Statistics of N-body Simulations I. Equal Masess Before Core Collapse

We study the dynamical evolution of idealised stellar systems by averaging results from many $N$-body simulations, each having modest numbers of stars. For isolated systems with stars of uniform mass, we discuss aspects of evolution up to the point of core collapse: relaxation and its $N$-dependence, the evolution of the density profile, the development of the velocity dispersion and anisotropy, and the rate of stellar escape.