Small public-high schools in the city that are open to kids at all academic levels have strikingly increased students’ prospects of graduating, a new report has found.

MDRC, a nonprofit research organization, studied 123 smaller high schools created between 2002 and 2008. They “serve mostly disadvantaged students of color’’ and have about 100 students per grade in grades 9 through 12, it said.

The students, who were looked at between 2005 and 2010, had a 67.9 percent graduation rate, compared with 59.3 percent for a control group of kids who couldn’t get in because of space considerations, MDRC said.