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Question 15
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(a) In a test, eight students obtained the following marks in Biology and Physics.
Student |
A |
B |
C |
D |
E |
F |
G |
H |
Biology |
76 |
52 |
63 |
48 |
84 |
36 |
28 |
70 |
Physics |
75 |
78 |
28 |
45 |
56 |
71 |
54 |
58 |
- Calculate, correct to two decimal places, the spearman’s rank correlation coefficient of the distribution.
- Comment on your results in (a)(i).
(b)(i) Three-digit numbers are to be formed from 1,2,3,4, and 5. If repetition is not allowed, how many numbers can be formed?
(ii) What is the probability of selecting an odd number from the numbers formed in (b)(i)?
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It was reported that this question was attempted by majority of the candidates and their performance was commendable. They were able to obtain the sum of the squared differences in their ranks SD2 = 70, apply the formular r = 1 -  correctly to obtain r = 0.17 which implied a weak correlation.
In part (b), the number of numbers that can be formed = 5 x 4 x 3 = 60. The number of odd numbers that can be formed = 4 x 3 x 3 = 36. Therefore probability of selecting an odd number = 36/60 = 3/5. |
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