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.
A. R= 0.5,     S(X)= 8,     S(Y)= 10
B. R= 4/7,     S(X)= 7,     S(Y)= 9
C. R= 0.7,     S(X)= 12,     S(Y)= 5
D. R= 19/42, S(X)= 14,     S(Y)= 6
Choose the correct answer from the options given below:

Correct option is C

Formula:
Covariance(X, Y) = R × S(X) × S(Y)

We will calculate this for each case:

A
R = 0.5
S(X) = 8
S(Y) = 10
Cov = 0.5 × 8 × 10 = 40

B
R = 4/7
S(X) = 7
S(Y) = 9
Cov = (4/7) × 7 × 9 = 4 × 9 = 36

C
R = 0.7
S(X) = 12
S(Y) = 5
Cov = 0.7 × 12 × 5 = 0.7 × 60 = 42

D
R = 19/42
S(X) = 14
S(Y) = 6
Cov = (19 × 14 × 6) ÷ 42 = (19 × 84) ÷ 42 = 1596 ÷ 42 = 38

Summary of Covariances:
B = 36
D = 38
A = 40
C = 42

Ascending Order:
B < D < A < C

Match with Options:
Option 3: B, D, A, C — Correct