Question

xi 10,30,50,70,90,110 fi 5,?, 10,?, 7,8 mean of the following data is 62.8 and the sum of all frequencies is 50.find the missing frequencies

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Asked on December 26, 2019 by

Satvik Praveen

The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency f

1

and f

2

.

Class 0-20 20-40 40-60 60-80 80-100 100-120

Frequency 5 f

1

10 f

2

7 8

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ANSWER

Class

Frequency(f)

ClassMark (x)

fx

0-20

5

10

50

20-40

f

1

30

30f

1

40-60

10

50

500

60-80

f

2

70

70f

2

80-100

7

90

630

100-120

8

110

880

Total

30+f

1

+f

2

2060+30f

1

+70f

2

Given 30+f

1

+f

2

=50

=>f

1

+f

2

=20 -- (1)

Given, Mean =

∑f

∑fx

=62.8

=>

30+f

1

+f

2

2060+30f

1

+70f

2

=62.8

=>2060+30f

1

+70f

2

=1884+62.8f

1

+62.8f

2

32.8f

1

−7.2f

2

=176

=> 8.2f

1

−1.8f

2

=44

=> 4.1f

1

−0.9f

2

=22 -- (2)

Solving both equations 1, 2, we get

f

1

=8,f

2

=12