Arrange the correlation coefficients computed from the following information on covariance i.e., cov (x, y) and standard deviations ( and ), in increasing order:
(A) cov(x, y) = 18, σx = 4, σy = 9
(B) cov(x, y) = 15, σx = 8, σy = 3
(C) cov(x, y) = 16, σx = 7, σy = 4
(D) cov(x, y) = 21, σx = 6, σy = 5
Choose the most appropriate answer from the options given below:

Correct option is A

Given:

We are provided with the covariance cov(x,y) and the standard deviations $$\sigma_x$$​ and $$\sigma_y$$​ for each pair of variables.

Formula Used:

The correlation coefficient r is given by the formula:

r = $$\frac{\text{cov}(x, y)}{\sigma_x \sigma_y}$$​​

Solution:

For (A):

​$$r_A = \frac{18}{4 \times 9} = \frac{18}{36} = 0.5$$​​

For (B):

​$$r_B = \frac{15}{8 \times 3} = \frac{15}{24} = 0.625$$​​

For (C):

​$$r_C = \frac{16}{7 \times 4} = \frac{16}{28} = 0.5714$$​​

For (D):

​$$r_D = \frac{21}{6 \times 5} = \frac{21}{30} = 0.7$$​​

Arranging in increasing order:

​$$r_A = 0.5, \, r_C = 0.5714, \, r_B = 0.625, \, r_D = 0.7$$​​
Thus, The correct option is (a) (A), (C), (B), (D).