Question

If a variable takes discrete values $x+4,x-\frac{7}{2},x-\frac{5}{2},x-3,x-2,x+\frac{1}{2},x-\frac{1}{2},x+5,(x>0)$ then the median is

• A. $x-\frac{5}{4}$
• B. $x-\frac{1}{2}$
• C. $x-2$
• D. $x+\frac{5}{4}$

Answer 1

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

Given data's are, $x+4,x-\frac{7}{2},x-\frac{5}{2},x-3,x-2,x+\frac{1}{2},x-\frac{1}{2},x+5,(x>0)$
Now arranging in ascending order, $x-\frac{7}{2},x-3,x-\frac{5}{2},x-2,x-\frac{1}{2},x+\frac{1}{2},x+4,x+5$
Hence required mean $=$ mean of $4^{th}$ and $5^{th}$ term $=x-\frac{5}{4}$ (Since number of terms are even.)