Revision Library

revisionlibrary.co.uk

FOUNDATION

F02 Correlation and Causation

EDEXCEL 1ST0 · Calculator allowed · about 75 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

For each statement about correlation, write down True or False.

(i)Positive correlation means that as one variable increases, the other variable also tends to increase.(1)

(ii)Negative correlation means that both variables always decrease at exactly the same rate.(1)

(iii)If there is no correlation between two variables, the points on a scatter graph show no clear pattern.(1)

(Total for Question 1 is 3 marks)

Complete each sentence with the correct word.

(a)Just because two variables show a correlation, this does not mean that one _______ the other.(1)

(b)A hidden variable that affects both of the variables being studied, and so creates an apparent relationship between them, is called a _______ variable.(1)

(Total for Question 2 is 2 marks)

For each description, write down whether it shows positive correlation, negative correlation or no correlation.

(a)As the age of a car increases, its value tends to decrease.(1)

(b)A pupil's shoe size compared with the last two digits of their home phone number.(1)

(c)As the midday temperature increases, the number of cold drinks sold at a shop tends to increase.(1)

(Total for Question 3 is 3 marks)

For each pair of variables, state whether you would expect positive correlation, negative correlation or no correlation between them.

(a)The distance a delivery driver travels in a day and the amount of fuel used.(1)

(b)The age of a car and its value in pounds.(1)

(c)A person's height and the day of the week they were born on.(1)

(d)The number of hours spent revising for a test and the number of mistakes made in the test.(1)

(Total for Question 4 is 4 marks)

A market trader records the number of hours of sunshine and the number of ice lollies sold on 10 days. The scatter graph shows the results.

(a)Describe the correlation shown on the scatter graph.(2)

(b)Using the scatter graph, describe what this correlation shows about hours of sunshine and ice lolly sales.(1)

(Total for Question 5 is 3 marks)

Three scatter graphs, Graph A, Graph B and Graph C, are shown below. For each graph, write down the type of correlation shown and, where appropriate, its strength.

(a)Graph A(1)

(b)Graph B(1)

(c)Graph C(1)

(Total for Question 6 is 3 marks)

A cafe manager records the midday temperature, in degrees C, and the number of hot chocolates sold on 10 days. The scatter graph shows the results.

(a)Describe the correlation shown on the scatter graph, ignoring the unusual point.(2)

(b)What name is given to a point, such as the one at 16 degrees C, that does not fit the pattern of the rest of the data?(1)

(Total for Question 7 is 3 marks)

For each statement about lines of best fit, write down True or False.

(i)A line of best fit must always pass through the origin (0, 0).(1)

(ii)A line of best fit should be drawn so that it passes through the data with roughly the same number of points above the line as below it.(1)

(iii)Using a line of best fit to estimate a value inside the range of the given data (interpolation) is generally more reliable than using it to estimate a value far outside that range (extrapolation).(1)

(Total for Question 8 is 3 marks)

A student records the number of hours spent revising (x) and the test score out of 50 (y) for 10 classmates.

Hours revising (x)	1	2	3	4	5	6	7	8	9	10
Test score out of 50 (y)	10	16	15	21	22	27	28	34	33	39

The points for 1 to 8 hours have already been plotted on the grid below.

(a)Plot the remaining two points from the table on the grid.(2)

(b)Draw a line of best fit on the scatter graph.(2)

(Total for Question 9 is 4 marks)

The scatter graph below shows the completed data for all 10 classmates from Question 9, together with a line of best fit.

(a)One of the classmates revised for 6.5 hours. Use the line of best fit to estimate their test score.(2)

(b)Another student plans to revise for 15 hours. Use the line of best fit to estimate their test score.(2)

(c)Comment on the reliability of the estimate found in part (b).(2)

(Total for Question 10 is 6 marks)

A researcher collected data from 12 primary school classes and found a strong positive correlation between the average shoe size of pupils in a class and their average score on a reading test. A newspaper headline claims: 'Bigger feet make children better readers.'

(a)Explain why the newspaper's claim is not a valid conclusion to draw from this data.(2)

(b)Suggest one factor, other than age, that could affect a pupil's reading score.(1)

(Total for Question 11 is 3 marks)

A shop owner notices that in months when sunglasses sales are higher, ice cream sales are also higher. Suggest a factor, other than one causing the other, that could explain this correlation, and explain how it affects both variables.

