Sound absorbing materials such as acoustic tile, carpets, and drapes placed on ceiling, floor or wall surfaces can reduce the noise level in most  rooms by about 5 to 10 DB for high-pitched sounds, but only by 2 or 3 DB for low-pitched sounds.  For greatest effectiveness, sound absorbing materials should be installed as close to the noise source as possible. 

If you have a limited amount of sound absorbing material and wish to make the most effective use of it in  a noisy room, the best place to  put it is in the upper trihedral corners of the room.

Because of the light weight and porous nature of foam absorbers, they are ineffectual when applied to wall or ceiling surfaces to prevent the transmission of either airborne or structure borne sound from one room to another.  In other words, if you can hear people walking or talking in the room or apartment above, installing acoustical tile on your ceiling will not reduce the noise transmission.

Noise transmitted through ducts, pipe chases and electrical channels can be effectively reduced by lining the inside surfaces of such passageways with sound absorbing materials (2" pyramids or wedges, composite foam)  Lower frequencies often require doubling the thickness and/or length of the acoustical treatment.