Question

Question 12
If the mean of the observations x, x+3, x+5, x+7 and x+10 is 9, then mean of the last three observation is:

A) $10\frac{1}{3}$
B) $10\frac{2}{3}$
C) $11\frac{1}{3}$
D) ​​​​​​​$11\frac{2}{3}$​​​​​​​

Answer 1

The answer is C.
Given that, the mean of the observations $x,x+3,x+5,x+7$ and $x+10$ is 9.
$\therefore \frac{x+x+3+x+5+x+7+x+10}{5}=9$
$\Rightarrow 5x+25=45$
$\Rightarrow 5x=20$
$\Rightarrow x=4$
Last three observations are $x+5=4+5=9,x+7=4+7=11$
And $x+10=4+10=14$
So, the mean of last three observations $=\frac{9+11+14}{3}=\frac{34}{3}=11\frac{1}{3}$
Hence, the mean of last three observations is $11\frac{1}{3}$.