Will the Average Kinetic Energy of ejected Electrons in Photo electric effect change with Intensity of Radiation?

Please realize, that I am not talking about the Maximum Kinetic energy of Photoelectrons. I understand that the Max K.E. depends upon the energy of radiation used.

But the Kinetic enrgy of most electrons is less than Max K.E. so will the average K.E. of all electrons also be unaffected on increasing Intensity of Light, or as the no. of ejected electrons increase then their average K.E. will also increase?
Or is this indeterminable?