In this work we explore the nature of single-point statistical descriptions of sprays and the quantities derived therefrom. Specifically, we introduce the concept of what constitutes a complete and fundamental single-point description, and show how this can be developed in each of two basic forms: concentration-based anf flux-based statistics. The results of this development show that a complete single-point description of a spray has two components: The first is the spray intensity-expressing the quantity of spray present in a suitable form. The second is the well-known spray distribution function-expressing how the droplets of the spray are partitioned over their characteristics. Transformation expressions between the two descriptions are developed, as are derivations of the various quantities that depend on these descriptions. Specifically, quantities such as marginal distribution functions, droplet-dependent expected values, and various property flux rates and concentrations are defined and derived in each of the basic forms. These latter developments are included both for the sake of completeness and to rectify common misconceptions about the definition and interpretation of these derived quantities.