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

 Arrange the data as follows:
$\begin{array}{l}\alpha -\frac{7}{2},\alpha -3,\alpha -\frac{5}{2},\alpha -2,\alpha -\frac{1}{2},\alpha +\frac{1}{2},\alpha +4,\alpha +5\\ \text{ Median }=\frac{1}{2}\text{ [value of }4\text{ th item }+\text{ value of }5\text{ th item] }\\ \therefore \text{ Median }=\frac{\alpha -2+\alpha -\frac{1}{2}}{2}=\frac{2\alpha -\frac{5}{2}}{2}=\alpha -\frac{5}{4}\end{array}$