  When a granular system is tapped, its volume changes. Here, using a
well-defined macroscopic protocol, we prepare an ensemble of granular systems
and track the statistics of volume changes as a function of the number of taps.
This is in contrast to previous studies, which have focused on single
trajectories and assumed ergodicity. We devise a new method to assess the
convergence properties of a sequence of ensemble volume histograms and
introduce a reasonable approximate version of an invariant histogram. We then
compare these invariant histograms with histograms generated by sampling a long
trajectory for one system and observe nonergodicity, which we quantify.
Finally, we use the overlapping histogram method to assess potential
compatibility with Edwards' canonical assumption. Our histograms are
incompatible with this assumption.
