WASHINGTON — The 2020 census undercounted the population of six states and overcounted residents in eight others, the Census Bureau said on Thursday, a finding that highlighted the difficulties of conducting the most star-crossed population count in living memory.

The conclusions come from a survey of 161,000 housing units conducted after the census was completed, a standard procedure following each once-in-a-decade head count of the U.S. population. The results showed that six states — Arkansas, Florida, Illinois, Mississippi, Tennessee and Texas — most likely have a larger population than was officially counted.

Eight states probably have fewer residents than were recorded, the survey found: Delaware, Hawaii, Massachusetts, Minnesota, New York, Ohio, Rhode Island and Utah. The count in the remaining 36 states and the District of Columbia was basically accurate, the bureau said.

The results were markedly worse than in the 2010 census, in which none of the states had a statistically significant overcount or undercount, the agency found. But they were not unlike the conclusions from the 2000 census post-mortem, which found overcounts in 22 states and an undercount in the District of Columbia.

John H. Thompson, the director of the Census Bureau from 2013 to 2017, said he was not surprised by the variations given the problems that dogged the 2020 census. “All censuses have overcounts and undercounts,” he said. “That does not preclude using the results.”

Still, for the states that missed the mark, the numbers were striking. The bureau said the greatest undercount was in Arkansas, where the census likely missed 5.04 percent of the population — some 160,000 people, or the equivalent of nearly 80 percent of the state’s largest city, Little Rock.

However, that was just the midrange of a much wider band of estimates. The undercount could have been as small as about 43,000 people, the agency said, or as large as 286,000.

Similarly, the bureau pegged the undercount in fast-growing Texas at 570,000 people, but said it could range roughly between 167,000 and 985,000. And in New York, the bureau estimated that it counted 695,000 more people than actually lived there, but said the estimate could be as low as 382,000 or as high as one million.

The Census Bureau said in March that the same survey had found undercounts of Black and Hispanic people in the national population totals, as well as overcounts of white people and people of Asian descent. Overcounts of white people and undercounts of other racial and ethnic groups have been a persistent problem in past censuses.

The survey was not broad enough to offer reliable estimates of those racial and ethnic discrepancies on a state-by-state basis, the bureau said.

The post-mortem will not change the official state-by-state results of the census, which said 331,449,281 people were living in the United States in 2020. Nor will it alter the allotment of seats in the House of Representatives or the map boundaries in state and local political districts, which are redrawn every 10 years using census results.

The Supreme Court has barred the use of surveys in apportioning seats in the House, and in any case, the large margin of error in the post-2020 census survey makes its conclusions more like educated guesses than solid findings.

“There definitely would have been changes in reapportionment,” said Andrew Beveridge, a demographics expert and a professor emeritus of sociology at Queens College. “But just how isn’t clear.”

One of many possible scenarios to consider is Minnesota, which came within a few thousand people of not getting the 435th and last House seat after the 2020 census reapportionment. The post-mortem concluded that the census overcounted the state’s population by somewhere between 128,000 and 310,000 people.

Minnesota might still have held on to the seat after a more accurate count because competing states like New York overcounted an even greater number of people. But it also could have lost the seat to a state like Texas, where the undercount was sizable.

The survey did not attempt to determine why some states were miscounted, but experts say there are many possible explanations, led by the Covid-19 pandemic, which roared across the country as the census was being conducted.

In particular, the pandemic made many people reluctant to open their doors to census takers in the late summer of 2020, when the bureau was trying to get information about tens of millions of people whose households had not filled out census forms.

The geography of the miscounts also points to other potential causes. Five of the six states with population undercounts were in the Deep South, while six of the eight states that were most overcounted were in the North, and particularly the Northeast.

Some Southern states like Florida and Texas have large populations of Hispanic people, who were badly undercounted on a national scale. The South also was hit by hurricanes in the latter stages of the count. And when census takers began fanning out to conduct personal interviews in August 2020, the South was coming off a major summertime spike in coronavirus cases.

There could also be a political dimension to the results. Five of the six undercounted states are solidly Republican, while six of the eight overcounted ones are largely Democratic.

The antigovernment tenor of the Trump administration and Republican governors in 2020 could have raised suspicions about the census in some states, just as attacks on immigrants depressed responses by Hispanics and other people of color, said Steve Jost, a census consultant who was deeply involved in the effort to increase response to the count.

“Leaders who attack the government in the middle of the government’s biggest peacetime enterprise shouldn’t be surprised to discover their states didn’t perform as well as others.” Mr. Jost said.

He also noted another telling indicator: All but one of the states with population overcounts, an inaccuracy that can prove beneficial through additional political representation and federal funding, mounted their own campaigns to convince residents to fill out census forms. All but one of the states that were undercounted spent no money to promote the census.

“Some states put money into it big-time, and other states did not,” said Kenneth Prewitt, a Columbia University scholar who oversaw the 2000 census. “And the states that put in money did better in terms of getting to the plus or minus that you want.”