We establish a moderate deviation principle (MDP) for the number of
eigenvalues of a Wigner matrix in an interval. The proof relies on fine
asymptotics of the variance of the eigenvalue counting function of GUE matrices
due to Gustavsson. The extension to large families of Wigner matrices is based
on the Tao and Vu Four Moment Theorem and applies localization results by
Erd\"os, Yau and Yin. Moreover we investigate families of covariance matrices
as well.Comment: 20 page