Mathematical Education of Teachers II (METII), echoed by the American Statistical Association publication, Statistical Education of Teachers, recommended teacher preparation programs support future teachers in developing deep understandings of mean and median, such that middle grades teachers may use them to “summarize, describe, and compare distributions” (Conference Board of Mathematical Sciences, 2012, p. 44; Franklin et al., 2015). Georgia Standards of Excellence require statistical reasoning from students beginning as early as 6-7 years old, including interpretation of measures of center and statistical reasoning about best measures of center (Georgia Department of Education, 2015). This level of understanding and interpretation of measures of center, however, has been a persistent struggle for students and their teachers (e.g., Jacobbe & Carvalho, 2011). Jacobbe and Carvalho argued that an over-reliance on computation with little focus on conceptual understanding has created these barriers to statistical reasoning. To impact students’ understanding, a starting point is to address teachers’ understanding, particularly by supporting conceptual understanding of measures of center in teacher preparation programs (Jacobbe & Carvalho, p. 207). Our research question was: What conceptual understandings of mean and median do preservice teacher candidates (PSTs) exhibit when presented with a mean and median statistical task? We present findings from a two-part study, comparing PSTs’ responses to a task written to elicit conceptual understandings and statistical reasoning in one semester, with PSTs’ responses to a revised task in a second semester, both given at the end of a senior-level Statistics for K-8 Teachers course.