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Q.

The mean of following frequency is 53 But the frequency f and f1 in the classes 20-40 and 60-80 are passing. Find the missing frequencies

Age in year
0-20
20-40
40-60
60-80
80-100

No of people
15
F1
21
F2
17
100

Class: 9

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a

f1 = 20 f2 = 28

b

f1 = 17 f2 = 19

c

f1 = 19 f2 = 25

d

f1 = 19 f2 = 29

answer is D.

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Detailed Solution

Class	xi	fi	Fi xi
0-20	10	15	150
20-40	30	f1	30f1
40-60	50	21	1050
60-80	70	f2	70f2
80-100	90	17	1530
		53+f1+f2	2730 + 30f1 + 70f2

53 + f1 + f2 = 100
f1 + f2 = 47 ⇒ f1 = 47 – f2 …(1)
5300 = 2370 + 30 f1 + 70f2
2570 = 30f1 + 7f2
3 f1 + 7f2 = 257
putting value of f1
3(47 – f2) + 7f2 = 257
141 – 3f2 + 7f2 = 257
141 + 4f2 = 257
4f2 = 116
f2 = 29
putting in (1)
f1 = 47 – 29
= 18
Hence option 4 is correct

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