Arrange the correlation coefficients computed from the following covariance and standard-deviation data in ascending order. Choose the correct answer from the options given below.

1.Cov(x, y) = 18, sigma-x = 4, sigma-y = 9

2.Cov(x, y) = 15, sigma-x = 8, sigma-y = 3

3.Cov(x, y) = 16, sigma-x = 7, sigma-y = 4

4.Cov(x, y) = 21, sigma-x = 6, sigma-y = 5

A1, 3, 2, 4 ✓ Correct

B2, 3, 4, 1

C3, 2, 1, 4

D4, 2, 1, 3

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

Explanation

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

Dataset 1, 18 over 4 times 9, gives 0.50.

Dataset 3, 16 over 7 times 4, gives about 0.57.

Dataset 2, 15 over 8 times 3, gives about 0.63.

Dataset 4, 21 over 6 times 5, gives 0.70.

A correlation nearer one signals a stronger linear association.

Want more like this? Create a free account to practise a full test, track your progress, and get spaced-repetition review.