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Question

The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency f1 and f2
Class: 0-20    20 - 40   40 - 60    60 - 80    80 - 100      100 - 120
Frequency:    5    f1   10    f2     7   8


Solution

Soln:

Class interval Mid value xi  Frequency  fi fixi
0 – 20 10 5 50
20 – 40 30 f1 30f1
40 – 60 50 10 500
60 – 80 70 f2 70f2
80 – 100 90 7 630
100 – 120 110 8 880
    N = 50 Sum = 30f1 + 70f2 +  2060


Given,
sum of frequency = 50

5+f1+10+f2+7+8=50

f1+f2=20

Multiply with 3 on both sides,3f1+3f2=60(1)


And mean = 62.8

SumN=62.8

30f1+70f2+206050=62.8

30f1+70f2=31402060=1080

3f1+7f2=108(2)(Dividing by 10)

subtract equation (1) from equation (2)

3f1+7f23f13f2=10860

4f2=48  ;   f2=12       and   f1=8

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