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

Detailed Method:
`"Variance"=(sumd^(2))/(n)`
`5=(sumd^(2))/(20)rArr sumd^(2)=100`
According to question
`sum(d_(1))^(2)=sum(2d)^(2)=4sumd^(2)=4xx100=400`
`"New variance"=(400)/(20)=20`
Shortcut Method:
If each observation is multiplied by 2
New variance `=2^(2)xx5=20`