For different sets of datasets X and Y, correlation coefficient between X and Y, that is R and standard deviation of X and Y, that is, S(X) and S(Y) are given in A-D below. Estimate the covariance between X and Y for each dataset and arrange in ascending order.
1.R= 0.5, S(X)= 8, S(Y)= 10
2.R= 4/7, S(X)= 7, S(Y)= 9
3.R= 0.7, S(X)= 12, S(Y)= 5
4.R= 19/42, S(X)= 14, S(Y)= 6
A2, 1, 4, 3
B3, 2, 1, 4
C2, 4, 1, 3 ✓ Correct
D1, 3, 4, 2
Correct answer: (C) 2, 4, 1, 3
Explanation
Covariance equals R multiplied by S(X) multiplied by S(Y). For A it is 0.5 times 8 times 10, that is 40. For B it is 4 by 7 times 7 times 9, that is 36. For C it is 0.7 times 12 times 5, that is 42. For D it is 19 by 42 times 14 times 6, that is 38. Ascending order is B, D, A, C, which is the sequence 2, 4, 1, 3.
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