How is it possible that more than half of the molecules in an ideal gas have Kinetic Energies < avg K. energy

Question

Shouldn't half have less and half have more?

Answer 1

As a previous answer has pointed out, there's a difference between the average in this sense and the median. One thing to consider is that there is no maximum speed for the particles in an ideal gas, but you can't have a particle with less than zero speed (velocity sure, but that still means positive kinetic energy). Therefore you can see that the distribution of kinetic energies can't be a simple symmetric curve. (The actual distribution is exponential.)
As an example, here're some numbers- say you have five particles with different kinetic energies:
ke1=1
ke2=2
ke3=3
ke4=6
ke5=8
The average is (1+2+3+6+8)/5=4, whereas the median kinetic energy is 3.

Answer 2

Be careful when dealing with averages and medians -- they are not the same. It is possible for a molecule to have an arbitrarily large energy, but the least possible is obviously zero. This will give the effect that you describe.

Answer 3

If the variance of the of molecules below the mean is greater than the variance of the molecules above the mean, this would be the case.