Subject: The difference between the root mean square and the mean speed of molecules

I study chemistry and have to do a physical chemistry test based on 
P.W. Atkins "Physical Chemistry" book. Usually a pretty good book, but 
not on this subject.
There are 2 kinds of molecular speeds:
the root mean square speed which is equal to srqt(3RT/M)
and the mean speed which is equal to sqrt(8RT/piM).
Because 8/pi is not too far away from 3 the difference between the 
speeds is not that big, but there is a difference. What is the meaning 
of the different mean speeds? Why aren't they the same? I've asked 
several people but nobody can explain the difference to me.

Re: The difference between the root mean square and the mean speed of molecules