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Nov 2021 p51 q6
2504
The weights, in kg, of 15 rugby players in the Rebels club and 15 soccer players in the Sharks club are shown below.
Rebels
75
78
79
80
82
82
83
84
85
86
89
93
95
99
102
Sharks
66
68
71
72
74
75
75
76
78
83
83
84
85
86
92
(a) Represent the data by drawing a back-to-back stem-and-leaf diagram with Rebels on the left-hand side of the diagram.
(b) Find the median and the interquartile range for the Rebels.
A box-and-whisker plot for the Sharks is shown below.
(c) On the same diagram, draw a box-and-whisker plot for the Rebels.
(d) Make one comparison between the weights of the players in the Rebels club and the weights of the players in the Sharks club.
Solution
(a) The back-to-back stem-and-leaf diagram is constructed as follows:
Rebels
Sharks
9 8 5
6
6 8
9 6 5 4 3 2
7
1 2 4 5 5 6 8
0 9 3 2
8
3 3 4 5 6
5 3 9 2
9
2
2
10
Key:8 | 7 | 2 means 78 kg for Rebels and 72 kg for Sharks.
(b) To find the median for the Rebels, arrange the data in order: 75, 78, 79, 80, 82, 82, 83, 84, 85, 86, 89, 93, 95, 99, 102. The median is the 8th value, which is 84 kg.
To find the interquartile range (IQR), calculate the lower quartile (Q1) and upper quartile (Q3). Q1 is the 4th value: 80 kg. Q3 is the 12th value: 93 kg. Thus, IQR = Q3 - Q1 = 93 - 80 = 13 kg.
(c) Draw a box-and-whisker plot for the Rebels with endpoints at 75 and 102, and median and quartiles as found in part (b).
(d) One comparison is that the average weight of the Rebels is higher than the average weight of the Sharks.