How do I increase my jumper count?

Your jumper count is the number of people who have jumped out of a window. You can increase this by making people jump out of windows (obviously) and you're correct - it does increase your score.

There is an achievement, called The Final Curtain:

Cause 10 window jumpers

And an achievement called The Friendly Ghost:

Complete the game with no window jumpers.

You can cause window jumpers by making them TOTALLY freaked out, when their eyes are shut, and their mouth is taking up most of the face. In this state they will run around randomly, but you can herd them to windows by possessing objects and making the 'Oooooh' sounds. Make sure they are NOT NEAR the door, because that will cause them to leave through the door. Using the methods above, herd them to a flapping window and there is a random (but convenient) chance that they will jump out of the window. Remember they face away from you if you face them, so do that near a window. In the original stage (the mansion) once you scare everyone away, a cutscene will take place where a man is running out of the house and you are staring out the window smiling. After that, you will see a view of in front of the ghost and see the window jumpers' ghosts come back. They will have the exact same hairstyle and things that the original jumpers had. So they couldn't take it anymore and they COMMITED SUICIDE. That's dark for a kids' game. But there you have it, how to get window jumpers in Haunt The House!