Homework Help: Question if expectation value is considered a measurement?

An expectation value is a weighted average of all of the eigenvalues. So it may or may not actually be a valid eigenvalue itself.

As an example, the X component of the spin operator has two eigenvalues: -1/2 and 1/2. However, if you take the X expectation value of a Z state (which is a linear combination of both of those eigenstates), the expectation value will be 0, since both -1/2 and 1/2 states appear in equal combination. 0 is not actually a valid eigenvalue of the X operator, but it's the average of the two actual eigenvalues.