Question

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

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

Answer 1

Answer: (A)

Since, $\alpha>0$ (given) arrange the data in ascending order,
$\alpha-\frac{7}{2}, \alpha-3, \alpha-\frac{5}{2}, \alpha-2, \alpha-\frac{1}{2}, \alpha+\frac{1}{2} \,,\alpha+4, \alpha+5$
Median $=\frac{\alpha-2+\alpha-\frac{1}{2}}{2}=\frac{2 \alpha-\frac{5}{2}}{2}=\alpha-\frac{5}{4}$