Question

17) Find out the standard deviation of the following data after finding mean. (4)
C-I
0-10
10-20
20-30
30-40
40-50
F
8
13
16
8
5

Answer 1

Answer:

Calculate the standard deviation of the following data (by Assumed mean method).

Assumed Mean =25

C.I 0−10 10−20 20−30 30−40 40−50

f 7 10 15 8 10

Medium

Solution

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C.I Class mark (x

i

) f

i

d

i

=x

i

−M f

i

d

i

f

i

d

i

2

0−10 5 7 −20 −140 12800

10−20 15 10 −10 −100 1000

20−30 25 15 0 0 0

30−40 35 8 10 80 800

40−50 45 10 20 200 4000

Total =40 Total =8600

Given, assumed mean(A)=25

Standard deviation(σ)=

n

∑f

i

di

2

−

⎩

⎪

⎨

⎪

⎧

n

∑f

i

d

i

⎭

⎪

⎬

⎪

⎫

2

∴ σ=

5

8600

−{

5

40

}

2

=

1720−64

=

1656

=40.69

∴ σ=40.69.

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