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Question 3:

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 Rs)

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

Answer:

It can be observed from the given data that the maximum class frequency is 40, belonging to 1500 − 2000 intervals.

Therefore, modal class = 1500 − 2000

Lower limit (l) of modal class = 1500

Frequency (f1) of modal class = 40

Frequency (f0) of class preceding modal class = 24

Frequency (f2) of class succeeding modal class = 33

Class size (h) = 500

Therefore, modal monthly expenditure was Rs 1847.83.

To find the class mark, the following relation is used.

Class size (h) of the given data = 500

Taking 2750 ...

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