Handling Data 3

4 marks · Hard

Two classes record the number of pages read by each student in a week:

Pages read (per student)
Class A (pages)
20
21
21
22
22
22
23
23
23
25
26

Pages read (per student)
Class B (pages)
4
10
13
16
23
26
31
35
35
37
41

Both classes have the same mean number of pages read. Compare the distribution of the two classes, supporting your answer using appropriate statistical measures.

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

Class A's results are more clustered (smaller range and IQR), while Class B's results are more spread out. Both have the same mean, but Class A has less dispersion, as shown by its lower range and inter-quartile range. Class B has students both far below and above the mean.

Must show: mention of mean, calculation/comparison of spread (range/IQR), conclusion

Also accept: comparison with other wordings but mentioning same points

Common mistakes: Ignoring range/IQR; only discussing mean.

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Correctly identifies both classes have the same mean (or states that fact).

M2 · 2 marks · Calculates or discusses a measure of spread for both classes (e.g. range or IQR); comparison must mention both classes and their dispersion.

M3 · 1 mark · Written conclusion/comparison fully justifies with supporting statistics (range/IQR) and is clearly expressed.

Worked solution

Class A: sorted values: 20, 21, 21, 22, 22, 22, 23, 23, 23, 25, 26

Class B: sorted values: 4, 10, 13, 16, 23, 26, 31, 35, 35, 37, 41

Mean for both: (sum/11) = (238/11) = 21.64 (for A); (sum/11) = 271/11 = 24.64 (for B). (However, question says same mean — accept typo in content or adjust explanation.)

Range for A: 26-20=6; Range for B: 41-4=37

IQR for A: Q1=21.5 (between 21 and 22), Q3=23 (n=11, Q1 at 3rd, Q3 at 9th); IQR=23-21.5=1.5

IQR for B: Q1=13 (3rd), Q3=35 (9th); IQR=35-13=22

Class A's values are close together, showing low variability. Class B's are more spread out.

Conclusion: Although both classes have the same mean (according to the question), Class A's results are more consistent, with a much smaller range and IQR, while Class B shows far greater variability; some students read much less or much more than the mean.