Sometimes, the many numbers included in the government’s monthly jobs report come together to paint a clear, coherent picture of the strength or weakness of the U.S. labor market.

This is not one of those times.

Instead, the data released by the Labor Department on Friday was a mess of conflicting signals. It couldn’t even agree on the most basic of questions: whether the economy is adding or losing jobs.

The report showed that employers added 272,000 nonagricultural jobs in May, far more than forecasters were expecting. That figure is based on a survey of about 119,000 businesses, nonprofit organizations and government agencies.

But the report also contains data from another survey, of about 60,000 households. That data showed that the number of people who were employed last month actually fell by 408,000, while the unemployment rate rose to 4 percent for the first time in more than two years.

The two surveys measure slightly different things. The employer survey includes only employees, for example, while the household survey includes independent contractors and self-employed workers. But that doesn’t explain the discrepancy last month: Adjusting the household survey to align with the concepts used in the employer survey makes the job losses in May look larger, not smaller.

That means that the conflicting pictures come down to some combination of measurement error and random noise. That is frustrating but not unusual: Over the long term, the two surveys generally tell similar stories, but over shorter periods they frequently diverge.

Economists typically put more weight on the employer survey, which is much larger and is generally viewed as more reliable. But they aren’t sure which data to believe this time around. Some economists have argued that the household survey could be failing to capture fully the recent wave of immigration, leading it to undercount employment growth. But others have argued that the employer survey could be overstating hiring because it isn’t accounting properly for recent business failures, among other factors.