(Total for Question 12 is 2 marks)

Fire brigade records show that fires attended by a larger number of fire engines tend to result in more damage, in pounds. A local councillor claims: 'Sending fewer fire engines to fires would reduce the amount of damage caused.' Explain why the councillor's claim is not supported by this data.

(Total for Question 13 is 2 marks)

A student wants to investigate whether there is a relationship between the number of hours people spend using a smartphone each day and the number of hours they sleep at night. She plans to survey 15 adults.

(a)Plan: Give one reason why the student should choose a random sample of adults, rather than just asking her friends, when planning her survey.(1)

(b)Collect: Give a method the student could use to collect the smartphone usage data, and state one advantage of this method over asking people to estimate from memory.(2)

(c)Process: The student plots her data on a scatter graph and adds a line of best fit. Describe one way she could check that her line of best fit is appropriate.(1)

(d)Interpret: The completed scatter graph shows a negative correlation. State what this suggests about smartphone use and sleep, and explain why the student should not conclude that using a smartphone directly causes people to sleep less.(3)

(Total for Question 14 is 7 marks)

A seaside museum's ice cream van keeps a record, over 9 days, of the number of museum visitors and the van's daily takings, in pounds. One day's data is unusual: a school arranged a large visit to the museum on a cold, wet day, giving high visitor numbers but very low ice cream takings.

(a)Describe the correlation shown by the scatter graph, ignoring the unusual point.(2)

(b)A visitor comments: 'More people visiting the museum causes more ice cream to be sold.' Using the context, explain why this conclusion is not fully reliable, referring to a possible confounding factor.(2)

(Total for Question 15 is 4 marks)

Mark scheme · F02 Correlation and Causation

Question 1

(i) B1 True cao
(i) Answer: True
(ii) B1 False cao
(ii) Answer: False
(iii) B1 True cao
(iii) Answer: True

Question 2

(a) B1 causes oe (e.g. causing)
(a) Answer: causes
(b) B1 confounding oe (accept third)
(b) Answer: confounding

Question 3

(a) B1 Negative correlation cao
(a) Answer: Negative correlation
(b) B1 No correlation cao
(b) Answer: No correlation
(c) B1 Positive correlation cao
(c) Answer: Positive correlation

Question 4

(a) B1 Positive correlation cao
(a) Answer: Positive correlation
(b) B1 Negative correlation cao
(b) Answer: Negative correlation
(c) B1 No correlation cao
(c) Answer: No correlation
(d) B1 Negative correlation cao
(d) Answer: Negative correlation

Question 5

(a) B1 positive correlation
(a) B1 strong (correlation)
(a) Answer: Strong positive correlation
(b) B1 as the number of hours of sunshine increases, the number of ice lollies sold tends to increase, oe (stated in context)
(b) Answer: As the hours of sunshine increase, more ice lollies tend to be sold.

Question 6

(a) B1 strong positive correlation
(a) Answer: Strong positive correlation
(b) B1 weak negative correlation
(b) Answer: Weak negative correlation
(c) B1 no correlation
(c) Answer: No correlation

Question 7

(a) B1 negative correlation
(a) B1 strong (correlation)
(a) Answer: Strong negative correlation
(b) B1 outlier cao
(b) Answer: Outlier

Question 8

(i) B1 False cao
(i) Answer: False
(ii) B1 True cao
(ii) Answer: True
(iii) B1 True cao
(iii) Answer: True

Question 9

(a) B1 point (9, 33) plotted correctly
(a) B1 point (10, 39) plotted correctly
(a) Answer: (9, 33) and (10, 39)
(b) B1 a single ruled straight line with a positive gradient
(b) B1 line passes through the data with a roughly equal number of points on each side, e.g. from about (0, 8) to (10, 38)
(b) Answer: A straight line of best fit, for example from about (0, 8) to (10, 38).

