At times, the numerous numbers included in the government’s monthly employment report combine 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, data released by the Labor Department on Friday was a mess of mixed signals. They couldn’t even agree on the most basic question: whether the economy is adding or losing jobs.

The report showed that employers added 272,000 nonfarm jobs in May, much more than forecasters expected. 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, carried out on 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 last month’s discrepancy: 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 conflicting images boil down to some combination of measurement error and random noise. This 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 give more weight to the employer survey, which is much larger and generally considered more reliable. But they’re not sure what data to believe this time. Some economists have argued that the household survey may not fully capture the recent wave of immigration, leading it to underestimate job growth. But others have argued that the employer survey could be overstating hiring because it doesn’t adequately take into account recent business failures, among other factors.