Plancherel measure on set of irreducible representations of a finite group

Definition
Suppose $$G$$ is a finite group. Let $$\operatorname{Irr}(G)$$ 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 $$\operatorname{Irr}(G)$$ the measure $$d^2/|G|$$ 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.