Welcome to the community. I think the most common rank would be F because not every player plays online, some just play in lobbies and generally they really don't mean that much.
Based on my sample of 1700+ ranked matches, the most common rank seems to be either A or B.
I don't think it's distributed like a normal distribution since it takes way longer to grind through the higher ranks than the lower ones. F, E, D and C are a breeze to grind through so I expect a distribution with a skew to the right.