White dwarfs with helium-dominated atmospheres comprise approximately 20% of all white dwarfs. Among the open questions are the total masses and the origin of the hydrogen traces observed in a large number and the nature of the deficit of DBs in the range from 30000 - 45000K. We use the largest-ever sample (by a factor of 10) provided by the Sloan Digital Sky Survey (SDSS) to study these questions. The photometric and spectroscopic data of 1107 helium-rich objects from the SDSS are analyzed using theoretical model atmospheres. Along with the effective temperature and surface gravity, we also determine hydrogen and calcium abundances or upper limits for all objects. The atmosphere models are extended with envelope calculations to determine the extent of the helium convection zones and thus the total amount of hydrogen and calcium present. When accounting for problems in determining surface gravities at low Teff, we find an average mass for helium-dominated white dwarfs of 0.606+-0.004 Msun, which is very similar to the latest determinations for DAs. There are 32% of the sample with detected hydrogen, but this increases to 75% if only the objects with the highest signal-to-noise ratios are considered. In addition, 10-12% show traces of calcium, which must come from an external source. The interstellar medium (ISM) is ruled out by the fact that all polluted objects show a Ca/H ratio that is much larger than solar. We also present arguments that demonstrate that the hydrogen is very likely not accreted from the ISM but is the result of convective mixing of a residual thin hydrogen layer with the developing helium convection zone. It is very important to carefully consider the bias from observational selection effects when drawing these conclusions.
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