Abstract: In this paper, the authors made Q -model and R - model analyses of the scores of the entrance examination of four sorts of middle schools in Xiamen, and calculated the factor scores as well . Based on the investigation of the similarity coefficient ma. trix of the sampling units (students) , three typical representations which govern all the students were found , furthermore based on the investigation of the indexes correlation matrix, four kinds of mathematical abilities which govern all the indexes were found and estimated too.

Key words: Q-Model (R-Model), Factor Analysis, Principle Fatctor