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Let x1, x2, x3, x4, x5 be the observations with mean m and standard deviation s.

The standard deviation of the observations kx1, kx2, kx3, kx4, kx5 is

A. k + s
B. s/k
C. ks
D. s

1 Answer

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by (50.2k points)
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Best answer

Given observations are x1, x2, x3, x4, x5

So the mean of the 5 observations is

⇒ ∑xi= x1+x2+ x3+x4+x5 =5m……..(i)

And the standard deviation of the 5 observations is

Now we will find the mean and standard deviation of the observations kx1, kx2, kx3, kx4, kx5, we get

So the mean of these 5 observations is

m1=mk…………(iii)

And the standard deviation of the 5 observations is

Substituting equation (iii) in above equation we get

σ=ks

Hence the standard deviation of new set of observations, i.e., kx1, kx2, kx3, kx4, kx5 is ks.

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