Question

If the mean of x, x + 3, x + 5, x + 7, x + 10 is 9, the mean of the last three observations is
(a) $10\frac{1}{3}$
(b) $10\frac{2}{3}$
(c) $11\frac{1}{3}$
(d) $11\frac{2}{3}$

Answer 1

(c) 11$\frac{1}{3}$
Mean of 5 observations = 9
We know:
$$\begin{gathered} \mathrm{Mean}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{observations}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{observations}} \\ \Rightarrow 9=\frac{x+x+3+x+5+x+7+x+10}{5} \\ \Rightarrow 9=\frac{5x+25}{5} \\ \Rightarrow 5x+25=45 \\ \Rightarrow 5x=20 \\ \Rightarrow x=4 \\ \mathrm{Therefore},\mathrm{the}\mathrm{last}\mathrm{three}\mathrm{observations}\mathrm{are}(4+5),(4+7)\mathrm{and}(4+10),\mathrm{i}.\mathrm{e}.,9,11\mathrm{and}14. \\ \mathrm{Now}, \\ \mathrm{Mean}\mathrm{of}\mathrm{the}\mathrm{last}\mathrm{three}\mathrm{terms}=\frac{9+11+14}{3}=\frac{34}{3}=11\frac{1}{3} \end{gathered}$$