WASHINGTON — Depending on which Labor Department survey is used, employment in the United States either surged the most in 29 years or grew the least in three months.

Employers added 114,000 workers to payrolls last month, the fewest since June, according to the Labor Department’s survey of employers released in Washington on Friday. A separate poll of households showed hiring surged by 873,000, the biggest gain since June 1983 excluding annual Census population adjustments. The surge helped push down the jobless rate to 7.8 percent, the lowest since President Barack Obama took office in January 2009.

Averaging the job gains of the two surveys helps produce a more consistent view of the labor market as Americans prepare to head to the polls to choose between Obama and Republican challenger Mitt Romney. The unexpected drop in the jobless rate prompted former General Electric head Jack Welch to accuse the White House of manipulating the data.

“The two surveys tell you generally the same thing,” said Michael Gapen, senior U.S. economist in New York for Barclays. “These numbers are consistent with what we’ve generated on average. This suggests the labor market has normalized after a pretty volatile spring and summer.”

Payrolls grew by 146,000 on average from July through September, while the household survey showed employment climbed by 186,000, the data showed.

The jobless rate is derived from a survey of about 60,000 households that is conducted by the Census Bureau and includes groups like the self-employed and agricultural workers that are not captured by the payroll figures. The latter is calculated based on a Labor Department survey of almost 500,000 worksites.

After adjusting the data to make it comparable to the payroll count, the household figures showed a 294,000 gain in hiring in September, according to the Bureau of Labor Statistics.

Over time these surveys show a very similar development in the labor market, said Kevin Logan, chief economist at HSBC Securities USA Inc. in New York.

“Even if the sample jumps around each month as long as everything is jumping the same way, then you’re actually getting a pretty accurate measure with you ratios,” Logan said. “So then it’s probably the case that the unemployment rate is trending down, but I don’t think we’re going to see 0.3 percent every month.”

The household survey may be more accurate at turning points in the economy because it is more likely to pick up hiring and firing at small companies and new firms that may be under the government’s radar. Yet the benefits of that real-time information are offset by the fact that the survey is much smaller and the results are therefore more volatile than the establishment figures, according to Bruce Kasman, chief economist at JPMorgan Chase in New York.

The drop in the unemployment rate gives Obama a new chance to talk about an improving economy and reset the campaign after a tepid debate performance against Romney.

Welch, in a Twitter message, accused the White House of altering the data for political advantage.

“Unbelievable jobs numbers..these Chicago guys will do anything..can’t debate so change numbers,” Welch, 76, wrote in a message posted immediately after the Labor Department’s release.

Ray Stone is among some economists who said such unsubstantiated theories are “absolutely garbage.”

“The idea that these numbers are somehow manipulated is an insult to the character of the government analysts,” Stone, managing director of Stone & McCarthy Research Associates in Princeton, N.J., said in an interview. “I’ve been dealing my whole career with these people. That just doesn’t happen.”