Question

two series of X and Y with 50 items each of standard deviations of 4.8 and 3.5 respectively if the sum of products of deviation of x and y series from respective arithmetic means is 420 then find the correlation Coefficient between X and Y.​

Answer 1

The correlation Coefficient between X and Y is 0.476.

Given, numberof items (N) is equal to 50.

So, N = 50.

Standard deviation of x is given as 4.8

So, σx = 4.8

Standard deviation of y is given as 3.5

So, σy = 3.5

Also, the sum of the products of deviation of x and y series from their respective arithmetic means is 420.

This statement is represented as ∑xy = 420.

We know,coefficient of relation (r) is given as:

r = ∑xy/(N×σx×σy)

 = 420/(50×4.8×3.5)

 = 0.476

This is correlation coefficient value.