A) Sum/n can be odd only if sum and n are both odd or both even.
If n is even, the average of n numbers is not an integer. So both sum and n are odd..
I just want to add something: when even/even
the sum= n/2 *( z1+zn)
average= [(n/2)*(z1+zn)]/n= (z1+zn)/2
when n is even (z1+zn) is always odd thus the average is not an integer as gsr pointed out.