Apps. and Interpretation for IBDP Maths Ebook 1 | Page 331

In the table below, the number of goals for each team is going to be ranked, such that 1
represents the team with the most number of goals and 8 represents the team with the
least number of goals.
Team A B C D E F G H
Number of
goals’ rankings
1 b 6 d 8 f g 7
Position in the
league
3 1 6 2 8 4 5 7
(a) Write down the values of b , d , f and g .
(b) Find the Spearman’s rank correlation coefficient for the second table.
(c) Comment on the conclusion of the result in (b).
[2]
[2]
[1]
4. The following table shows the rankings of the six observations for two variables X and
Y , where 1 represents the highest rank and 6 represents the lowest rank:
Observation First Second Third Fourth Fifth Sixth
X 2 4 3 5 6 1
Y 1 2 3 4 5 6
(a) Find the Spearman’s rank correlation coefficient for the above data set.
[2]
The sixth observation of both X and Y are said to be the outlier of the data set and are
deleted. The following table shows the updated rankings:
Observation First Second Third Fourth Fifth
X a b c d e
Y 1 2 3 4 5
22
(b) (i) Write down the values of a and e .
(ii) Find the value of the R
s
, the Spearman’s rank correlation coefficient for
the updated data set.
(iii)
Comment on the change in the values of the Spearman’s rank correlation
coefficient.
[4]
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