Question 10

(a) M1 reads from the line of best fit at 6.5 hours
(a) A1 answer in the range 25 to 30, e.g. 27.5
(a) Answer: 27.5 (accept 25 to 30)
(b) M1 extends the line of best fit to 15 hours
(b) A1 answer around 50 to 56, e.g. 53
(b) Answer: 53 (accept 50 to 56)
(c) B1 identifies that 15 hours is outside the range of the data collected (extrapolation)
(c) B1 recognises the estimate is not reliable, e.g. because 53 is impossible as the test is only out of 50
(c) Answer: The estimate is not reliable, since 15 hours is well outside the range of the data (extrapolation), and a score of 53 is impossible because the test is out of 50.

Question 11

(a) B1 correlation does not prove causation
(a) B1 identifies age as a plausible confounding variable: older pupils tend to have both bigger feet and higher reading scores (from more years of practice), so age affects both variables rather than foot size causing better reading
(a) Answer: The correlation does not prove causation. A likely explanation is a confounding variable, age: older pupils tend to have both bigger feet (as they grow) and higher reading scores (from more years of practice), so age affects both variables rather than foot size causing better reading.
(b) B1 any sensible factor, e.g. the amount of reading practice at home, the quality of teaching, or whether English is the pupil's first language, oe
(b) Answer: For example, the amount of time spent reading at home (or any other sensible factor affecting reading ability).

Question 12

B1 identifies a plausible common cause, e.g. warm or sunny weather
B1 explains that this factor increases both variables, e.g. on hot sunny days people are more likely to buy both sunglasses and ice cream
Answer: Warm, sunny weather is a likely confounding factor: on hot sunny days people are more likely to buy both sunglasses and ice cream, so the weather affects both variables rather than one causing the other.

Question 13

B1 correlation does not prove causation
B1 identifies the size or severity of the fire as the confounding variable: a larger, more serious fire causes both more fire engines to be sent and more damage, rather than the fire engines causing the damage
Answer: The claim is not supported. The confounding variable is the size (severity) of the fire: a larger fire causes both more fire engines to be sent and more damage, so the number of fire engines does not cause the damage. Sending fewer engines to a serious fire could make the damage worse, not better.

Question 14

(a) B1 a random sample is more likely to be representative of adults in general, whereas her friends may share similar ages or habits and could bias the results
(a) Answer: A random sample is more likely to represent the whole adult population fairly; her friends might have similar ages or habits, which could bias the results.
(b) B1 valid method, e.g. use the 'screen time' data recorded automatically in the smartphone's settings
(b) B1 advantage, e.g. this is more accurate and objective than people's memory or estimates
(b) Answer: Use the screen time feature built into each participant's phone to record actual daily usage; this is more accurate than relying on people's memory or estimates.
(c) B1 check that the line passes through (or close to) the middle of the data, with a roughly equal number of points above and below it
(c) Answer: Check that the line passes through the main body of the points, with roughly equal numbers of points on each side of the line.
(d) B1 as daily smartphone use increases, hours of sleep tends to decrease, oe
(d) B1 correlation does not prove causation
(d) B1 identifies a plausible confounding variable, e.g. stress levels or a demanding work schedule could cause both more smartphone use (e.g. late-night messages) and less sleep
(d) Answer: As daily smartphone use increases, hours of sleep tends to decrease. However, correlation does not prove causation: a third factor, such as a person's stress levels or a demanding work schedule, could cause both more smartphone use (e.g. checking messages late at night) and less sleep, without one directly causing the other.

Question 15

(a) B1 positive correlation
(a) B1 identifies/excludes the outlier, e.g. the point at 260 visitors, £15 takings, before describing the trend
(a) Answer: Positive correlation (ignoring the outlier at 260 visitors, £15 takings).
(b) B1 correlation does not prove causation
(b) B1 identifies a plausible confounding factor, e.g. warm sunny weather brings more people out to both the museum and the ice cream van; the unusual school-trip day shows visitor numbers can rise for reasons unrelated to ice cream sales
(b) Answer: The correlation does not prove that museum visitors directly cause ice cream sales. Warm, sunny weather is a likely confounding factor, bringing more people out to both the museum and the ice cream van. The unusual day (high visitors, low takings, due to a school trip on a cold, wet day) shows that visitor numbers can rise for reasons unrelated to ice cream sales, supporting the idea that a third factor, not direct causation, explains the pattern.

Correlation and Causation - Worksheets, Questions and Revision