Find the various and S.D. for the following set of numbers.7, 11, 2, 4, 9, 6, 3, 7, 11, 2, 5, 8, 3, 6, 8, 8, 8, 2, 6 - Mathematics and Statistics

Sum

Find the various and S.D. for the following set of numbers.
7, 11, 2, 4, 9, 6, 3, 7, 11, 2, 5, 8, 3, 6, 8, 8, 8, 2, 6

Solution

Given data: 7, 11, 2, 4, 9, 6, 3, 7, 11, 2, 5, 8, 3, 6, 8, 8, 2, 6
The tabulated form of the above data is as given below:

 x1 2 3 4 5 6 7 8 9 11 f1 3 2 1 1 3 2 3 1 2

We prepare the following table for the calculation of variance and S. D.

 xi fi fixi fixi2 2 3 6 12 3 2 6 18 4 1 4 16 5 1 5 25 6 3 18 108 7 2 14 98 8 3 24 192 9 1 9 81 11 2 22 242 Total N = 18 ∑fixi = 108 ∑fixi2 = 792

bar"x"= (sum"f"_"i""x"_"i")/"N"=108/18 = 6

var (X) = σ_"x"^2=(sum"f"_"i""x"_"i"^2)/"N"-(bar"x")^2

= 792/18-(6)^2

= 44 – 36
= 8
∴ S.D. sigma_x = sqrt("Var"("X")

= sqrt(8)

= 2sqrt(2)

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