Fewer children met the city’s standards to enter gifted programs this year, but wide disparities remained between students in middle-class districts and poor ones, according to data that the Department of Education released today.

Just over a quarter of the nearly 38,000 children who took two screening exams won the right to apply to gifted and talented programs this year, according to the department. Children who score in the 90th percentile may apply to district programs, and children in the 97th percentile may apply to a handful of elite citywide programs, although admission is not guaranteed.

Last year, more than 32 percent of children met the standards, which at the time favored non-verbal communication skills more highly in an attempt to reduce the influence of test prep. This year’s screening test weighed verbal and non-verbal skills equally, and just over 26 percent of children made the cut.

As in the past, children met the screening standard most often in middle-class parts of the city. In District 2, which includes the Upper East Side and much of Manhattan below 59th Street, 1,577 children — or 43 percent of those screened — hit the eligibility bar. In District 12 in the Bronx, that was true for just 44 kids, or 10 percent of children screened.

A Department of Education spokeswoman signaled that the city was not satisfied with the inequities in the screening results.

“We continue to look at alternative ways to identify gifted students through verbal and non-verbal assessments and promote geographical diversity in these programs,” said the spokeswoman, Devora Kaye.

The results come a year after a massive scoring error by Pearson, the testing company that handles the city’s gifted screening process, that caused thousands of children to be told wrongly that they were not eligible for gifted programs. (Pearson paid a $500,000 penalty, including $420,000 that city officials said would be used to boost diversity in gifted programs.) Both the Department of Education and a third-party auditor reviewed Pearson’s scoring process this year, according to department officials.

Chancellor Carmen Fariña has downplayed the role of gifted programs since taking office at the beginning of the year.

“My children did not go to gifted and talented, and I think they had wonderful educations because their teachers taught all the kids in that class to the highest level,” Fariña said at a forum in Queens in February. She said her “goal would be to have neighborhood schools that provide gifted practices to all students.”