Question

If the mean of the observation $x,2x+1,2x+5,2x+9$ is $30$. What is the mean of last two observations?

Answer 1

$\Rightarrow$ $\sum x_i=x+2x+1+2x+5+2x+9=7x+15$

$\Rightarrow$ $n=4$

$\Rightarrow$ $\overline{x}=30$

$\overline{x}=\frac{\sum x_i}{n}$

$30=\frac{7x+15}{4}$

$120=7x+15$

$\therefore$ $x=15$

$\Rightarrow$ After substituting value of $x$ last two numbers become $35$ and $39$

$\therefore$ Mean of last two numbers $=\frac{35+39}{2}=\frac{74}{2}=37$