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To understand the role of educational opportunities in shaping average test-score patterns, it is necessary to distinguish between individual scores and average scores in a given school, geographic district, county, or state.

Differences in two students’ individual test scores at a given age reflect both differences in their individual characteristics and abilities and differences in the educational opportunities they have had. However, because the average innate abilities of students born in one community do not differ from those born in another place, any difference in average test scores must reflect differences in the educational opportunities available in the two communities.