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Let x(1), x(2), x(3), x(4),x(5) be the o...

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

A

1. k+s

B

2. `(s)/(k)`

C

3. ks

D

4. s

Text Solution

Verified by Experts

The correct Answer is:
C
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`
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