ABSTRACTDiscrete‐state compartment (DSC) models and their associated age distribution functions permit the quantitative interpretation of environmental radioisotope data such as carbon‐14 ground‐water decay ages. These mixing‐cell models offer a means for constructing ground‐water flow models that can be used to relate decay ages to ground‐water mean ages. In addition, DSC models can also generate the entire distribution of ages in various subregions of a ground‐water reservoir. A preexisting DSC model of a portion of the Tucson Basin alluvial aquifer is used as an example. Ground‐water mean ages in this aquifer range from 100 to almost 15,000 years old, with the oldest waters about 40,000 years old. Since the ground‐water ages are not normally distributed, means and medians are not equivalent. The results indicate that care must be used in interpreting both ground‐water radioisotope decay ages as well as mean ground‐water ages and that knowledge of the entire age distribution is preferable. Age distributions are especially useful in hydrogeologic studies in which mixing is important and may find use in paleohydroge