  We quantify the degree of inhomogeneity in the Luminous Red Galaxy (LRG)
distribution from the SDSS DR7 as a function of length scales by measuring the
Shannon entropy in independent and regular cubic voxels of increasing grid
sizes. We also analyze the data by carrying out measurements in overlapping
spheres and find that it suppresses inhomogeneities by a factor of 5 to 10 on
different length scales. Despite the differences observed in the degree of
inhomogeneity both the methods show a decrease in inhomogeneity with increasing
length scales which eventually settle down to a plateau at $\sim 150 \, h^{-1}
\rm {Mpc}$. Considering the minuscule values of inhomogeneity at the plateaus
and their expected variations we conclude that the LRG distribution becomes
homogeneous at $150 \, h^{-1} \rm {Mpc}$ and beyond. We also use the
Kullback-Leibler divergence as an alternative measure of inhomogeneity which
reaffirms our findings. We show that the method presented here can effectively
capture the inhomogeneity in a truly inhomogeneous distribution at all length
scales. We analyze a set of Monte Carlo simulations with certain periodicity in
their spatial distributions and find periodic variations in their inhomogeneity
which helps us to identify the underlying regularities present in such
distributions and quantify the scale of their periodicity. We do not find any
underlying regularities in the LRG distribution within the length scales
probed.
