Question:
If the variance of the following frequency distribution :
Class
$: \begin{array}{lll}10-20 & 20-30 & 30-40\end{array}$
Frequency: $\begin{array}{lll}2 & x & 2\end{array}$
is 50 , then $\mathrm{x}$ is equal to
Solution:
$\because$ Variance is independent of shifting of origin
$\begin{array}{rlrrrrrr}\Rightarrow & \mathrm{x}_{\mathrm{i}}: 15 & 25 & 35 & \text { or } & -10 & 0 & 10 \\ & \mathrm{f}_{\mathrm{i}}: 2 & \mathrm{x} & 2 & 2 & \mathrm{x} & 2\end{array}$
$\Rightarrow \quad$ Variance $\left(\sigma^{2}\right)=\frac{\sum x_{i}{ }^{2} f_{i}}{\sum f_{i}}-(\vec{x})^{2}$
$\Rightarrow \quad 50=\frac{200+0+200}{x+4}-0$ $\{\overline{\mathrm{x}}=0\}$
$\Rightarrow \quad 200+50 x=200+200$
$\Rightarrow \quad x=4$