Question

There are 10 observations arranged in ascending order as given below.
$45,47,50,52,x,x+2,60,62,63,74.$
The median of these observation is $53$. Find the value of $x$

Answer 1

since there are even numbers of terms(10)

medial is the average of 5th$\left(\frac{n^{th}}{2}\right)$ and 6th $(\frac{n}{2}+1^{th})$ term

$\Rightarrow$ $53=\frac{\left(x\right)+(x+2)}{2}$

$\Rightarrow$$106=x+x+2$

$\Rightarrow$$106=2x+2$

$\Rightarrow$$2x=104$

$\Rightarrow$$x=\frac{104}{2}=52$

$\Rightarrow$$x=52$