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We are interested in determining the bound of the average of the degrees ofthe irreducible characters whose degrees are not divisible by some prime $p$that guarantees a finite group $G$ of odd order is $p$-nilpotent. We find abound that depends on the prime $p$. If we further restrict our average byfixing a subfield $k$ of the complex numbers and then compute the average ofthe degrees of the irreducible characters whose degrees are not divisible by$p$ and have values in $k$, then we will see that we obtain a bound thatdepends on both $p$ and $k$. Moreover, we find examples that make those boundsbest possible.

The Average of Some Irreducible Character Degrees