If the variance of the following frequency distribution: $\begin{array}{llll} ext { Class }: & 10-2

Question

If the variance of the following frequency distribution: $\begin{array}{llll}	ext { Class }: & 10-20 & 20-30 & 30-40\end{array}$ Frequency : $2 \quad x \quad 2$ is 50 , then $x$ is equal to

Professor PC Thomas Classes · Answer

(4) :\ Here, $\bar{x}=\frac{\sum f_{i} x_{i}}{N}=\frac{100+25 x}{4+x}$ $$ =\frac{25(4+x)}{4+x}=25 $$ Variance, $\left(\sigma^{2}ight)$\ $=\frac{\Sigma f_{i} x_{i}^{2}}{N}-(\bar{x})^{2}=\frac{2900+625 x}{4+x}-625$\ $=\frac{2900+625 x-2500-625 x}{4+x}=\frac{400}{4+x}$\ Also, $\sigma^{2}=50$ (Given)\ $	herefore \frac{400}{4+x}=50 \Rightarrow 400=200+50 x \Rightarrow x=4$\