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 C) 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

Mode: The class which has the highest frequency.
In this case, class interval 1500-2000 is the modal class.
Now, Lower limit of modal class, l = 1500, h = 500, f1 = 40, f0 = 24, f2 = 33
We know that,
Mode = l + ((f1 - f0) / (2f1 - f0 - f2)) * h
= 1500 + ((40 - 24) / (2(40) - 24 - 33)) * 500
= 1500 + (16 / (80 - 57)) * 500
= 1500 + (16 / 23) * 500
= 1500 + (16/23) * 500
= 1500 + 347.826
Mode = 1847.83
Let's take assumed mean, A as 3250.
Class interval = 500
N = 200, Σfiui = -235
¯x = A + (hΣfiui / N)
= 3250 + (-235 / 200) * 500
= 3250 + (-1175 / 2)
= 3250 - 587.5
= 2662.5
Hence, the average expenditure is Rs 2662.50.