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

$$\begin{gathered} \text{Arrange the data as follows:} \\ \text{α−}\frac{7}{2},\alpha -3,\alpha -\frac{5}{2},\alpha -2,\alpha -\frac{1}{2},\alpha +\frac{1}{2},\alpha +4,\alpha +5 \end{gathered}$$

$\begin{array}{l} Median =\frac{1}{2} [value\mathrm{of} 4 th\mathrm{item} + value\mathrm{of} 5 th\mathrm{item}] \\ \therefore Median =\frac{\alpha -2+\alpha -\frac{1}{2}}{2}=\frac{2\alpha -\frac{5}{2}}{2}=\alpha -\frac{5}{4}\end{array}$