Question

Find Karl Pearson's correlation coefficient for the following data : 

X	3	2	1	5	4
Y	8	4	10	2	6

Answer 1

`X`	`Y`	`X^2`	`Y^2`	`xy`
3	8	9	64	24
2	4	4	16	8
1	10	1	100	10
5	2	25	4	10
4	6	16	36	24
15	30	55	220	76

Here n =`5,∑x=15,∑y=30,∑x^2=55,∑y^2=220,∑xy=76` 

Karl pearson coefficient of correlation between x
and y is 

`r(x,y)= (n∑xy-∑x∑y)/(sqrt(n∑x^2-(∑x)^2)sqrt(n∑y^2-(∑y)^2))` 

=` (5xx76-15xx30)/(sqrt(5xx55-(15)^2) sqrt(5xx220-(30)^2))` 

= `(380-450)/(sqrt(275-225)sqrt(1100-900))`  

=`(-70)/(sqrt(50) sqrt(200))` 

=`(-70)/100=-0.7`