A number of problems arise in the teaching of statistics to university social science students of heterogeneous mathematical ability and varied subject interests. An investigation of these problems carried out by the authors at the University of Sussex has followed two main lines. One concerns the relationships among aptitude for statistics, previous attainment in mathematics, performance in school and university subjects and certain other directly related factors. The paper is devoted mainly to a presentation of some preliminary results of this work. The other aspect concerns the development of a more appropriate curriculum for such students. Some reference to this is also included.