The ability of a finite, autonomous, quantum mechanical system to reflect the ergodic behavior of its classical counterpart is discussed. It is argued that an attempt to identify unambiguously the consequences of rigorous ergodicity in such a quansum system would be futile. Instead, an approximate, temporary, form of ergodicity, called pseudoergodicity, is introduced and compared for the classical and quantum analogs of the Henon-Heiles system. The numerical results illustrate the extent to which quantum systems imitate classical statistical tendencies.