Perceptual biases found experimentally are often taken to indicate that we should be cautious about the veridicality of our perception in everyday life. Here we show, to the contrary, that such biases may be a consequence of the experimental protocol that cannot be generalized to other situations. We show that the central tendency, an overestimation of small magnitudes and underestimation of large ones, strongly depends on stimulus order. If the same set of stimuli is, rather than being presented in the usual randomized order, is applied in an order that displays only small changes from one trial to the next, the central tendency decreases significantly. This decrease is predicted by a probabilistic model that assumes iterative trial-wise updating of a prior of the stimulus distribution. We conclude that the commonly used randomization of stimuli introduces systematic perceptual biases that may not relevant in everyday life.