Question

If the mean of five observations x, x + 2, x + 4, x + 6, x + 8 is 13, find the value of x and hence find the mean of the last three observations.

Answer 1

We know that,

$\mathrm{Mean}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{observa}\mathrm{tions}}{\mathrm{Number}\mathrm{of}\mathrm{observations}}$

The first five observations are x, x + 2, x + 4, x + 6 and x + 8.

Mean of these numbers = $\frac{x+\left(x+2\right)+\left(x+4\right)+\left(x+6\right)+\left(x+8\right)}{5}$
$$\begin{gathered} \Rightarrow 13=\frac{5x+20}{5} \\ \Rightarrow 13\times 5=5x+20 \\ \Rightarrow 65=5x+20 \\ \Rightarrow 5x=65-20 \\ \Rightarrow 5x=45 \\ \Rightarrow x=\frac{45}{5} \\ \Rightarrow x=9 \end{gathered}$$

Hence, the value of x is 9.

Now, the last three observations are 13, 15 and 17.
Mean of these observations = $\frac{13+15+17}{3}$
= $\frac{45}{3}$
= 15

Hence, the mean of the last three observations is 15.