In 1973, the graduate school at the University of California, Berkeley, admitted 44% of its male applicants, but only 35% of its female applicants. As a result, the university was later sued over gender discrimination in its admissions process. In court, however, the university pointed out that most of the graduate departments actually admitted women at a higher rate than their male peers. How could that be?

In this lesson, students use frequency tables and conditional probability to explore Simpson’s Paradox and try to settle the discrimination case once and for all.

Students will

  • Use frequency tables of graduate school admissions to create circle graphs
  • Calculate probabilities of being accepted to the graduate program, conditioned on gender
  • Compare aggregated and disaggregated data sets to explore their differences
  • Explain apparent inconsistencies in observed trends in terms of lurking variables

Before you begin

Students should have a basic familiarity with frequency tables, and they should be able to complete part/whole probability calculations.

Common Core Standards

Content Standards
Mathematical Practices


UC Berkeley, P. J. Bickel, E. A. Hammel, J. W. O'Connell