Examples of Correlation
Calculate and analyze the correlation coefficient between the number of study hours and the number of sleeping hours of different students.
Number of Study hours 
2

4

6

8

10

Number of Sleeping hours 
10

9

8

7

6

Solution:
The necessary calculation is given below:







2

10

4

+2

8

16

4

4

9

2

+1

2

4

1

6

8

0

0

0

0

0

8

7

+2

1

2

4

1

10

6

+4

2

8

16

1








and
There is perfect negative correlation between the number of study hours and the number of sleeping hours.
Example:
From the following data, compute the coefficient of correlation between and :
Series

Series


Number if Items 
15

15

Arithmetic Mean 
25

18

Sum of Square Deviations 
136

138

Summation of products of deviations of and series from their arithmetic means = 122.
Solution:
Here
and hence