Chhetri AcademyGCSE & A level Paper Builder

S6Scatter graphs and correlation

Edexcel GCSE Maths (1MA1), Higher tier · Statistics

Practise Scatter graphs and correlation. 1 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.

Build a paper on this topic

▶ Watch videos on Scatter graphs and correlation (Corbettmaths on YouTube) · Practise all of Statistics

Sample questions

Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.

Question 1Easy3 marks
The scatter graph shows the number of hours that each of 10 students spent revising and the mark each student scored in a test.
[object Object]
(a) Write down the type of correlation shown.[1]
(b) Liam says, 'The graph proves that revising for longer causes a student to get a higher mark.'
Explain why Liam may be wrong.[1]
(c) Explain why the graph should not be used to estimate the mark of a student who revised for 30 hours.[1]
Show the answer and mark scheme
(a) Answer: Positive
  • B1 for positive

Worked solution: As the number of hours increases, the mark tends to increase: positive correlation.

(b) Answer: Correlation does not prove causation: another factor (such as interest in the subject) could affect both.
  • C1 for stating that correlation does not show that one variable causes the other

Worked solution: A scatter graph only shows that the two variables are related. It cannot show that one causes the other.

(c) Answer: 30 hours is far outside the range of the data (1 to 10 hours), so the trend may not continue; for example, the mark cannot go above 100.
  • C1 for explaining that 30 hours is outside the range of the data (extrapolation), so the pattern may not continue

Worked solution: The data only go up to 10 hours. Continuing the trend to 30 hours would give a mark over 100, which is impossible.

Question 2Medium6 marks
The table shows the number of hours of sleep some students had one night and their reaction times in a test the next morning.
[object Object]
(a) On the grid, draw a scatter graph to show this information.[2]
[object Object]
(b) Describe the relationship between the amount of sleep and the reaction time.[1]
(c) Draw a line of best fit on your scatter graph.
Use your line of best fit to estimate the reaction time when the amount of sleep is 8.2 hours.[2]
(d) Explain why it may not be reliable to use your line of best fit to estimate the reaction time when the amount of sleep is 14 hours.[1]
Show the answer and mark scheme
(a) Answer: Points plotted at (4.8, 300), (5.2, 300), (5.4, 310), (5.6, 305), (6.8, 265), (7.8, 260), (8.4, 245), (9.4, 230).
  • B2 for all 8 points plotted correctly, each within ½ small square (B1 for at least 6 points correct)

Worked solution: Plot each pair of values from the table as a cross: (4.8, 300), (5.2, 300), (5.4, 310), (5.6, 305), (6.8, 265), (7.8, 260), (8.4, 245), (9.4, 230).

(b) Answer: Negative correlation: as the amount of sleep increases, the reaction time tends to decrease.
  • B1 for negative correlation, or for a correct description in context (as the amount of sleep increases, the reaction time decreases)
(c) Answer: 250 ms (accept 235 to 265)
  • B1 for a single ruled straight line of best fit that follows the trend of the points, with points roughly evenly spread on each side and extending across the data
  • B1 for an answer in the range 235 to 265 ms (ft from their line of best fit, if it is acceptable)

Worked solution: Draw a ruled line through the middle of the points. Read up from 8.2 hours to the line, then across: about 250 ms.

(d) Answer: 14 hours is outside the range of the data, so the estimate would be an extrapolation: the trend may not continue.
  • C1 for a correct reason, e.g. 14 hours is outside the range of the data collected (extrapolation), so the trend may not continue
Question 3Hard7 marks
The table shows the average wind speed and the number of ferry crossings cancelled on some days.
[object Object]
(a) On the grid, draw a scatter graph to show this information.[2]
[object Object]
(b) One of the days does not fit the pattern shown by the others.
Write down the values for this day.[1]
(c) Ignoring the outlier, draw a line of best fit on your scatter graph.
Use your line of best fit to estimate the wind speed when the number of ferry crossings cancelled is 6.[2]
(d) Describe the relationship between the wind speed and the number of ferry crossings cancelled.[1]
(e) Explain why it may not be reliable to use your line of best fit to estimate the number of ferry crossings cancelled when the wind speed is 50 mph.[1]
Show the answer and mark scheme
(a) Answer: Points plotted at (2, 1), (11, 3), (14, 4), (16, 10), (17, 6), (24, 6), (27, 8), (28, 8), (30, 9), (34, 10).
  • B2 for all 10 points plotted correctly, each within ½ small square (B1 for at least 8 points correct)

Worked solution: Plot each pair of values from the table as a cross: (2, 1), (11, 3), (14, 4), (16, 10), (17, 6), (24, 6), (27, 8), (28, 8), (30, 9), (34, 10).

(b) Answer: Wind speed (mph) 16, ferry crossings cancelled 10
  • B1 for (16, 10)

Worked solution: The point (16, 10) is far from the trend of the other points, so it is an outlier.

(c) Answer: 20 mph (accept 17 to 23)
  • B1 for a single ruled straight line of best fit that follows the trend of the points (ignoring the outlier), with points roughly evenly spread on each side and extending across the data
  • B1 for an answer in the range 17 to 23 mph (ft from their line of best fit, if it is acceptable)

Worked solution: Draw a ruled line through the middle of the other points. Read across from 6 to the line, then down: about 20 mph.

(d) Answer: Positive correlation: as the wind speed increases, the number of ferry crossings cancelled tends to increase.
  • B1 for positive correlation, or for a correct description in context (as the wind speed increases, the number of ferry crossings cancelled increases)
(e) Answer: 50 mph is outside the range of the data, so the estimate would be an extrapolation: the trend may not continue.
  • C1 for a correct reason, e.g. 50 mph is outside the range of the data collected (extrapolation), so the trend may not continue

Related subtopics

Stuck? Get 1-to-1 help. Chhetri Academy tutors GCSE and A level Maths and Science online, with a free 30-minute trial lesson.

Book a free trial