Question

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

Answer 1

Correct Answer - C
Given , `barx=50,n=100 and sigma=5`
`Sigmax_(i)^(2)=?`
`therefore " "barx=(Sigmax_(i))/n`
`rArr 50=Sigma=(Sigmax_(i))/100`
` therefore Sigmax_(i)=50xx100=5000`
Now `sqrt((Sigmax^(2))/n-((Sigmax_(i))/n)^(2) )rArr sigma^(2)=(Sigmax_(i)^(2))/n-(barx)^2`
`rArr 25=(Sigmax_(i)^2)/100-(50)^(2) rArr 25 =(Sigmax_(i)^(2))/(100)-2500`
`rArr 2525=(Sigmax_(i)^(2))/100`
`there" " Sigmax_(i)^(2)=252500`