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:
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

Answer 1

The modal monthly expenditure of the families is Rs. 1847.83

The mean monthly expenditure is Rs. 2662.5

xi = (1000+1500)/2 = 1250

Expenditure(in Rs)    Frequency  (fi)      xi                      xi*fi

1000-1500                            24               1250              30000

1500-2000                            40              1750               70000

2000-2500                            33              2250              74250      

2500-3000                             28             2750              77000

3000-3500                             30              3250              97500

3500-4000                             22              3750               82500

4000-4500                             16               4250              68000

4500-5000                             7                 4750              33250

From the above table it's clear that, the class interval with the highest frequency is 1500 - 2000

Therefore, the modal class is 1500 - 2000

l = lower interval of the modal class = 1500

h = height = 2000 - 1500 = 500

f0 =  frequency of the class interval before the modal frequency = 24

f1 =  frequency of the modal class interval = 40

f2 =  frequency of the class interval after the modal frequency = 33

$Mode = l + \dfrac{f_1-f_0}{2f_1 - f_0 -f_2} * h$

Mode = 1500 + [ (40-24) / (2*40 - 24 - 33) ] * 500

= 1500 + 16/23 * 500

= 1500 + 347.82

= 1847.83

Therefore, the modal monthly expenditure of the families is Rs. 1847.83

Mean = ∑ fi * xi / ∑ xi

= (30000 + 70000 + 74250 + 77000 + 97500 + 82500 + 68000 + 33250) / (1250 + 2250 + 2750 + 3250 + 3750 + 4250 + 4750)

= 532500 / 200

= 2662.5

Therefore, the mean monthly expenditure is Rs. 2662.5