There is no "average." You can order special short throw lenses for more expensive 3 chip DLP projectors that have a throw ratio as low as .65 to 1. So you multiply the width of the screen by .65 and then add the length of the projector with lens, and then add 2 to 4 inches to that to give the projector room to breathe.
If you use a Blue Ocean screen in 133" size, it will have a width of 116". With that screen you can use a very short throw projector. If the projector lens has a throw ratio of .75 to 1, you multiply the screen width by .75, then add for the projector length, then add at least 2" to give the projector room to breathe. So you might end up with a requirement for 10.25 feet behind the projector. You can use a mirror to fold the light path and make that shorter.
If you have lots of room behind the screen as I do, then you can use almost any projector. If you had 17 feet behind the screen, you could use a Vutec Fusion HD screen in 133" diagonal size, and then use a relatively inexpensive single chip DLP projector with a lens throw ratio of 1.5 to 1. If the projector is rated at 4,000 lumens, you should get a nice bright picture. For rear projection viewing with lights on, brightness is more important than the contrast ratio of the projector. BenQ, ViewSonic, InFocus, and Knoll Systems make affordable one chip DLP projectors that would work with that screen.
An Epson PowerLite Pro Cinema 6010 LCD projector would give you enough light and the right throw ratio for a Vutec Fusion HD screen in 133" diagonal size. That would be an excellent combination because it has both high brightness and excellent contrast. With that projector you might be able to get away with just 14' behind the screen.http://www.projectorcentral.com/Epso...inema_6010.htm
Vutec sells those screens with nice metal frames, so they look like plasma TVs once installed. You can get them in 110", 123", and 133" size. The smaller the screen, the shorter the distance you need behind the screen and the brighter the image for any given projector.