The mean of `100` numbers observations is `50` and their standards deviation is `5`. The sum of all squares of all the observations is

Options

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

Answer

C

Explanation

Here, Mean, `bar X = 50`

Standard deviation,`(sigma) = 5`

`:.` Variance ` = sigma^2 = 5^2 = 25`

`:. 25 = 1/n [sum (x_i^2 - barX^2) ]`

Here, `n = 100`

`:. 25 = 1/100[sum x_i^2 - 100(50)^2]`

`=>2500 = sum x_i^2 - 100(50)^2`

`=>sum x_i^2 =250000+2500 =252500`

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