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Question

Calculate the arithmetic mean for the following data using step deviation method.
Marks01010202030304040505060
No. of students 8 15 22 20 10 5

Solution
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Marks

Midpoint(xi)

No. of students(fi)

Deviation(di)

ui

uifi

0-10

5

8

-30

-3

-24

10-20

15

15

-20

-2

-30

20-30

25

22

-10

-1

-22

30-40

35

20

0

0

0

40-50

45

10

10

1

10

50-60

55

5

20

2

10

N=fi=80, h=10
A=35,di=xiA , ui=dih
Mean=A+h(uifiN)=35+10(5680)
Mean=28

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