Question

If the variance of the following frequency distribution :

$\begin{matrix}{\text{Class}}& :&10-20&20-30&30-40\\ {\text{Frequency}}&:&2&x&2\end{matrix}$

is $50,$ then $x$ is equal to ____

Answer 1

$\because$ Variance is independent of shifting of origin
$\begin{matrix}\Rightarrow &X_{i}&:&15&25&35&or&-10&0&10\\ &f_{i}&:&2&x&2&&2&x&2\end{matrix}$
$\Rightarrow \quad$ Variance $\left(\sigma^{2}\right)=\frac{\sum x_{i}^{2} f_{i}}{\Sigma f_{i}}-(\vec{x})^{2}$
$\Rightarrow \quad 50=\frac{200+0+200}{x+4}-0 \quad\{\bar{x}=0\}$
$\Rightarrow \quad 200+50 x=200+200$
$\Rightarrow \quad x=4$