Just over half of all students attending public schools in the United States are now eligible for free or reduced-price lunches, according to a new analysis of federal data.

In a report released Friday by the Southern Education Foundation, researchers found that 51 percent of children in public schools qualified for the lunches in 2013, which means that most of them come from low-income families. By comparison, 38 percent of public school students were eligible for free or reduced-price lunches in 2000.

According to the report, which analyzed data from the National Center for Education Statistics, a majority of students in 21 states are poor. Close to two-thirds of those states are in the South, which has long had a high concentration of poor students. In Mississippi, for example, close to three-fourths of all public school students come from low-income families.

But the West also has a large and growing proportion of low-income students. Arizona, California, Hawaii and Nevada have high rates of students eligible for free or reduced-price lunches.