If the variance of the following frequency distribution: Class: 10...

Given data can also be expressed as:

$\begin{cases}{x}_{i} & 15 & 25 & 35 \\ {f}_{i} & 2 & x & 2\end{cases}$

So,

$\overset{¯}{x} = \dfrac{∑ {f}_{i}{x}_{i}}{Σ{f}_{i}} = \dfrac{30 + 25x + 70}{4 + x} = \dfrac{25\left(4 + x\right)}{4 + x} = 25$

Now, $$\begin{array}{ll}{\sigma}^{2} = 50 = \dfrac{∑ {f}_{i}{x}_{i}^{2}}{Σ{f}_{i}} - {\left(\overset{¯}{x}\right)}^{2}\end{array}$$

$50 = \dfrac{450 + 625x + 2450}{4 + x} - {25}^{2}$

$⇒ 50 = \dfrac{2900 + 625x}{4 + x} - 625$

$⇒ 675 ( 4 + x ) = 2900 + 625x$

$⇒ 50x = 200 ⇒ x = 4$