Recent work by Kanim and Cid suggests that the data used in PER is not representative of students enrolled in physics courses at the national level. Using university-level demographics, Kanim and Cid showed that PER studies oversample from white, wealthy, mathematically-prepared populations of students. What we do not yet know is whether these university-level demographics are representative of introductory physics courses, which are a primary site of research in PER. In this paper we present data from six US institutions, comparing the composition of introductory physics classes to aggregate university demographics in terms of gender and race and/or ethnicity. Our aim is to make progress in characterizing the demographics of introductory physics courses, which is imperative to deepening our understanding of how social disparity is manifested in physics classrooms and the institutions that host them. We discuss limitations of our approach, including problematizing the use of statistics to make sense of who is enrolling in introductory physics.