Question

The following observations have been arranged in ascending order:
$11,12,14,18,x+2,x+4,30,32,35,41$. If the median of the data is $24$, find $x$.

Answer 1

Here, the number of observations $n=10$, since n is even, therefore

$Median=\frac{{\left(\frac{n}{2}\right)}^{th}observation+{(\frac{n}{2}+1)}^{th}observation}{2}$

$\Rightarrow 24=\frac{5^{th}observation+6^{th}observation}{2}$

$\Rightarrow 24=\frac{(x+2)+(x+4)}{2}$

$\Rightarrow 24=\frac{2x+6}{2}$

$\Rightarrow 24=x+3$

$\Rightarrow x=21$

Hence, $x=21$