If the total number of observations is `20,sumx_i = 1000 and sum x_i^2 = 84000`, then what is the variance of the distribution?

Options

A. 1500
B. 1600
C. 1700
D. 1800

Answer

C

Explanation

Total no. of observation (n) = 20
`Sigmax_(i)=1000`
`barx=(Sigmax_(i))/(n)=(1000)/(20)=50`
Variance `=sd^(2)`
`sd=sqrt((1)/(n)Sigmax_(i)^(2)-(barx)^(2))`
`(sd)^(2)=(1)/(2)Sigmax_(i)^(2)-(barx)^(2)=(84000)/(20)-(50)^(2)`
`=4200-2500=1700.`
Variance = 1700