Question

If the mean of five observations $x,x+2,x+4,x+6$ and $x+8$ is $11$, find the value of $x$.

Answer 1

Given five observations are,

$x,x+2,x+4,x+6$ and $x+8$.

Mean of the observations $\left(\overline{x}\right)=11$

Since,

Mean $\left(\overline{x}\right)=\frac{\text{Sum of observations}}{\text{Number of observations}}$

$\Rightarrow \frac{x+x+2+x+4+x+6+x+8}{5}=11$

$\Rightarrow \frac{5x+20}{5}=11$

$\Rightarrow 5x+20=55$

$\Rightarrow 5x=55-20$

$\Rightarrow 5x=35$

$\Rightarrow x=\frac{35}{5}$

$\Rightarrow x=7$

Therefore, the value of $x$ is $7$.