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 men monthly expenditure:
Expenditure (in Rs.) | Frequency |
1000-1500 | 24 |
1500-2000 | 40 |
2000-2500 | 33 |
2500-3000 | 28 |
3000-3500 | 30 |
3500-4000 | 22 |
4000-4500 | 16 |
4500-5000 | 7 |
We may observe that the given data be maximum class frequency is 40 belonging to 1500- 2000 intervals
So, modal class = 1500- 2000
l=1500, f=40, f0=24, f2=33, h=50
=
=1500 + 347.826
=1847.826
So, modal class monthly expenditure was Rs. 1847.83
We may compute class marks (xi) as per the relation:
Xi=
h= 500, A=2750
Expenditure(in Rs) | N0.of families(fi) | xi | di=xi -2750 | ui | 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 |
∑xi=200,
(x̅) mean =
(x̅) =
=2750-87.5
=2662.5
So, mean monthly expenditure was Rs. 2662.50