Statistical Mechanics Partition Function

We know from Boltzmann’s Distribution for the canonical ensemble that $overline{E}=frac{-partial{lnZ}}{partial{beta}}$, which for the translational degree of freedom comes out to be $overline{E}=frac{3NkT}{2}$.
Later, we define average energy per molecule, which is: $frac{overline{E}}{N}=frac{3kT}{2}$.
We know from mathematics that the average of the sample is the number that we can assign to each of the sample members. So, once we have calculated the average energy, what’s the point of calculating the average energy per particle? I cannot apprehend the reason for the appearance of $N$ in the average energy formula. Can someone help me out? Am I going wrong somewhere?