  In equilibrium systems, time and ensemble averages of physical quantities are
equivalent due to ergodic exploration of phase space. In driven systems, it is
unknown if a similar equivalence of time and ensemble averages exists. We
explore effective limits of such convergence in a sheared bubble raft using
averages of the bubble velocities. In independent experiments, averaging over
time leads to well converged velocity profiles. However, the time-averages from
independent experiments result in distinct velocity averages. Ensemble averages
are approximated by randomly selecting bubble velocities from independent
experiments. Increasingly better approximations of ensemble averages converge
toward a unique velocity profile. Therefore, the experiments establish that in
practical realizations of non-equilibrium systems, temporal averaging and
ensemble averaging can yield convergent (stationary) but distinct
distributions.
