Question

let a,b,c,d,e be the observations with the mean m and standard deviation s. The standard deviations of the observations kx1, kx2,kx3, kx4,kx5 is?
A. k+s
B. s/k
C. ks
D. s

Answer 1

Answer: The standard deviation of the new sample will be ks i.e. option C

Step-by-step explanation:

we know that standard deviation

s = √[Σxi²/5   -   (Σxi/5)²]

Now for the new sample kx1, kx2, kx3, kx4, kx5 i.e when each term is multiplied by k, standard deviation is

S = √[Σkxi²/5   -   (Σkxi/5)²]

= √[k² Σxi²/5   -   k²(Σxi/5)²]

= k √[Σxi²/5   -   (Σxi/5)²]

=> S = ks.