More high schools are serving offering healthier food options to its students, according to a recent study.

Researchers at the University of Michigan found that more secondary students had access to healthier foods on more lunch menus in 2013 than in 2011, resulting in fewer nutrition disparities for small schools or those with racially diverse student bodies. There were also significant improvements made in the National School Lunch Program, a federally assisted meal program, at public middle and high schools in 2013 after many years of meal disparities based on school size or demographics.

"While these improvements are encouraging, continued progress is needed," Yvonne Terry-McElrath, lead author of the study, said in a statement.

The U.S. Department of Agriculture updated its nutrition standards for the 2012-13 school year. For the study, researchers examined how schools implemented those changes in food and beverages. They asked public school principals and administrators if lunch meals had sugar-sweetened drinks, candy or regular-fat snacks, high-fat milk, French fries, whole grains, or fruits and vegetables.

By 2013, at least 80 percent of secondary students attended schools that offered nonfat milk and fruits and vegetables daily.

Whole grains were also found on more plates at high schools, increasing to 73 percent in 2013, up from 62 percent in 2011. The availability of fruits and vegetables improved to 87 percent in 2013, up from roughly 78 percent in 2011.

When it came to school size, 91 percent of high schools with fewer than 500 students offered fruits and vegetables in 2013, compared with 67 percent in 2011. High schools with more than 1,000 students reported available fruits and vegetables at 85 percent and 84 percent for 2013 and 2011, respectively.

Middle and high schools with predominately white students were more likely to have whole grains and fruits and vegetables in 2011 than their counterparts in diverse schools. By 2013, those differences were largely eliminated.

"Smaller schools that were experiencing prior disparities have largely caught up to larger schools," Terry-McElrath said. "It is clear that the first year of implementation of the updated NSLP standards saw reduced disparities in the quality of NSLP nutrition for students across the board."

The findings are detailed in the journal Preventative Medicine.