Question

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

Answer 1

We know that
$\text{M}ean=\frac{\text{S}umofobservations}{\text{N}umberofobservations}$ [0.5 Marks]

$\Rightarrow$$\frac{x+x+2+x+4+x+6+x+8}{5}=11$
$\Rightarrow \frac{5x+20}{5}=11\Rightarrow x+4=11$
$\Rightarrow x=7$ [1 Mark]

So, the first three observations are $x$, $x$ + 2 and $x$ + 4.

$x=7$
$x+2=7+2=9$
$x+4=7+4=11$ [0.5 Marks]

Hence, the required mean of first three observations is

$\Rightarrow \frac{7+9+11}{3}=\frac{27}{3}=9$. [1 Mark]