(Q12) 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 (₹)	1000-1500	1500-2000	2000-2500	2500-3000	3000-3500	3500-4000	4000-4500	4500-5000
Number of families	24	40	33	28	30	22	16	7

Answer :

Expenditure (C.I)	Number of families (fi)	Class Marks (xi)	ui = xi - a h (h = 500)	fiui
1000-1500	24	1250	-4	-
1500-2000	40	1750	-3	-
2000-2500	33	2250	-2	-
2500-3000	28	2750	-1	-
3000-3500	30 (x̄)	3250 (a)	0
3500-4000	22	3750	1
4000-4500	16	4250	2
4500-5000	7	4750	3
-	∑fi = 200	-	-	∑fiui = -

Since the maximum families 40 lies in the class 1500-2000, this is the required modal class.

Lower boundary of the modal class (l) = 1500

Frequency of the modal class (f₁) = 40

Frequency of the class preceding the modal class f₀ = 24

Frequency of the class succeeding the modal class f₂ = 33

Height of the class, h = 500

Hence, modal monthly income = Rs. 1847.83.

Assumed mean (a) = 3250

∑f_i = 200 , ∑f_iu_i = -