Question

The mean of the above frequency distribution is 3.5, then find the value of x.
$\begin{array}{cccccc}Variable& 1& 2& x& 4& 5\\ Frequency& 2& 3& 4& 5& 6\end{array}$

Answer 1

Given, mean of the observations = 3.5

$\because Mean=$ $\frac{{\sum }_i^n{f}_i{x}_i}{{\sum }_i^n{f}_i}$

$\Rightarrow 3.5=\frac{1\times 2+2\times 3+x\times 4+4\times 5+5\times 6}{20}$

$\Rightarrow 3.5=\frac{58+4x}{20}$

$\Rightarrow 4x+58=70$
$\Rightarrow 4x=12$
$\Rightarrow x=3$