Team A has a mean score of 24 and a range of 6. Team B has a mean score of 19 and a range of 14. Write down which team has the higher average score.
(Total for Question 1 is 1 mark)
2
Class X has test scores with a range of 18 marks. Class Y has test scores with a range of 7 marks. Write down which class is more consistent.
(Total for Question 2 is 1 mark)
3
Route 1 has a median journey time of 22 minutes and an interquartile range of 4 minutes. Route 2 has a median journey time of 22 minutes and an interquartile range of 11 minutes. Write down which route has the more consistent journey times.
(Total for Question 3 is 1 mark)
4
Write down whether the following statement is True or False. When comparing two data sets, a smaller range or interquartile range always means the data is more consistent.
(Total for Question 4 is 1 mark)
5
Bakery A sold loaves with a mean price of 2.40 pounds and Bakery B sold loaves with a mean price of 2.65 pounds. Work out the difference between the two mean prices.
(Total for Question 5 is 2 marks)
6
Café P served drinks with a median wait time of 6 minutes and a range of 9 minutes. Café Q served drinks with a median wait time of 6 minutes and a range of 3 minutes. Work out how much smaller Café Q's range is than Café P's range, and state which cafe has more consistent wait times.
(Total for Question 6 is 2 marks)
7
Two shifts at a warehouse pack parcels. Shift 1 has a mean of 145 parcels packed per day and a standard deviation of 12. Shift 2 has a mean of 145 parcels packed per day and a standard deviation of 20. Work out which shift has more variable daily output, and by how much the standard deviations differ.
(Total for Question 7 is 2 marks)
8
A survey of two book clubs recorded the number of books read last year. Club A: median 14 books, IQR 5 books. Club B: median 11 books, IQR 5 books. Give one similarity and one difference between the two clubs' data.
(Total for Question 8 is 2 marks)
9
Two swim squads recorded their fastest 100m times, in seconds. Squad 1: mean 68.4, range 5.2. Squad 2: mean 71.1, range 2.6. Work out the difference in the mean times, and state which squad is faster and which is more consistent.
(Total for Question 9 is 2 marks)
10
Two garages record the time taken, in minutes, to service a car. Garage X: median 42, IQR 10. Garage Y: median 38, IQR 16. Work out the difference between the two medians, and state which garage has more variable service times.
(Total for Question 10 is 2 marks)
11
Class 9A has a mean test score of 58 with a standard deviation of 9. Class 9B has a mean test score of 64 with a standard deviation of 9. Give one similarity and one difference between the two classes' results.
(Total for Question 11 is 2 marks)
12
A gym's morning class has a mean attendance of 22 with a range of 8. Its evening class has a mean attendance of 22 with a range of 15. Write down which class has more variable attendance.
(Total for Question 12 is 1 mark)
13
Write down whether the following statement is True or False. When two data sets have the same median, they must also have the same spread.
(Total for Question 13 is 1 mark)
14
Two farms recorded the mass, in kg, of lambs at birth. Farm A: mean 4.2, standard deviation 0.6. Farm B: mean 4.2, standard deviation 0.9. Work out the difference between the two standard deviations, and state which farm's lambs have more variable birth masses.
(Total for Question 14 is 2 marks)
15
Two production lines record the mass, in grams, of bags of crisps. Line 1: mean 152.4, range 6.0. Line 2: mean 148.9, range 2.5. A quality target requires a mean mass of at least 150 g with low variability. (a) Work out the difference in mean mass between the two lines. (b) State, with a reason, which line better meets the quality target.
(Total for Question 15 is 3 marks)
16
Two hospitals record patient waiting times, in minutes, in A&E. Hospital A: median 38, lower quartile 25, upper quartile 52. Hospital B: median 44, lower quartile 30, upper quartile 46. (a) Work out the interquartile range for each hospital. (b) Compare the typical waiting time and the consistency of waiting times at the two hospitals.
(Total for Question 16 is 3 marks)
17
Two call centres record how long, in minutes, calls take to resolve. Centre 1: mean 6.8, standard deviation 1.4. Centre 2: mean 5.9, standard deviation 2.6. A manager wants calls to be resolved quickly and consistently. (a) Work out the difference between the two means. (b) Explain, using both the means and standard deviations, which centre is performing better overall.
(Total for Question 17 is 3 marks)
18
A teacher compares two classes' end-of-year exam marks (out of 100). Class P: mean 61, standard deviation 8. Class Q: mean 61, standard deviation 15. The pass mark is 40. (a) Give one similarity between the two classes' results. (b) Explain which class is more likely to have students scoring below the pass mark, giving a reason.
(Total for Question 18 is 3 marks)
19
Two orchards record the mass, in kg, of apples picked from a random sample of trees. Orchard A: median 42, lower quartile 36, upper quartile 50. Orchard B: median 45, lower quartile 41, upper quartile 49. (a) Work out the interquartile range for each orchard. (b) State which orchard produces a more consistent yield per tree, giving a reason based on your answer to part (a).
