In ${\mathrm{KO}}_2$, the nature of oxygen species and the oxidation state of oxygen atom are, respectively

 In ${\mathrm{KO}}_2$, the nature of oxygen species and the oxidation state of oxygen atoms are superoxide and $-1/2$ respectively.

Superoxide ion is ${\mathrm{O}}_2^{-}$.

Let $\mathrm{X}$ be an oxidation state of oxygen. The oxidation state of $\mathrm{K}$ is $+1$.

$+1+2\left(\mathrm{X}\right)=0$

$2\mathrm{X}=-1$

$\mathrm{X}=-\frac{1}{2}$