Question

The monthly salaries (in Rs.) of $10$ employees of a factory are: $12000,8500,9200,7400,11300,12700,7800,11500,10320,8100$. The median salary is:

• A. Rs. $9670$
• B. Rs. $9760$
• C. Rs. $6970$
• D. Rs. $7960$

Answer 1

The correct option is B Rs. $9760$

Arranging the observation in ascending order :
$7400,7800,8100,8500,9200,10320,11300,11500,12000,12700$
Total number of observations $\left(n\right)=10$
$\therefore median=\frac{1}{2}[{\left(\frac{n}{2}\right)}^{th}observation+{(\frac{n}{2}+1)}^{th}observation]$
$=\frac{1}{2}[{\left(\frac{10}{2}\right)}^{th}observation+{(\frac{10}{2}+1)}^{th}observation]$
$=\frac{1}{2}[5^{th}observation+6^{th}observation]$
Median $=\frac{1}{2}[9200+10320]=\frac{19520}{2}$
$⟹$ Median $=9760$
$\therefore$ Median salary $=Rs.9760$