$\begin{array}{1 1}(A)\;50000\\(B)\;250000\\(C)\;252500\\(D)\;255000 \end{array} $

- The formula used for the problem are Mean $ \bar(x)=\large\frac{\sum x_i}{n}$
- $SD= \sqrt {\large\frac{\sum x^2}{n} - \bigg( \large\frac{\sum x}{n}\bigg)^2}$

Given $\bar x =50$

$SD= 5$

$h= 100$

$\sigma =5 $

$\sigma^2 =25$

$\sigma^2=\large\frac{\sum x^2}{n} - \bigg( \large\frac{\sum x}{n}\bigg)^2$

$25= \large\frac{\sum x_i^2}{100} $$-50^2$

$\large\frac{\sum x_i^2}{100}$$=25 + 50^2$

$\qquad= 25+ 2500$

$\qquad= 2525$

$\sum x_i^2 =2525 \times 100 =252500$

Hence C is the correct answer.

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