Question

Following tale gives income (X) and expenditure (Y) of 25 families:

Y/X	200 – 300	300 – 400	400 – 500
200 – 300	IIII I	IIII I	I
300 – 400	–	IIII	IIII I
400 – 500	–	–	II

Find How many families have their income Rs. 300 and more and expenses Rs. 400 and less?

Answer 1

Bivariate frequency distribution table for Income (X) and Expenditure (Y) is as follows:

Y/X	200 – 300	300 – 400	400 – 500	Total (fy)
200 – 300	6	6	1	13
300 – 400	0	4	6	10
400 – 500	0	0	2	2
Total (fx)	6	10	9	25

The cells 300 – 400 and 400 – 500 are having income ₹ 300 and more and the cells 200 – 300 and 300 – 400 are having expenditure ₹ 400 and less. Now, the following table indicates the number of families satisfying the above condition.

Y/X	300 – 400	400 – 500	Total
200 – 300	6	1	7
300 – 400	4	6	10
Total	10	7	17

∴ There are 17 families with income ₹ 300 and more and expenditure ₹ 400 and less.