When President Trump started dismantling federal agencies and dismissing rank-and-file civil servants, Peggy Carr, the chief statistician at the Education Department, immediately started to make a calculation.

She was the first Black person and the first woman to hold the prestigious post of commissioner of the National Center for Education Statistics. As a political appointee, she knew there was a risk of becoming a target.

But her 35-career at the department spanned a half dozen administrations, including Mr. Trump’s first term, and she had earned the respect of officials from both parties. Surely, she thought, the office tasked with tracking the achievement of the nation’s students could not fall under the president’s definition of “divisive and harmful” or “woke.”

But for the first time in her career, Dr. Carr’s data points didn’t add up.

On a February afternoon, a security guard showed up to her office just as she was preparing to hold a staff meeting. Fifteen minutes later, the staff watched in tears and disbelief as she was escorted out of the building.

“It was like being prosecuted in front of my family — my work family,” Dr. Carr said in an interview. “It was like I was being taken out like the trash, the only difference is I was being taken out the front door rather than the back door.”

While tens of thousands of employees have lost their jobs in Mr. Trump’s slash-and-burn approach to shrinking the federal work force, experts say the cuts disproportionately affect Black employees — and Black women in particular. Black women make up 12 percent of the federal work force, nearly double their share of the labor force overall.