Question

The median of the following observations $11,12,14,(x-2),(x+4),(x+9),32,38,47$ arranged in ascending order is $24$. Find the value of $x$ and hence find the mean.

Answer 1

Given observation are $11,12,14,(x-2),(x+4),(x+9),32,38,47$ and median $=24$.
$\because n=9\left(odd\right)$
$\therefore$ Median$=\frac{n+1}{2}$th term
$=\frac{9+1}{2}$th term
$24=5$th term
$\therefore x+4=24$
$x=24-4$
$x=20$
Therefore, $11,12,14,(20-2),(20+4),(20+9),32,38,47$=$11,12,14,18,24,29,32,38,47$
Now Mean$=\frac{\sum x}{n}$
$=\frac{11+12+14+18+24+29+32+38+47}{9}$
$=\frac{225}{9}=25$.