
Find the difference D = R_{1}  R_{2
}where R_{1 }= Rank of x and R_{2} = Rank of y
Note that S D = 0 (always) 
Calculate D^{2} and then find S D^{2} 
Apply the formula.
¬ Note :
In some cases, there is a tie between two or more items. in such a case each items have ranks 4th and 5th respectively then they are given = 4.5th rank. If three items are of equal rank say 4th then they are given = 5th rank each. If m be the number of items of equal ranks, the factor is added to S D^{2}. If there are more than one of such cases then this factor added as many times as the number of such cases, then
Example Calculate ‘ R ’ from the following data.
Student No.:

1

2

3

4

5

6

7

8

9

10

Rank in Maths :

1

3

7

5

4

6

2

10

9

8

Rank in Stats:

3

1

4

5

6

9

7

8

10

2

Solution :
Student
No.

Rank in
Maths (R_{1})

Rank in
Stats (R_{2})

R_{1}  R_{2
}D

(R_{1}  R_{2} )^{2
}D^{2}

1

1

3

2

4

2

3

1

2

4

3

7

4

3

9

4

5

5

0

0

5

4

6

2

4

6

6

9

3

9

7

2

7

5

25

8

10

8

2

4

9

9

10

1

1

10

8

2

6

36

N = 10



S D = 0

S D^{2} = 96

Calculation of R :

Index
6. 1 Introduction
6. 2 Correlation
6. 3 Types of Correlation
6. 4 Degrees of Correlation
6. 5 Methods of determining correlation
6. 6 Coefficients of Correlation for Bivariate
Grouped Data
6. 7 Probable Error
6. 8 Rank Correlation Coefficient
6. 9 Linear Regression
Chapter 7
