The variance of 20 observation is 5. If each observation is multiplied by 2, then what is the new variance of the resulting observation?

Options

A. 5
B. 10
C. 20
D. 40

Answer

C

Explanation

Let `x_(1),x_(2),………,x_(20)` be the given observations.
Given, `(1)/(20)sum_(i=1)^(20)(x_(i)-barx)^(2)=5`
To find variance of `2x_(1),2x_(2),2x_(3),….,2x_(20),`
Let `barx` denotes the mean of new observation,
Clearly, `barx=(sum_(i=1)^(20)2x_(i))/(20)=(2sum_(i=1)^(20)x_(i))/(20)=2barx`
Now, variance of new observation
`=(1)/(20)sum_(i=1)^(20)(2x_(i)-barx)^(2)=(1)/(20)sum_(i=1)^(20)(2x_(i)-2barx)^(2)`
`=(1)/(20)sum_(i=1)^(20)4(x_(i)-barx)^(2)=4((1)/(20)sum_(i=1)^(20)(x_(i)-barx)^(2))=4xx5=20`