This study measures the variance of classical social variables (gender, race/skin color, and age) among groups of the same school which have shown the highest and the lowest levels of proficiency in Reading and Math. Variance is the measurement we adopt here in order to show inequality levels. The research has used longitudinal data collected by GERES from 2005 to 2006, considering primary school students of 27 municipal schools in Rio de Janeiro. The object has been to investigate if the variance observed through proficiency results among groups of the same school can also be found when referring to students social characteristics such as gender, race/skin color, and age. The research considers not only students fulfillment in cognitive tests, but also their demographical and social characteristics. This study has brought up evidences which reveal that differences in fulfillment among groups of municipal schools in Rio de Janeiro are not clearly marked by social aspects, what means that the process of organizing students in groups is not determined by classical social variables of gender, race/skin color, and age. On the other hand, our results show that students different abilities in Reading and Math lead to their allocation in groups.