reasonably reliable.

Working

\[6 \text{ hours lies within the data range}\]this is interpolation rather than extrapolation
\[\text{The correlation is strong}\]points lie close to the line, so the line predicts well
\[\text{So the estimate is reliable}\]state the conclusion in context

Example 3

Explain why a strong positive correlation between ice cream sales and sunburn cases does not mean one causes the other.

Working

\[\text{Correlation does not imply causation}\]state the principle
\[\text{Hot weather increases both}\]identify a third factor affecting both variables
\[\text{So neither causes the other}\]give the conclusion

Common mistakes

  • Joining the points instead of drawing one straight line.

    A line of best fit is a single straight line summarising the trend, not a zigzag through every point.

  • Describing correlation without context.

    Writing negative correlation alone often scores one mark of two. Say what it means for the variables in the question.

  • Forcing the line through the origin.

    The line should follow the data. Only pass through the origin if the trend genuinely goes there.

  • Treating an extrapolated estimate as reliable.

    Predicting outside the data range assumes the trend continues, which the data does not support.

Exam tips

  • Draw reading lines on the graph when estimating, since they earn method marks.
  • Always add a sentence putting the correlation in the context of the variables.
  • Ignore an outlier when drawing the line, but mention it in your answer.
  • State whether an estimate is interpolation or extrapolation when judging reliability.

Key terms

Correlation
A relationship between two variables shown by the trend on a scatter graph.
Line of best fit
A straight line drawn to summarise the trend of the points.
Interpolation
Estimating a value within the range of the collected data.
Outlier
A point that lies well away from the general trend.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.