Question

If the variance of the following frequency distribution :

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

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

Answer 1

Answer: 4

$\because$ Variance is independent of shifting of origin
$\begin{array}{cccccccccc}\Rightarrow & X_i& :& 15& 25& 35& or& -10& 0& 10\\ & f_i& :& 2& x& 2& & 2& x& 2\end{array}$
$\Rightarrow$ Variance $\left({\sigma }^2\right)=\frac{\sum x_i^2{f}_i}{\Sigma f_i}-(\vec{x}{)}^2$
$\Rightarrow 50=\frac{200+0+200}{x+4}-0\{\bar{x}=0\}$
$\Rightarrow 200+50x=200+200$
$\Rightarrow x=4$