Let `x_(1), x_(2), x_(3), x_(4),x_(5)` be the observations with mean m and standard deviation s. The standard deviation of the observations `kx_(1), kx_(2), kx_(3), kx_(4), kx_(5)` is

Options

A. k+s
B. `(s)/(k)`
C. ks
D. s

Answer

C

Explanation

Here, `m=(sum x_(i))/(5),s=sqrt((sum x_(i)^(2))/(5)-((sum x_(i))/(5))^(2))`
So, for observations `kx_(1),kx_(2),kx_(3),kx_(4),kx_(5)`,
`S.D.=sqrt((k^(2)sum x_(i)^(2))/(5)-((ksum x_(i))/(5))^(2))`
`=sqrt((k^(2)sum x_(i)^(2))/(5)-k^(2)((sum x_(i))/(5))^(2))`
`=ksqrt(((sum x_(i)^(2))/(5))-((sum x_(i))/(5))^(2))=ks`