“We are heading into a critical dry run of the 2020 census without any experienced person at the helm,” she said, referring to the 2018 field test that will put into practice some of the new techniques implemented by Mr. Thompson.

Is it expensive?

Yes. Taking a head count of the American people is hugely expensive. The 2010 census cost $13 billion to complete, according to a report from the Government Accountability Office, making it the priciest in history. In 2011, the office advised the bureau to “re-examine and perhaps fundamentally transform” its process. But in January, the decennial census was added to the office’s list of high-risk operations, indicating concerns that it might not be able to complete its mission.

Robert Goldenkoff, the director of strategic issues at the Government Accountability Office, said that Mr. Thompson’s departure simply adds to the complications that the bureau has to contend with in the run-up to the 2020 census as it overhauls its process in order to cut costs and make use of new digital resources.

“The lack of a permanent director to keep the preparations on track with budgetary factors and to mitigate risks only adds to the uncertainties facing 2020,” he said.

Spending on the Census Bureau typically rises sharply in the final years before the decennial is conducted. But the $1.47 billion Congress granted the bureau at the end of April for the 2017 financial year is about 10 percent less than was requested by the Obama administration in February 2016 and President Trump’s recommendation of $1.5 billion for 2018 does not meet the needs of the bureau, experts say.

How will this affect the next census?

At an occasionally contentious hearing last week, Mr. Thompson informed lawmakers that the cost for a new program to collect and process data was more than $300 million higher than had been estimated in 2013. Representative John Culberson, the chairman of a House appropriations subcommittee that oversees the bureau responded that it was “just not acceptable” to see that the 2020 census looked as if it were “heading in the same direction as the 2010 census, with terrific cost overruns.” Mr. Thompson said at the hearing that the best cost estimate for the 2020 census was $12.5 billion, but that the estimate would be renewed.