Question

Following data gives the age of husbands (X) and age of wives (Y) in years. Construct a bivariate frequency distribution table and find the marginal distributions.

X	27	25	28	26	29	27	28	26	25	25	27
Y	21	20	20	21	23	22	20	20	19	19	23
X	26	29	25	27	26	25	28	25	27	26
Y	19	23	23	22	21	20	22	23	22	21

Find conditional frequency distribution of age of husbands when the age of wife is 23 years.

Answer 1

Let X: Age of husbands in years
Y: Age of Wives in years

Y/X	25	26	27	28	29
1	II	I	–	–	–
2	II	I	–	II	–
3	–	III	I	–	–
4	–	–	III	I	–
5	II	–	I	–	II

Bivariate frequency distribution is

Y/X	2	3	4	5	6	Total ()
1	–	1	2	–	1	4
2	–	1	–	2	–	3
3	2	1	3	–	–	6
4	–	2	–	–	1	3
5	5	–	3	1	–	9
Total ()	7	5	8	3	2	26

Marginal frequency distribution of X (Age of husbands)

X	25	26	27	28	29	Total
()	6	5	5	3	2	21

Margin frequency distribution of Y (Age of wives)

Y	19	20	21	22	23	Total
()	3	5	4	4	5	21

Conditional distribution of Xage of husbands) when Y (age of wives) is 23 years.

X	25	26	27	28	29	Total
Frequency	2	–	1	–	2	5

Answer 2

Given, X =  Age of Husbands (in years)

Y = Age of Wives (in years)

Now, minimum value of X is 25 and maximum value is 29.

Also, minimum value of Y is 19 and maximum value is 23.

Bivariate frequency distribution is as follows:

Y/X	25	26	27	28	29	Total (fy)
19	II	I	–	–	–	3
20	II	I	–	II	–	5
21	–	III	I	–	–	4
22	–	–	III	I	–	4
23	II	–	I	–	II	5
Total (fx)	6	5	5	3	2	21

Marginal frequency distribution of X:

X	25	26	27	28	29	Total
Frequency	6	5	5	3	2	21

Marginal frequency distribution of Y:

Y	19	20	21	22	23	Total
Frequency	3	5	4	4	5	21

Conditional frequency distribution of X when Y is 23:

X	25	26	27	28	29	Total
Frequency	2	0	1	0	2	5