Question

The median of the variables $x+4,x-\frac{7}{2},x-\frac{5}{2},x-3,x-2,x+\frac{1}{2}$$x-\frac{1}{2},x+5(x>0)$, is

• A. $x-3$
• B. $x-2$
• C. $x+\frac{5}{4}$
• D. $x-\frac{5}{4}$

Answer 1

The correct option is D $x-\frac{5}{4}$

$x+4,x-\frac{7}{2},x-\frac{5}{2},x-3,x-2,x+\frac{1}{2}$$x-\frac{1}{2},x+5(x>0)$
This can be written as
$x+4,x-3.5,x-2.5,x-3,x-2,x+0.5$$x-0.5,x+5(x>0)$
we can arrange it in ascending order as
$x-3.5,x-3,x-2.5,x-2,x-0.5,x+0.5,x+4,x+5$
As there are $8$ observation
so, Median= $\frac{{\left(\frac{8}{2}\right)}^{th}+{(\frac{8}{2}+1)}^{th}}{2}=\frac{x-2+x-\frac{1}{2}}{2}=x-\frac{5}{4}$