  In this work we study families of $\mathbb{Z}_2$ orbifolds of toroidal
conformal field theories based on both factorizable and non-factorizable target
space tori. For these classes of theories, we analyze their moduli spaces, and
compute their partition functions. Building on previous work, we express the
calculated partition functions in terms of suitable Siegel-Narain theta
functions that allow us to determine their ensemble averages. We express the
derived averaged partition functions of the studied families of conformal field
theories in a manifest modular invariant finite sum of products of real
analytic Eisenstein series. We speculate on a tentative holographic
three-dimensional dual bulk interpretations for the considered $\mathbb{Z}_2$
orbifold classes of ensembles of conformal field theories.
