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 is positive), then the median is :

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

Answer 1

Answer: (A)

First we arrange the given data in ascending or descending order we have
$x+5,x+4,x+\frac{1}{2},x-\frac{1}{2},x-2,x-\frac{5}{2},x-3,x-\frac{7}{2}$
Total no. of observation = 8 (even)
$\therefore$ Median $=\frac{4^{th}\text{observation}+5^{th}\text{observation}}{2}$
$=\frac{x-1/2+x-2}{2}=\frac{2x-\frac{1}{2}-2}{2}=x-5/4$