Mayor Bill de Blasio gave New York’s museums and arts groups an ultimatum last month: Take steps to make your staff and leadership more diverse, or risk losing part of your city funding.

The cultural organizations are starting with a mixed record. In a city known for its racial and ethnic diversity, the percentage of people of color serving on boards remains strikingly low at most institutions, and some elite Manhattan museums and arts groups employ overwhelmingly white staffs even as they try to attract a broad cross-section of visitors, according to data collected by The New York Times.

Becoming more diverse is clearly possible, the results also show. At the Studio Museum in Harlem, 82 percent of the board members are people of color, compared with 25 percent at the Metropolitan Museum of Art and 10 percent at New York City Ballet. Minority staff members also account for 66 percent of employees at the Brooklyn Museum, which prides itself on reaching a diverse audience, while they make up about 41 percent at MoMA PS 1.

The Times asked for the information from the cultural groups to get a snapshot of where they are starting. City officials, in assessing diversity, are also looking at categories like people’s gender, sexual orientation, age, and whether they have a disability. The Times focused on data specifically about racial diversity because increasing it is perhaps the biggest challenge for many of these institutions.