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

Options

A. (a) 50,000
B. (b) 250,000
C. (c) 252500
D. (d) 255000

Answer

(c) 252500

Explanation

Correct option is option 3

We know, Standard deviation, `sigma^2=frac{Sigmax^2}{n}-(barx)^2`

Given,
`sigma=5, Sigmax =50, n=100`

`implies 25=sigma^2=frac{Sigmax^2}{100}-(50)^2`

`implies Sigmax^2=252500`


Thus, sum of squares of all the observation is `252500.`

Hence, correct option is option `3`