Current MMR distribution based on players publicly showing their MMR. See dataset stats for more details.
Generally, about 1 in 3 players plays ranked consistently, and a small fraction display their MMR on profile. Lower ranked players, under 3k, are much more likely to not display it. That results in a self-selection bias as seen by the prominent features of the MMR graphs. The distribution release by Valve and how the way MMR of new accounts is seeded suggest that the real mean is under 2500 MMR. The difference is the bias.

The dataset aims to capture all DOTA players, which is not technically possible due to limitation of the access to that data. A small fraction of the player base will always remain hidden. The case is similar with MMR.