6.6 Coefficient Of Correlation For Bivariate Grouped Data
When the number of observations is very large, we need to arrange the data into different classes, which are either discrete or continuous. Items having values falling in a particular class are placed together and those having values falling in another class are placed together. Due to this the whole data is divided into horizontal rows and vertical columns, with one variable placed horizontally and the other placed vertically. The table so obtained is a twoway frequency distribution table and is called the correlation table or Bivariate frequency distribution table. The formula for calculating and for bivariate distribution is given by
STEPS:

First write down the midpoints of x along a horizontal raw and those of y along a vertical column.

Find

Multiply each frequency by the corresponding value of u then by corresponding value of v to get fuv. Write these numbers in the same box at the top.

Add the frequencies horizontally, and write down the total. Similarly add the frequencies vertically and write down its total.

Multiply this additions of x by u to get f u.

Multiply this addition of y by v to get f v.

Multiply these frequencies by the square of u to get f u^{2}.

Multiply these frequencies by the square of v to get f v^{2}.

Add horizontally ( or vertically ) the top numbers denoting f u v written in each box ( or cell )
Write down S f u, S f u^{2}, S f v, S f v^{2} and S f u v and then use the above formula.
Example Calculate the coefficient of correlation
for the following data.
Age (years) of Husband

Age (years) of wife

Total

10 20

20 30

30 40

40 50

50 60

10  25
25  35
35  45
45  55
55  65

5
3

3
15
11

11
14
7

7
12
3

3
6

8
29
32
22
9

Total

8

29

32

22

9

100


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
