As has long been understood, the noise on a spectrometric signal can be reduced by averaging over time, and the averaged noise is expected to decrease as t1/2, the square root of the data collection time. However, with contemporary capability for fast data collection and storage, we can retain and access a great deal more information about a signal train than just its average over time. During the same collection time, we can record the signal averaged over much shorter, equal, fixed periods. This is, then, the set of signals over submultiples of the total collection time. With a sufficiently large set of submultiples, the distribution of the signal's fluctuations over the submultiple periods of the data stream can be acquired at each wavelength (or frequency). From the autocorrelations of submultiple sets, we find only some fraction of these fluctuations consist of stochastic noise. Part of the fluctuations are what we call "fast drift", which is defined as drift over a time shorter than the complete measurement period of the average spectrum. In effect, what is usually assumed to be stochastic noise has a significant component of fast drift due to changes of conditions in the spectroscopic system. In addition, we show that the extreme values of the fluctuation of the signals are usually not balanced (equal magnitudes, equal probabilities) on either side of the mean or median without an inconveniently long measurement time; the data is almost inevitably biased. In other words, the unbalanced data is collected in an unbalanced manner around the mean, and so the median provides a better measure of the true spectrum. As is shown here, by using the medians of these distributions, the signal-to-noise of the spectrum can be increased and sampling bias reduced. The effect of this submultiple median data treatment is demonstrated for infrared, circular dichroism, and Raman spectrometry.