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.