GCSE Maths revision · Probability and statistics

Scatter graphs

Foundation and Higher

The idea

A scatter graph shows whether two variables are related. Correlation can be positive, negative or none. A line of best fit lets you estimate values inside the range of the data.

Describe the correlation: positive, negative or none, and how strong.
Draw a line of best fit through the middle of the points.
Read estimates from the line, staying within the data.

Watch out Correlation does not prove that one thing causes the other.

See it worked

Worked exampleNon-calculator2 marks

Each part describes two variables.

(a) The age of a car and its value. What type of correlation would you expect?

(b) The shoe sizes of 30 adults and their scores in the same spelling test. What type of correlation would you expect?

(a) As age increases, value tends to decrease.
(b) For adults, shoe size and spelling have no link, so expect no correlation.

Answer (a) Negative; (b) No correlation

Your turn

Question 1Non-calculator2 marks

The scatter graph shows the hours of revision and the test scores of 12 students.

(a) Write down the type of correlation.

(b) Kai says, "This proves that revising more causes higher scores." Explain why Kai is wrong.

Write your answer, then show the working

(a) As hours of revision increase, scores tend to increase.
(b) A scatter graph shows the variables are linked, but other factors (such as interest in the subject) could affect both.

Answer (a) Positive; (b) Correlation shows an association, not that one causes the other.

Question 2Non-calculator3 marks

For a sample of cars, the line of best fit for $y$ , the stopping distance in metres, against $x$ , the speed in m/s, is $y = 3.2x - 15$ for speeds from 10 m/s to 30 m/s.

(a) Interpret the gradient 3.2 in this context.

(b) Lily says stopping distance is directly proportional to speed. Is she correct? Give a reason.

(c) Estimate the stopping distance at 20 m/s.

Write your answer, then show the working

(a) The gradient is the change in $y$ for each increase of 1 in $x$ .
(b) Direct proportion means $y = kx$ : a straight line through $(0, 0)$ .
This line has intercept $-15$ , so doubling the speed does not double the distance.
(c) $3.2 \times 20 - 15 = 49$ .

Answer (a) For each extra 1 m/s of speed, the stopping distance increases by about 3.2 m.; (b) No: the line does not pass through the origin (intercept $-15$ ).; (c) 49 m

Question 3Calculator allowed1 mark

The scatter graph shows the length and mass of 12 objects of one type. A line of best fit has been drawn.

Use the line of best fit to estimate the mass of an object of length 24 cm.

In past papers

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