If the mean of 100 observations is 50 and their standard deviations is 5,than the sum of all squares of all the observations is

Options

A. 50000
B. 250000
C. 252500
D. 255000

Answer

C

Explanation

Given, `overline(x)=50, n=100 " and" sigma=5`
`implies 50=(sum x_(i))/(100)`
`implies sum x_(i)=50xx100=5000`
Now, `s^(2)=(sum x_(i)^(2))/(n)-(overline(x))^(2)`
`implies 25=(sum x_(i)^(2))/(100)-(50)^(2)`
`implies 2525=(sum x_(i)^(2))/(100)`
`therefore sum x_(i)^(2)=252500`