A scatter graph shows the heights and shoe sizes of 12 adults. The points lie close to a straight line going up from left to right.
- (a)Describe the correlation.[1]
- (b)Describe the relationship between height and shoe size.[1]
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A scatter graph plots pairs of values — such as hours revised and test score — as points, to see whether the two quantities are related. From it you can describe the correlation, draw a line of best fit, make estimates, and judge whether those estimates can be trusted.
The big picture
Correlation describes a pattern, not a cause. Ice-cream sales and sunburn cases rise together, but ice cream does not cause sunburn — hot weather drives both. AQA regularly asks you to explain exactly this distinction.
A line of best fit is only reliable inside the range of the data. Estimating within that range (interpolation) is usually sensible; going beyond it (extrapolation) assumes the pattern continues, which it may not.
What you'll learn
correlation: as one variable increases, the other tends to increase. correlation: as one increases, the other tends to decrease. correlation: no clear pattern.
Describe the strength too: points close to a straight line show strong correlation; widely scattered points show weak correlation. In context: "the more hours revised, the higher the score tends to be."
What type of correlation would you expect between the outside temperature and the amount of energy used to heat homes? Type positive, negative or none.
Draw a single straight line with a ruler that follows the trend, with roughly equal numbers of points on each side. It does not have to pass through the origin or through any particular point, and should ignore outliers.
To estimate, go up from the value to the line, then across to read (or the reverse).
Tip — Leave your reading lines on the graph — they show your method.
(estimating within the data range) is fairly reliable. (beyond it) is unreliable: using the graph to predict a score for 20 hours would give more than 100%.
An is a point that does not fit the pattern. It may be an error, or a genuine unusual case, such as a student who was ill on the test day.
Correlation does not prove causation. Two variables may be linked by a third factor, or the link may be coincidence.
A line of best fit is a model of the relationship, and every model has a range where it works. Predicting a 25-year-old's height from a graph of children aged 2 to 12 would suggest they are over 2 metres tall — the growth pattern simply stops.
Think like an examiner
Key ideas
Watch out for these
Stretch yourself
A line of best fit for score (, %) against hours revised () passes through and . Find its equation, use it to estimate the score for 5 hours, and explain why it should not be used for 15 hours.
Hint — Find the gradient, then the intercept, as for any straight line.
Questions students ask
Key takeaways
Exam-style questions
2 original questions · 5 marks, written to match the style and mark allocation of the real papers. Work on paper, then open the mark scheme and tick the marks you earned — method marks count even if the final answer slips.
A scatter graph shows the heights and shoe sizes of 12 adults. The points lie close to a straight line going up from left to right.
A line of best fit for ice-cream sales () against temperature (, °C) passes through and . The data was collected for temperatures between 12°C and 32°C.
Test yourself
Ready to practise Scatter Graphs? Pick a mode and earn XP & Dobloons.
Real past-paper questions on Scatter Graphs, marked mark-by-mark. How you do feeds straight into your weak-topic list, so your revision keeps targeting what actually needs work.