Carouseling is an efficient method to mitigate the measurement errors of inertial sensors, particularly MEMS gyroscopes. In this article, the effect of carouseling on the most significant stochastic error processes of a MEMS gyroscope, i.e., additive bias, white noise, 1/f noise, and rate random walk, is investigated. Variance propagation equations for these processes under averaging and carouseling are defined. Furthermore, a novel approach to generating 1/f noise is presented. The experimental results show that carouseling reduces the contributions of additive bias, 1/f noise, and rate random walk significantly in comparison with plain averaging, which can be utilized to improve the accuracy of dead reckoning systems.