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Question

Find the arithmetic mean of each of the following frequency distributions using step-deviation method:
Class 0-20 20-40 40-60 60-80 80-100 100-120 120-140
Frequency 12 18 15 25 26 15 9

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Solution

Class

Frequency fi

Mid valuesxi

ui=(xiA)h=(xi70)20

(fi×ui)

0-20

12

10

3

36

20-40

18

30

2

36

40-60

15

50

1

15

60-80

25

70 = A

0

0

80-100

26

90

1

26

100-120

15

110

2

30

120-140

9

130

3

27

fi=120

(fi×ui)=4

Now, A=70, h=20, fi=120 and (fi×ui)=4Mean, x¯=A+{h×(fi×ui)fi}=70+{20×(4)120}=70-0.67=69.33x¯=69.33


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