Question

The mean of $x$, $x$ + 2, $x$ + 4, $x$ + 6 and $x$ + 8 is 22, then find the mean of first three observations.

• A. 20
• B. 22
• C. 24
• D. 26

Answer 1

The correct option is A 20

We know,
Mean = $\frac{Sumofallobservations}{Numbersofobservations}$

Given the mean of $x$,$x$ + 2,$x$ + 4 ,$x$ + 6 and $x$ + 8 is 22.
So, here first we find the value of$x$,
$\therefore$ Mean =$\frac{\left(x\right)+(x+2)+(x+4)+(x+6)+(x+8)}{5}$

$\Rightarrow 22=\frac{x+x+2+x+4+x+6+x+8}{5}$
$\Rightarrow 22=\frac{5x+2+4+6+8}{5}$
$\Rightarrow 22=\frac{5x+20}{5}$
$\Rightarrow 22\times 5=5x+20$
$\Rightarrow 110=5x+20$
$\Rightarrow 90=5x$
$\Rightarrow x$ = $\frac{90}{5}$
$\Rightarrow x=18$

Now, we subsitute the value of $x$ in the observation and we get the observations as 18, 20, 22, 24 and 26.

Mean of first three observations, = $\frac{18+20+22}{3}$
= $\frac{60}{3}$
= 20
Thus, mean of first three observations is 20.