The figures for Boston University represent averages, and needy students with strong academic backgrounds often get more aid, up to the full cost of attendance, said spokesman Colin Riley. Many of those receiving merit awards would also be eligible for need-based aid, he said.

“We are very concerned about being affordable,” Riley said in a phone interview. “We’re extremely generous with financial assistance, but we do not have unlimited financial resources.”

About 60 percent of George Washington undergraduates receive financial aid, Michelle Sherrard, a spokeswoman, said in an e-mail. The school has also recruited more low-income students.

“We are committed to ensuring the affordability and accessibility of a George Washington education,” Sherrard said.

Schools such as Harvard University and Yale University have received considerable attention for giving a free ride to the lowest-income families. Yet, they have relatively few of those students, the report said. In the 2010-2011 school year, 11 percent of students at Harvard, based in Cambridge, Massachusetts, received Pell grants, scholarships for needy students, the report said. At Yale, the figure was 14 percent.

Extension School

The 11 percent figure at Harvard includes students at its extension school, which offers continuing education classes, said Jeff Neal, a Harvard spokesman. Most aren’t eligible for Pell grants because they aren’t pursuing degrees. In 2010-2011, the number of undergraduates at Harvard College receiving Pell Grants was 17 percent, he said.

Yale’s financial-aid program “ensures that every student who is admitted to Yale can afford to attend, no matter what their financial circumstances,” spokesman Tom Conroy said in an e-mail.

Amherst, Vassar

The report praised Amherst College in Massachusetts; Vassar College in Poughkeepsie, New York; and Grinnell College in Grinnell, Iowa, which all reported that more than 20 percent of their students had Pell grants and required low tuition payments from students whose families earn $30,000 or less a year. At Amherst, those students pay almost nothing, while Vassar seeks an average of $5,706, according to the report.