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 calculations are 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 a 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 of Items 
15

15

Arithmetic Mean 
25

18

Sum of Square Deviations 
136

138

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