Question

Why is an air-conditioner normally installed at the height in a room?

Answer 1

Air-conditioner supplies cool air.

As cool air is more dense than hot air so this cool air shift downward that is why the A.C. is installed at a height. If the A.C. would be installed at low level then coll air will not be able to cool whole room because then it become limited to areas near floor of the room.