Is it possible for a university to have a lower overall acceptance rate for female-identifying students, even if each department admits them at a higher rate than the others?

This question prompts you to examine a hypothetical situation and determine its feasibility. It focuses on a university's acceptance rates, particularly contrasting the overall acceptance rates for female-identifying students with their acceptance rates within each specific department. The inquiry seeks to understand whether the overall acceptance rate for female-identifying students could be lower even if every department admits them at a higher rate. To address this question, it's crucial to comprehend how acceptance rates are calculated at both the departmental level and across the university as a whole, as well as to consider any factors that could distort these rates in various ways.

Logically, if each department at the university accepts female-identifying students at a greater rate than others, one might expect that the overall acceptance rate for female-identifying students university-wide would also be elevated. However, there may be specific circumstances where this isn't true. For example, if the departments with higher acceptance rates for female-identifying students have fewer total positions available compared to other departments, it could lead to a lower overall acceptance rate for these students. Additionally, if the departments where female-identifying students most commonly apply have lower overall acceptance rates, this could also contribute to a lower overall acceptance rate for female-identifying students at the university.

Indeed, it is theoretically feasible for a university to exhibit a lower overall acceptance rate for female-identifying students, even if each individual department accepts them at a higher rate. This occurs because the overall acceptance rate is not merely an average of the departmental rates; rather, it is a weighted average that considers both the number of applicants and the number of students accepted in each department. Therefore, if female-identifying applicants tend to seek admission to more competitive or smaller departments with limited spots, the overall acceptance rate for female-identifying students could be lower at the university level. This underscores the necessity of examining more than just simple averages when evaluating acceptance rates and related statistics.