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