  Homogeneity and isotropy of the universe at sufficiently large scales is a
fundamental premise on which modern cosmology is based. Fractal dimensions of
matter distribution is a parameter that can be used to test the hypothesis of
homogeneity. In this method, galaxies are used as tracers of the distribution
of matter and samples derived from various galaxy redshift surveys have been
used to determine the scale of homogeneity in the Universe. Ideally, for
homogeneity, the distribution should be a mono-fractal with the fractal
dimension equal to the ambient dimension. While this ideal definition is true
for infinitely large point sets, this may not be realised as in practice, we
have only a finite point set. The correct benchmark for realistic data sets is
a homogeneous distribution of a finite number of points and this should be used
in place of the mathematically defined fractal dimension for infinite number of
points (D) as a requirement for approach towards homogeneity. We derive the
expected fractal dimension for a homogeneous distribution of a finite number of
points. We show that for sufficiently large data sets the expected fractal
dimension approaches D in absence of clustering. It is also important to take
the weak, but non-zero amplitude of clustering at very large scales into
account. In this paper we also compute the expected fractal dimension for a
finite point set that is weakly clustered. Clustering introduces departures in
the Fractal dimensions from D and in most situations the departures are small
if the amplitude of clustering is small. Features in the two point correlation
function, like those introduced by Baryon Acoustic Oscillations (BAO) can lead
to non-trivial variations in the Fractal dimensions where the amplitude of
clustering and deviations from D are no longer related in a monotonic manner.
