Solar wind research and studies of charged particle propagation often assume that the interplanetary magnetic field represents a stationary random process. In this paper we investigate the extend to which ensemble averages of the solar wind magnetic fields follow the asymptotic behavior predicted by the ergodic theorem. Several time periods, including a span of nearly two years, are analyzed. Data intervals that span many solar rotations are found to satisfy the conditions of ''weak'' stationarity if the effects of solar rotation are included in the asymptotic analysis. Shorter intervals, which include a small integral number of interplanetary sectors, also satisfy weak satisfy weak stationarity. The results are illustrated by using magnetometer data from the ISERE 3, Voyager and IMP spacecraft.