When I have seen instances of this, it's usually because there is another variable. Example from wikipedia:

>A common example of Simpson's paradox involves the batting averages of players in professional baseball. It is possible for one player to have a higher batting average than another player each year for a number of years, but to have a lower batting average across all of those years. This phenomenon can occur when there are large differences in the number of at bats between the years.

The per-year values aren't weighted in the combined total average.