You may not have completely made up that number about the average center averaging 2.5 blocks per 48 minutes, but it sounds pretty far fetched to me. Who knows? Maybe the Dwight Howards, Roy Hibberts, and Javale McGees of the league skew the numbers enough so that's true.
Last season, 36 players listed as a C or C-F by basketball-reference.com played at least 30 games averaging at least 10 minutes per game.
2.5 blocks/48 translates to 1.875 blocks/36. Last season, that would have been between the 17th (Nazr Mohammed) and 18th (Marc Gasol) of the 36 players who fit the criteria.
Looking at a couple of past seasons, that seems close to the median shot-blocking performance by centers.