If the variance of the following frequency distribution :

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 $\left(\sigma^{2}\right)=\frac{\sum x_{i}{ }^{2} f_{i}}{\sum f_{i}}-(\vec{x})^{2}$

$\Rightarrow \quad 50=\frac{200+0+200}{x+4}-0$        $\{\overline{\mathrm{x}}=0\}$

$\Rightarrow \quad 200+50 x=200+200$

$\Rightarrow \quad x=4$

 

 

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