In magnetic resonance imaging, it is usual to perform several repeated acquisitions in order to reduce the impact of the noise on the evaluation of the average signal intensity. The main goal of this paper is to examine whether it is preferable to consider the magnitude of each complex measurement, or the single magnitude of the averaged data at each voxel. A thorough information theoretic study is proposed, which shows that the second option is preferable in all cases. In order to reach such a conclusion, several properties of the Fisher information of Rician distributions are proved, the main mathematical result being that it is an increasing function of the signal intensity, at constant noise level, when the latter is known. The case of an unknown noise level is also considered, with essentially the same conclusion. We also propose a more empirical comparison involving maximum likelihood estimation from simulated data, which is in agreement with the information theoretic analysis. Finally, an extension to imaging systems where multiple-receiver coils are employed is considered.