# If the mean of x, x + 3, x + 5, x + 7, x + 10 is 9, the mean of the last three observations is

Question:

If the mean of xx + 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) $11 \frac{2}{3}$

Solution:

(c) $11 \frac{1}{3}$

Mean of 5 observations = 9
We know:

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

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

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

$\Rightarrow 5 x+25=45$

$\Rightarrow 5 x=20$

$\Rightarrow x=4$

Therefore, the last three observations are $(4+5),(4+7)$ and $(4+10)$, i. e., 9,11 and 14 .

Now

Mean of the last three terms $=\frac{9+11+14}{3}=\frac{34}{3}=11 \frac{1}{3}$