Roughly going by your statement, your crewmember got around 4125-4228 xp.
Remember there's a 5x multipler on free xp to crew xp (unless event with 10x)
And 825 difference in the free xp requirement, would match that quite well.
Spending 825 free xp on the crew member, would have given him what you gained in the battle.
Another edit:
And remember crew xp is quite exponential in growth.
Primary training is 105k xp
First skill is 210k xp
Second skill is 420k xp
Third is 840k xp
And so forth.. doubling with every skill.
Fun fact, the time it takes you to get first + second skill to 100%, is the same time you'll spend for this....:
"You will need roughly 611,195 exp from 99% to 100% of Seventh skill"