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 mean deviation about median is

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

Answer 1

The correct option is A $\frac{5}{2}$

$x-\frac{7}{2},x-3,x-\frac{5}{2},x-2,x+\frac{1}{2},x-\frac{1}{2},x+4,x+5Median=\frac{x-2+x-\frac{1}{2}}{2}=x-\frac{5}{4}$
$\therefore$ MD about median
$=\frac{2.25+1.75+1.25+0.75+0.75+1.75+5.25+6.25}{8}=\frac{20}{8}=\frac{5}{2}$