In the frequency distribution of families
given below, the number of families
corresponding to expenditure groups 2000-
4000 is missing from the table. However
value of 25th percentile is 2880. Find the
missing frequency
0-2 2-4
4-6
6-8
8-10
Weekly
Expenditure
(1000)
14
?
39
7
15
No. of
families
Answers
Given :-
Weekly Expenditure:- 0-2 2-4 4-6 6-8 8-10
(Rs.1000)
No. of Families :- 14 ? 39 7 15
However value of 25th percentile is 2880. Find the missing frequency ?
Solution :-
Let us assume that, missing frequency is x.
Weekly Expenditure (F) (C.F)
0 - 2000 14 14
2000 - 4000 x 14 + x
4000 - 6000 39 53 + x
6000 - 8000 7 60 + x
8000 - 10000 15 75 + x
Total (75 + x)
As, we can see P(25) lies between 2000 - 4000.
So, we have now :-
- N = (75 + x) (Total frequency.)
- L = 2000 (lower limit.)
- h = 2000 (width.)
- c.f = 14 ( previous CF.)
- f = x (missing frequency.)
- P(25) = 2880 . (given.)
we know that,
- P(25) = L + (h/f)[(25N/100) - c.f]
Putting all values we get,
→ 2880 = 2000 + (2000/x)[{25(75+x)/100} - 14]
→ 2880 - 2000 = (2000/x) * [ {(75 + x) / 4} - 14 ]
→ 880x = 2000[ (75 + x - 56) / 4 ]
→ 880x = 500(19 + x)
→ 880x = 9500 + 500x
→ 880x - 500x = 9500
→ 380x = 9500
dividing both sides by 19,
→ 20x = 500
dividing both sides by 20 now,
→ x = 25. (Ans.)
Hence, The Missing Frequency is 25.
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