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Nov 2021 p53 q2
2382
Lakeview and Riverside are two schools. The pupils at both schools took part in a competition to see how far they could throw a ball. The distances thrown, to the nearest metre, by 11 pupils from each school are shown in the following table.
Lakeview
10
14
19
22
26
27
28
30
32
33
41
Riverside
23
36
21
18
37
25
18
20
24
30
25
Draw a back-to-back stem-and-leaf diagram to represent this information, with Lakeview on the left-hand side.
Find the interquartile range of the distances thrown by the 11 pupils at Lakeview school.
Solution
(a) The back-to-back stem-and-leaf diagram is constructed as follows:
Lakeview
Stem
Riverside
940
1
88
8762
2
013455
320
3
067
1
4
Key: \( 6 \mid 2 \mid 3 \) means 26 m (Lakeview) and 23 m (Riverside).
(b) Arrange Lakeview’s data in ascending order:
10, 14, 19, 22, 26, 27, 28, 30, 32, 33, 41
Lower quartile (LQ) = 19 (3rd value in lower half).
Upper quartile (UQ) = 32 (3rd value in upper half).