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If the mean of 100 observations is 50 an...

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`

Text Solution

Verified by Experts

The correct Answer is:
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`
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Knowledge Check

  • The mean of 100 numbers observations is 50 and their standards deviation is 5. The sum of all squares of all the observations is (a)50,000          (b) 250,000         (c) 252500         (d) 255000

    A
    50,000
    B
    250,000
    C
    252500
    D
    255000

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    B
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    C
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    D
    1000

  • If the coefficient of variation of some observation is 60 and their standard deviation is 20, then their mean is

    A
    35
    B
    34
    C
    38.3
    D
    33.33

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