Question

If the mean of the observations: $x,x+3,x+5,x+7,x+10$ 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

The correct option is C

$11\frac{1}{3}$

Explanation for correct option:

Step 1: Find the value of variable $x$

$\mathrm{Mean}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{total}\mathrm{observations}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{observations}}$

Mean of $x,x+3,x+5,x+7,x+10$ is $9$

$\begin{array}{rcl}& \Rightarrow & 9=\frac{x+x+3+x+5+x+7+x+10}{5}\\ & \Rightarrow & 9=\frac{5x+25}{5}\\ & \Rightarrow & 9=x+5\\ & \Rightarrow & x=9-5\\ & \Rightarrow & x=4\end{array}$

Hence, the observations are $4,7,9,11,14$.

Step 2: Find the mean of last three observations

Now the last three observations are $9,11,14$.

$$\begin{gathered} \mathrm{Mean}=\frac{9+11+14}{3} \\ \Rightarrow \mathrm{Mean}=\frac{34}{3} \\ \Rightarrow \mathrm{Mean}=11\frac{1}{3} \end{gathered}$$

Hence the correct option is (c).