  We present a statistical study of the largest bibliographic compilation of
stellar and orbital parameters of W UMa stars derived by light curve synthesis
with Roche models. The compilation includes nearly 700 individually
investigated objects from over 450 distinct publications. Almost 70% of this
sample is comprised of stars observed in the last decade that have not been
considered in previous statistical studies. We estimate the ages of the
cataloged stars, model the distributions of their periods, mass ratios,
temperatures and other quantities, and compare them with the data from CRTS,
LAMOST and Gaia archives. As only a small fraction of the sample has radial
velocity curves, we examine the reliability of the photometric mass ratios in
totally and partially eclipsing systems and find that totally eclipsing W UMa
stars with photometric mass ratios have the same parameter distributions as
those with spectroscopic mass ratios. Most of the stars with reliable
parameters have mass ratios below 0.5 and orbital periods shorter than 0.5
days. Stars with longer periods and temperatures above 7000 K stand out as
outliers and shouldn't be labeled as W UMa binaries.
  The collected data is available as an online database at
https://wumacat.aob.rs.
