The following data gives the distribution of total monthly household expenditure of 200 families of a village. Expenditure (in Rs) 1000 - 1500

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 men monthly expenditure:

Answer 1

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

Mode = \(I+(\frac{f-f_0}{2f-f_0-f_2})h\)

\(=1500+(\frac{40-24}{2(40)-24-33})50\)

=1500 + 347.826 

=1847.826 

So, 

modal class monthly expenditure was Rs. 1847.83 

We may compute class marks (x_i) as per the relation:

x_i \(=\frac{upper\,class\,limit+lower\,class\,limit}{2}\)

h= 500, A=2750

∑x_i=200, \(\sum f_iu_i\)

(x̅) mean = A + \(\frac{\sum f_iu_i}{\sum f_i}\times h\)

(x̅) \(=2750+\frac{-35}{200}\times500\)

=2750-87.5 

=2662.5 

So, mean monthly expenditure was Rs. 2662.50