If the mean of five observations $x,x+2,x+4,x+6,x+8$ is $11$, then the mean of first three observations is:

The correct option is A: $9$

Given observations are $x,x+2,x+4,x+6,x+8$

$Mean=\frac{\text{sum of obsevations}}{\text{number of observations}}$

$\Rightarrow \frac{x+x+2+x+4+x+6+x+8}{5}=11$
$\Rightarrow \frac{5x+20}{5}=11$
$\Rightarrow x+4=11$
$\Rightarrow x=7$

so, given observation are $7,9,11,13,15$.
Hence, Required mean of three observations is
$Mean=\frac{7+9+11}{3}=\frac{27}{3}=9$