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. $11\frac{1}{3}$
• C. $10\frac{2}{3}$
• D. $11\frac{2}{3}$

Answer 1

The correct option is B

$11\frac{1}{3}$

Find the mean of the last three observations

Given that, the mean of $x,x+3,x+5,x+7,x+10$ is $9$

Formula used: $Mean=\frac{sumoftheobservation}{totalnumberofobservation}$

$\frac{x+x+3+x+5+x+7+x+10}{5}=9$

$\frac{5x+25}{5}=9$

$5x+25=45$

$x=\frac{45-25}{5}$

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

Therefore, $x=4$

The last three observations are calculated as follows: $x+5,x+7,x+10$

$$\begin{gathered} =4+5,4+7,4+10 \\ =9,11,14 \end{gathered}$$

The mean of the last three observations $=\frac{9+11+14}{3}$

$=\frac{34}{3}$

Hence, the mean of the last three observations is $11\frac{1}{3}$.

Therefore, option(b) $11\frac{1}{3}$ is the correct answer.