# The mean of 100 observation is 50 and their standard deviation 5. The sum of all the observations is

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

Toolbox:
• 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.