Covariance Cov(X, Y) and standard deviations of different datasets are given. Estimate the correlation coefficients and arrange them in increasing order. Choose the correct answer from the options given below.

1.Cov(X, Y) = 32, sigma-x = 8, sigma-y = 7

2.Cov(X, Y) = 36, sigma-x = 12, sigma-y = 5

3.Cov(X, Y) = 35, sigma-x = 7, sigma-y = 8

4.Cov(X, Y) = 39, sigma-x = 6, sigma-y = 13

A1, 2, 3, 4

B2, 3, 4, 1

C3, 4, 1, 2

D4, 1, 2, 3 ✓ Correct

Correct answer: (D) 4, 1, 2, 3

Explanation

The correlation coefficient equals covariance over the product of the standard deviations, ordering as 4, 1, 2, 3.

Dataset 4, 39 over 6 times 13, gives 0.50.

Dataset 1, 32 over 8 times 7, gives about 0.57.

Dataset 2, 36 over 12 times 5, gives 0.60.

Dataset 3, 35 over 7 times 8, gives about 0.63.

The correlation coefficient always lies between minus one and plus one.

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