Almost

Sovereign Base Areas of Akrotiri and Dhekelia Population: 15,000 (almost half British military and staff)
http://en.wikipedia.org/wiki/British_Overseas_Territory

In this instance, is it saying slightly more than half of the population or slightly less than half of the population are British military and staff? Thanks

slightly less

Almost is always a little less than the goal, so "almost half" is less than half, or not quite half.