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The motivation for this paper is to increase individuals' understanding of the way in which inequality in educational outcomes and in the relation between measures of backgrounds is related to levels and dispersion of educational performance of young persons. The article thus sheds light on the international variation in the importance of socioeconomic status in affecting the quality of educational outcomes. This paper uses test scores on eighth-grade mathematics from the 1999 and 2007 waves of the Trends in International Mathematics and Science Study (TIMSS) to examine the magnitude and correlates of country differences in levels and dispersion in test scores. It relates test scores of students to measures of their background characteristics within each country and examines the link between the estimated association of characteristics with the country level and dispersion of test scores. The evidence shows the following: (1) Wide cross-country variation in the level and dispersion of test scores, with a virtuous equity-efficiency relation in which higher test scores are associated with lower inequality in scores across countries; (2) Substantial variation among countries in the importance of measures of family background in predicting the mathematics test scores of eighth-grade students; and (3) Higher median test scores and lower variation in student test scores in countries in which family background as measured by the number of books in the home is strongly related to test scores than in countries where it is weakly related to test scores, but no such patterns when family background is measured by parents' educational attainments. Description of Figures 2a and 2b is appended. (Contains 3 tables, 8 figures and 12 footnotes.)