Nearly half of students nationwide are eligible for a subsidized meal in school. Children whose families earn less than 185 percent of the poverty threshold are eligible for a reduced-price lunch, while those below 130 percent get a free lunch. For a family of four, the cutoffs are $32,000 for a free lunch and $45,000 for a reduced-price one. By way of comparison, median household income in the United States was about $54, 000 in 2014.

Eligibility for subsidized school meals is clearly a blunt indicator of economic status. But that is the measure that policy makers, educators and researchers rely on when they gauge gaps in academic achievement in schools, districts and states.