$\begin{array}{1 1}(A)\;1122\\(B)\;251600\\(C)\;79087\\(D)\;15345\end{array} $

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Mean $\bar{x} =\large\frac{\sum x_i}{n}$

Given $\bar{x}=50$

$\qquad n=100$

$\qquad 50 =\large\frac{\sum x_i}{100}$

$\qquad =50 \times 100$

$\qquad =5000$

Sum of all the item= 5000

Step 2:

Standard deviation $\sigma =\sqrt { \large\frac{ \sum x_i^2}{n} - \bigg( \large\frac{\sum x_i}{n}\bigg)^2}$

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

Given $\sigma= 4, n=100,mean= 50$

$4^2=\large\frac{\sum x_i^2}{100}$$-50^2$

$16+2500=\large\frac{\sum x_i^2}{100}$

$=> 2516 \times 100 = \sum x_i^2$

$\sum x_i^2 =251600$

Hence B is the correct answer.

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