Question

Compute the coefficient of correlation for the following data : 

n = 100 ; `bar x` = 62 , ` bar y` = 53 . σx = 10 ; σ y = 12 ,

`sum ("x"_1 - bar x) ("y"_1 - bar y) = 8000`

Answer 1

Given that 

n = 100 ; `bar x` = 62 , ` bar y` = 53 . σx = 10 ; σ y = 12 ,

`sum ("x"_1 - bar x) ("y"_1 - bar y) = 8000`

To find correlation coefficient 

Cov (x, y) = `1/"n" sum ("x"_1 - bar x) ("y"_1 - bar y)`

`= 8000/100 = 80`

Cov (x, y) = 80 

Corr. (x,y) = `("Cov" (x , y))/(sigma x  sigma  y)`

`= 80/(10 xx 12)`

= 0.67

∴ Coefficient of correlation is 0.67.