Question

If the mean of the observation : x, x + 3, x + 5, x + 7, x + 10 is 9, the mean of last three observation is

$$\begin{gathered} \left(\mathrm{a}\right)\frac{31}{3} \\ \left(\mathrm{b}\right)\frac{32}{3} \\ \left(\mathrm{c}\right)\frac{34}{3} \\ \left(\mathrm{d}\right)\frac{35}{3} \end{gathered}$$

Answer 1

The given observations are x, x + 3, x + 5, x + 7, x + 10.

Mean of the given observations = 9

Number of observations = 5

Now,

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

$\Rightarrow 9=\frac{x+\left(x+3\right)+\left(x+5\right)+\left(x+7\right)+\left(x+10\right)}{5}$

$\Rightarrow 5x+25=45$

$\Rightarrow 5x=45-25=20$

$\Rightarrow x=\frac{20}{5}=4$

∴ x + 5 = 4 + 5 = 9

x + 7 = 4 + 7 = 11

x + 10 = 4 + 10 = 14

So, the last three observations are 9, 11 and 14.

∴ Mean of the last three observations = $\frac{9+11+14}{3}=\frac{34}{3}$ $\left(\mathrm{Mean}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{observations}}{\mathrm{Number}\mathrm{of}\mathrm{observations}}\right)$

Thus, the mean of the last three observations is $\frac{34}{3}$.

Hence, the correct answer is option (c).