Question

If the arithmetic mean of $27,23,x-4,x+4,15,3$ and $7$ is $13$, then find the value of $x$ .

Answer 1

Find the value of $x$

Total number of observation $=7$

$\mathrm{Mean}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{observation}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{observation}}$

$$\begin{gathered} \Rightarrow 13=\frac{27+23+\left(x-4\right)+\left(x+4\right)+15+3+7}{7} \\ \Rightarrow 91=75+2x \\ \Rightarrow 2x=16 \\ \Rightarrow x=8 \end{gathered}$$

Hence, the value of $x$ is $8$.