The measurement of the average received power is essential for power control and dynamic channel allocation in wireless communication systems. In this paper, the error statistics for average power measurements are considered; in particular, the probability distribution of the value of the average received power conditioned on a noisy measurement is obtained. The resulting expression should have high utility in the analysis of wireless communication systems; however, in this paper, this expression is employed in the design of power control algorithms that minimize the average transmitted power required to achieve a desired outage probability for the link. It is demonstrated that power control algorithms based on the accurate expression derived in this paper demonstrate significant gains over those based on previous approximate models