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.

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 as assumed mean (a), d_i, u_i, and f_iu_i are calculated as follows.

From the table, we obtain

Therefore, mean monthly expenditure was Rs 2662.50.

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