Question

Mean and Standard Deviation of $100$ items are $50$ and $4$ respectively. The sum of all squares of the items is...

• A. $266000$
• B. $251600$
• C. $261600$
• D. $256100$

Answer 1

The correct option is B $251600$

Let $x_1,x_2,...,x_{100}$ be the $100$ items.
Given that $\overline{x}=50$ and $\sigma =4$

${\sigma }^2=\frac{{\sum }_{r=1}^{r=100}{x}_r^2}{100}-{\overline{x}}^2$
$\Rightarrow 16=\frac{{\sum }_{r=1}^{r=100}{x}_r^2}{100}-2500$
$\Rightarrow 2516=\frac{{\sum }_{r=1}^{r=100}{x}_r^2}{100}$
$\Rightarrow 251600={\sum }_{r=1}^{r=100}{x}_r^2$
$\Rightarrow x_1^2+x_2^2+x_3^2+...+x_{100}^2=251600$