Question:
If the mean of five observations x, x + 2, x + 4, x + 6 and x + 8 is 11, then the value of x is
(a) 5
(b) 6
(c) 7
(d) 8
Solution:
(c) 7
Mean of 5 observations = 11
We know:
Mean $=\frac{\text { Sum of all observations }}{\text { Total number of observations }}$
$\Rightarrow 11=\frac{x+x+2+x+4+x+6+x+8}{5}$
$\Rightarrow 11=\frac{5 x+20}{5}$
$\Rightarrow 5 x+20=55$
$\Rightarrow 5 x=35$
$\Rightarrow x=7$