If the mean of the five observations x + 1, x + 3, x + 5, 2x + 2, 3x + 3 is 14, find the mean of first three observations.

By formula,

Mean = $\dfrac{\text{Sum of observations}}{\text{No. of observations}}$

Sum of observations = x + 1 + x + 3 + x + 5 + 2x + 2 + 3x + 3 = 8x + 14.

Given,

Mean of the five observations = 14.

$\Rightarrow \dfrac{8x + 14}{5} = 14 \\[1em] \Rightarrow 8x + 14 = 70 \\[1em] \Rightarrow 8x = 56 \\[1em] \Rightarrow x = \dfrac{56}{8} = 7.$

First three observations are

⇒ x + 1 = 7 + 1 = 8,

⇒ x + 3 = 7 + 3 = 10,

⇒ x + 5 = 7 + 5 = 12.

Mean = $\dfrac{8 + 10 + 12}{3} = \dfrac{30}{3}$ = 10.

Hence, the mean of first three observations is 10.