Plancherel measure on set of irreducible representations of a finite group

Definition

Suppose $G$ is a finite group. Let $\mathrm{I}\mathrm{r}\mathrm{r}(G)$ be the set of irreducible representations (up to equivalence) of $G$ over the field $\mathbb{C}$ of complex numbers. The Plancherel measure on this set assigns to each element of $\mathrm{I}\mathrm{r}\mathrm{r}(G)$ the measure $d^2/\left|G\right|$ where $d$ is the degree of the representation.

The Plancherel measure is a probability measure in the sense that the total measure of the set is $1$. This follows from the fact that sum of squares of degrees of irreducible representations equals group order.