Question

The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.

Expenditure (in Rs)	Number of families
1000 − 1500	24
1500 − 2000	40
2000 − 2500	33
2500 − 3000	28
3000 − 3500	30
3500 − 4000	22
4000 − 4500	16
4500 − 5000	7

Answer 1

It can be observed from the given data that the maximum class frequency is 40, belonging to 1500 − 2000 intervals.

Therefore, modal class = 1500 − 2000

Lower limit (l) of modal class = 1500

Frequency (f₁) of modal class = 40

Frequency (f₀) of class preceding modal class = 24

Frequency (f₂) of class succeeding modal class = 33

Class size (h) = 500

Therefore, modal monthly expenditure was Rs 1847.83.

To find the class mark, the following relation is used.

Class size (h) of the given data = 500

Taking 2750 as assumed mean (a), d_i, u_i, and f_iu_iare calculated as follows.

Expenditure (in Rs)	Number of families fi	xi	di = xi − 2750		fiui
1000 − 1500	24	1250	− 1500	− 3	− 72
1500 − 2000	40	1750	− 1000	− 2	− 80
2000 − 2500	33	2250	− 500	− 1	− 33
2500 − 3000	28	2750	0	0	0
3000 − 3500	30	3250	500	1	30
3500 − 4000	22	3750	1000	2	44
4000 − 4500	16	4250	1500	3	48
4500 − 5000	7	4750	2000	4	28
Total	200				− 35

From the table, we obtain

Therefore, mean monthly expenditure was Rs 2662.50.