(Total for Question 19 is 3 marks)
20
Three sprinters' race times over a season are summarised: Runner X: mean 11.85 s, standard deviation 0.12. Runner Y: mean 11.72 s, standard deviation 0.28. Runner Z: mean 11.85 s, standard deviation 0.05. A coach wants to select the runner who is both fast and consistent for a relay. (a) Identify the fastest runner on average. (b) Identify the most consistent runner. (c) Explain why the coach's choice is not straightforward, referring to both runners identified in (a) and (b).
(Total for Question 20 is 3 marks)
Mark scheme · S08D Comparing Data Sets: Fluency and Exam Drill
Question 1
B1 Team A cao
Answer: Team A
Question 2
B1 Class Y cao
Answer: Class Y
Question 3
B1 Route 1 cao
Answer: Route 1
Question 4
B1 True cao
Answer: True
Question 5
M1 correct method, 2.65 - 2.40
A1 0.25 (25p) cao
Answer: 0.25 pounds (25p)
Question 6
M1 correct method, 9 - 3
A1 6 minutes smaller, and Cafe Q is more consistent, both cao
Answer: 6 minutes smaller; Cafe Q has more consistent wait times
Question 7
M1 correct method, 20 - 12
A1 Shift 2, differ by 8, both cao
Answer: Shift 2 is more variable; the standard deviations differ by 8
Question 8
B1 correct similarity, e.g. both clubs have the same spread, since the IQR is 5 for both oe
B1 correct difference, e.g. Club A read more books on average, since its median (14) is higher than Club B's (11) oe
Answer: Similarity: both clubs have the same IQR (5), so the same spread. Difference: Club A has the higher median (14 vs 11), so Club A members typically read more books.
Question 9
M1 correct method, 71.1 - 68.4
A1 2.7 seconds; Squad 1 is faster (lower mean); Squad 2 is more consistent (smaller range), all cao
Answer: 2.7 seconds; Squad 1 is faster; Squad 2 is more consistent
Question 10
M1 correct method, 42 - 38
A1 4 minutes; Garage Y is more variable (larger IQR), both cao
Answer: 4 minutes; Garage Y has more variable service times
Question 11
B1 correct similarity, e.g. the two classes have the same spread, since the standard deviation is 9 for both oe
B1 correct difference, e.g. Class 9B scored higher on average, since its mean (64) is higher than 9A's (58) oe
Answer: Similarity: both classes have the same standard deviation (9), so the same spread of scores. Difference: Class 9B has the higher mean (64 vs 58), so 9B performed better on average.
Question 12
B1 Evening class cao
Answer: Evening class
Question 13
B1 False cao
Answer: False
Question 14
M1 correct method, 0.9 - 0.6
A1 0.3; Farm B is more variable, both cao
Answer: 0.3 kg; Farm B has more variable birth masses
Question 15
M1 correct method, 152.4 - 148.9
A1 3.5 g cao
B1 Line 1, with valid reason, e.g. only Line 1 has a mean above 150 g, and although its range is larger it still meets the mass target oe
Answer: (a) 3.5 g. (b) Line 1, because its mean (152.4 g) meets the 150 g target while Line 2's mean (148.9 g) does not.
Question 16
M1 correct method for at least one IQR, e.g. 52 - 25
A1 Hospital A: IQR 27; Hospital B: IQR 16, both cao
B1 correct comparison, e.g. Hospital B has a higher median (longer typical wait) but Hospital A has a larger IQR (less consistent) oe
Answer: (a) Hospital A: IQR = 27. Hospital B: IQR = 16. (b) Hospital B has the longer typical wait (higher median, 44 vs 38), but Hospital A's waiting times are less consistent (larger IQR, 27 vs 16).
Question 17
M1 correct method, 6.8 - 5.9
A1 0.9 minutes cao
B1 valid overall judgement using both statistics, e.g. Centre 2 resolves calls faster on average, but Centre 1 is more consistent since its standard deviation is smaller, so neither centre is better on both measures oe
Answer: (a) 0.9 minutes. (b) Centre 2 has the faster average resolve time (lower mean), but Centre 1 is more consistent (lower standard deviation), so the two centres trade off speed against consistency.
Question 18
B1 correct similarity, e.g. both classes have the same mean mark (61) oe
B1 correctly identifies Class Q
B1 valid reason, e.g. Class Q has a much larger standard deviation, so its marks are more spread out and more likely to include low scores below 40 oe
Answer: (a) Both classes have the same mean (61). (b) Class Q, because its larger standard deviation (15 vs 8) means marks are more spread out, making very low scores below the pass mark more likely.
Question 19
M1 correct method for at least one IQR, e.g. 50 - 36
A1 Orchard A: IQR 14; Orchard B: IQR 8, both cao
B1 Orchard B, with reason that its IQR (8) is smaller than Orchard A's (14), so its yields are less spread out
Answer: (a) Orchard A: IQR = 14. Orchard B: IQR = 8. (b) Orchard B, because its smaller IQR shows the yields per tree are more tightly grouped together.
Question 20
B1 Runner Y (lowest mean) cao
B1 Runner Z (lowest standard deviation) cao
B1 valid explanation, e.g. Runner Y is fastest on average but Runner Z is the most consistent, so no single runner is best on both measures oe
Answer: (a) Runner Y. (b) Runner Z. (c) Runner Y has the fastest average time but is not the most consistent, while Runner Z is the most consistent but not the fastest, so the coach must choose which quality matters more for the relay.