  This study uses students performance on standardized tests as evidence of the
quality of education and introduces a methodology based on the comparison of
performance distributions to produce indicators for both the level achieved by
the students and the learning gap between social groups, two inseparable
dimensions of quality of education. In the first case, the study compares the
distribution of the group observed with a reference distribution, which
represents an ideal situation of where students should be. In the second, it
compares the performance distribution of students belonging to social groups
defined by socioeconomic characteristics. This article uses the
Kullback-Leibler divergence to characterize the differences between the
distributions. This measure takes into account types of diferences not
considered by other measures and have solid conceptual justifications. The
proposed methodology is used to describe the quality of Brazilian basic
education using the test results applied biannually to all Brazilian students
of basic education.
