The variance of 20 observations is 5 . If each one of the observations is multiplied by 2 , then the variance of the resulting observations is

Step-by-step solution

Variance =5 and n=20 Variance =5= 1 n (x i- x )^2 (x i- x )^2=100...(1) Let after multiplication, the new observations be y₁, y₂ y₂₀ Where y_i=2(x i) for some i ...(2) New variance = 1 2 (y_i-y )^2 where y = 1 n y_i y = 1 20 2 x i=2 ( 1 20 x i )=2 x ...(3) (x i- x )^2=100 from (1) ( 1 2 y_i- 1 2 y )^2=100 ( 1 2 )^2 (y_i-y )^2=100 (y_i-y )^2=400 New variance = 1 n (y i- y )^2= 1 20 400=20