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. $12\frac{1}{3}$
• B. $12\frac{2}{3}$
• C. $11\frac{1}{3}$
• D. $13\frac{2}{3}$

Answer 1

The correct option is C $11\frac{1}{3}$

We know, Mean is given by,

$\text{Mean}=\frac{\text{Sum of the elements}}{\text{Total number of elements}}$.

The observations are $x,x+3,x+5,x+7,x+10$ and its mean is $9$.

Here, number of observations $=5$.

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

$\Rightarrow 45=5x+25$

$\Rightarrow 5x=20$

$\Rightarrow x=4$.

$\therefore$ Last three observations are:

$x+5\Rightarrow 4+5=9$

$x+7\Rightarrow 4+7=11$

$x+10\Rightarrow 4+10=14$.

Therefore, Mean of last three observation $=\frac{9+11+14}{3}=\frac{34}{3}=11\frac{1}{3}$.

Thus, option $C$ is correct.