Question

The following numbers are arranged in descending order of their values:

$78,64,57,x-3,x-7,x-11,30,25,22,20$

If their median is $39$, find the value of $x$.

• A. 48
• B. 48.5
• C. 60
• D. 50.5

Answer 1

The correct option is A 48

n = No. of terms = 10 (even)
If n is even,
Median $=\frac{{\left(\frac{n}{2}\right)}^{th}\text{term}+{(\frac{n}{2}+1)}^{th}\text{term}}{2}$
$\therefore \text{Median}=\frac{1}{2}[{\left(\frac{10}{2}\right)}^{th}\text{term}+{(\frac{10}{2}+1)}^{th}\text{term}]$
$\Rightarrow 39=\frac{1}{2}[5^{th}\text{term}+6^{th}\text{term}]\Rightarrow 39\times 2=x-7+x-11\Rightarrow 78=x-7+x-11$
$\Rightarrow 2x=96\Rightarrow x=48$