  We consider the grand canonical ensemble of the static and extremal black
holes, when the equivalence of the electric charge and mass of individual black
hole is postulated. Assuming uniform distribution of black holes in space, we
are finding the effective mass of test particle and mean time dilation at the
admissible points of space, taking into account the gravitational action of
surrounding black holes. Having specified the statistics that governs extremal
black holes, we study its effect on those quantities. Here, the role of
statistics is to assign a statistical weight to the configurations of certain
fixed number of black holes. We borrow these weights from Bose-Einstein,
Fermi-Dirac, classical and infinite statistics. Using mean field approximation,
the aforementioned characteristics are calculated and visualized, what permits
us to draw the conclusions on visible effect of each statistics.
