Apps. and Interpretation for IBDP Maths Ebook 1 | Page 335

4. Seven divers participated in a diving competition. There are two judges in total: A trainee
judge and a professional judge. The following table shows the scores of the seven divers
awarded by the two judges:
Diver A B C D E F G
Trainee judge 8.6 8.9 8.7 8.5 8.2 8.4 8.1
Professional judge 8.5 8.8 8.7 8.4 8.3 8.0 8.2
(a) Find the product moment correlation coefficient for the above data set.
[2]
In the table below, the scores of the seven divers awarded by the two judges are going to
be ranked, such that 1 represents the highest score and 8 represents the lowest score.
Diver A B C D E F G
Trainee judge 3 1 2 4 6 5 7
Professional judge a b c d e f g
(b) (i) Express b in terms of a .
(ii) Express g in terms of a .
[2]
(c) Find the Spearman’s rank correlation coefficient for the second table.
[2]
Later, the trainee judge adjusts the score of the diver B such that the score is increased.
(d)
Explain why the Spearman’s rank correlation coefficient in (c) is unchanged.
[1]
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