  A method for constructing statistically homogeneous and isotropic perfect
fluid universe models with significant cosmic backreaction is proposed. The
method is illustrated using a simplified model constructed as a Swiss-cheese
model with Lemaitre-Tolman-Bondi structures. The model exhibits significant
cosmic backreaction and is used to study methods proposed in the literature for
relating volume averaged quantities with observations. The comparison shows a
poor agreement between exact redshift-distance relations and the relations
predicted by schemes based on volume averages. Most of these deviations are,
however, clearly exaggerated by peculiarities of the example model, such as
large local expansion rates.
