  Using samples of structures identified by a multi-scale decomposition from
numerical simulation, we analyze the scale-dependence of the virialization of
clusters. We find that beyond the scale of full virialization there exists a
radius range over which clusters are quasi-virialized, i.e. while the internal
structure of an {\it individual} cluster is at substantial departure from
dynamical relaxation, some {\it statistical} properties of the multi-scale
identified clusters are approximately the same as those for the virialized
systems. The dynamical reason of the existence of quasi-virialization is that
some of the scaling properties of dynamically relaxed systems of cosmic
gravitational clustering approximately hold beyond the full virialization
regime. The "individual-statistical" duality of the quasi-virialization
provides an explanation of the observed puzzle that the total masses of
clusters derived from virial theorem are statistically the same as the
gravitational lensing determined masses, in spite of the presence of irregular
configuration and substructures in individual clusters. It also explains the
tight correlation between the velocity dispersion of optical galaxies and the
temperature of X-ray emitting gas. Consequently, the virial mass estimators
based on the assumptions of isothermal and hydrostatic model are statistically
applicable to scales on which the clusters are quasi-virialized. In the
quasi-virialization regime, the temperature functions of clusters also show
scaling. This feature is a useful discriminator among cosmological models.
