In this paper, we examine common methods for using individual-level data to represent classroom composition by examining exemplary studies that thoughtfully incorporate such measures. Building on these studies, and using data from the Chicago School Readiness Project (CSRP), this paper examines theoretical and analytical implications of a set of different transformations of individual ratings of child externalizing behaviors in order to examine and compare the influence of these representations of classroom composition on Kindergarten internalizing behaviors, social competence, and attention/impulsivity problems. Results indicate that each Kindergarten outcome is influenced by distinct aspects of classroom composition of externalizing behaviors. Kindergarten internalizing behaviors are positively associated with the proportion of children in the Head Start classroom who started with externalizing scores above the 75th percentile regardless of the average value of externalizing behaviors in the classroom. In contrast, Kindergarten social competence is predicted by three aspects of the classroom distribution of externalizing behaviors in the fall of Head Start -- the classroom mean, standard deviation, and skew. Finally, Kindergarten attention/impulsivity problems were not associated with any aspect of classroom composition of externalizing behavior examined in this paper. (author abstract)