The strong alignment of the average directions of minimum magnetic variance and mean magnetic field in interplanetary Alfv¿nic fluctuations is inconsistent with the usual wave-propagation models. We investigate the concept of minimum variance for nonplanar Alfv¿nic fluctuations in which the field direction varies stochastically. It is found that the tendency of the minimum variance and mean field directions to be aligned may be purely a consequence of the randomness of the field direction. In particular, a well-defined direction of minimum variance does not imply that the fluctuations are necessarily planar. The fluctuation power spectrum is a power law for frequencies much higher than the inverse of the correlation time. The probability distribution of directions a randomly fluctuating field of constant magnitude is calculated. A new approach for observational studies of interplanetary fluctuations is suggested.