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

Given, observations = x, x + 2, x + 4, x + 6 and x + 8

Mean = 11

Number of observations = 5

By formula,

Mean = $\dfrac{\text{Sum of observations}}{\text{Number of observation}}$

Substituting values we get :

$\Rightarrow 11 = \dfrac{x + x + 2 + x + 4 + x + 6 + x + 8}{5} \\[1em] \Rightarrow 11 = \dfrac{5x + 20}{5} \\[1em] \Rightarrow 55 = 5x + 20 \\[1em] \Rightarrow 5x = 55 - 20 \\[1em] \Rightarrow 5x = 35 \\[1em] \Rightarrow x = \dfrac{35}{5} \\[1em] \Rightarrow x = 7.$

Hence, the value of x = 7.