How long is an average 2v2 game?

[Juslas]

If average 2v2 game ends at turn 50, that's 12 and half turns per player. If just one of those players takes weekends off or skips a day now and then game would last 25 days. Maybe a month?
All fast players that take turns daily basis know that there are several 3-4 day turn interval players, too.

Is there public statistics how long is a typical game?

If 2v2 team has 2 ongoing games, then they have on average a match finished every other week. Team would end up having less than 30 games per year.