Question

A research study found that in one physics class, the correlation between pre-exam and post-exam grades was 0.90. The variance of pre-exam grades was 9 and the variance of post-exam grades was 16. Thus, the variance of the difference between pre-exam and post-exam grades is:_________.

Answer 1

Variance of difference between pre-exam and post-exam grades = 10.8

Explanation:

Correlation (X,Y) = Covariance (X,Y) / √ { Variance (X) . Variance (Y) }

Given : Correlation (Pre & post exam grade) = 0.9 ; Variance (Pre exam grade) = 0.90 ; Variance (Post exam grade) = 16

So, 0.9 = Covariance (X,Y) / √ { 16 x 9 }

0.9 = Covariance (X,Y) / 12

Covariance (X,Y) = 12 x 0.9 = 10.8