This paper addresses two major questions about children's understanding of average. The first question deals with children's own understanding of representativeness within the context of data sets. When asked to describe a data set, how do children construct and interpret representativeness? The second question focuses on how children think about the mean as a particular mathematical definition and relationship. It deals with the underlying issue of how children develop mathematical definitions and how they connect these definitions with their informal mathematical understanding. This question, which has been considered by other researchers primarily in the context of experimental research designs, is addressed here in an open-ended, descriptive manner.