Weekly household expenditure of families living in a housing society are shown below:
Find the modal value of the data.
Answers
Solution :-
weekly expenditure ------------- No. of families (f)
0 - 3000 -------------------------- 4
3000 - 6000 -------------------------- 25
6000 - 9000 -------------------------- 31
9000 - 12000 -------------------------- 48
12000 - 15000 -------------------------- 10
from data, highest frequency class = 9000 - 12000 = mode class .
so,
- Mode = l + [(f1 - f0) / (2f1 - f0 - f2)] * h .
from data we have :-
- lower limit of mode class = l = 9000
- size of class = 3000 = h .
- f1 = frequency of mode class = 48 .
- f0 = frequency of previous class = 31 .
- f2 = frequency of next class = 10 .
Putting all values we get :-
→ Mode = 9000 + [(48 - 31)/(2*48 - 31 - 10)] * 3000
→ Mode = 9000 + [17/(96 - 41)] * 3000
→ Mode = 9000 + (17 * 3000)/55
→ Mode = 9000 + 927.27
→ Mode = 9927.27 (Ans.)
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