Many long-lived stratospheric chemical constituents enter the stratosphere through the tropical tropopause, are transported throughout the stratosphere by the Brewer-Dobson circulation, and are photochemically destroyed in the upper stratosphere. These chemical constituents, or tracers, can be used to track mixing and transport by the stratospheric winds. Much of our understanding about the stratospheric circulation is based on large-scale gradients and other spatial features in tracer fields constructed from satellite measurements. The point of view presented in this paper is different, but complementary, in that transport is described in terms of tracer probability distribution functions. The probability distribution function is computed from the measurements and is proportional to the area occupied by tracer values in a given range. The flavor of this paper is tutorial, and the ideas are illustrated with several examples of transport-related phenomena, annotated with remarks that summarize the main point or suggest new directions. The examples illustrate how physically based statistical analysis can shed some light on aspects of stratospheric transport and dynamics that may not be obvious or quantifiable with other types of analyses. The dependence of the statistics on location and time is also shown to be important for practical problems related to statistical robustness and satellite sampling. An important motivation for the work presented here is the need for synthesis of the large and growing database of observations of the atmosphere and output generated by atmospheric models. ¿ 2000 American Geophysical Union