Q3 of 25 Page 337

The following data gives the distribution of total monthly household expenditure of 200 families of Gummandidala village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.

For mode:

Here, highest frequency is 40.


So, the modal class = 1500-2000


Mode is given by



Where,


L = Lower class limit of the modal class = 1500


h = class interval of the modal class = 500


f1 = frequency of the modal class = 40


f0 = frequency of the class preceding the modal class = 24


f2 = frequency of the class succeeding the modal class = 33


Substituting values in the formula of mode,



⇒


⇒ Mode = 1500 + 347.8


⇒ Mode = 1847.8


For mean:


Using assumed-mean method, as values of the data are large.


Let’s draw a table showing midpoints and frequencies.



Mean is given by



⇒


⇒ Mean = 2750 – 87.5


⇒ Mean = 2662.5


Thus, mode is 1847.8 and mean is 2662.5.


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