Arrange the data as
$\alpha-\frac{7}{2}, \alpha-3, \alpha-\frac{5}{2}, \alpha-2, \alpha-\frac{1}{2}, \alpha+\frac{1}{2}, \alpha+4, \alpha+5$
Median $=\frac{1}{2}\left[\right.$ value of $4^{\text {th }}$ item + value of $5^{\text {th }}$ item $]$
$\therefore$ Median $=\frac{\alpha-2+\alpha-\frac{1}{2}}{2}=\frac{2 \alpha-\frac{5}{2}}{2}=\alpha-\frac{5}{4}$.