Earlier this year, Mr. Trump said, “Don’t believe those phony numbers,” contending that the jobless rate was “probably 28, 29, as high as 35. In fact, I even heard recently 42 percent.” More recently, he declared the official 5 percent jobless rate “one of the biggest hoaxes in American modern politics.”

By affirming that view, Trump supporters are in effect signaling: “I’m with him.”

So how reliable is the government data on employment, which will be reported again on Friday? Like all statistical measurements, it can be both honest and imprecise; a best estimate given the available tools but nonetheless subject to ambiguity, misinterpretation and error.

“Every data collection comes with a set of strengths and weaknesses,” said Karen Kosanovich, an economist and 24-year veteran of the Bureau of Labor Statistics. “That’s part of the business of collecting information.”

There are some basic ground rules, however, that prevent the process from spitting out any answers you please and undermine claims that the results are rigged for a political purpose.

For starters, the people who generate the numbers are all career civil servants who have churned out reports for both Republicans and Democrats. And their basic methods do not swerve from one administration to the next. If the figures are biased, they are consistently biased in the same way regardless of what party is in office.

“I’ve never had any outside influence that tells me what to do or how to collect and interpret information,” Ms. Kosanovich said. “Our approach is based on methodologies that have been proven over time and approved statistical practices. They are not based on political influence.”

Image Jack Welch, the former chief of General Electric, caused a stir in 2012 by questioning favorable jobs data that did not match his personal observations. Credit... Richard Drew/Associated Press

The monthly employment report is derived from two separate surveys that serve different purposes. The first, collected by the Census Bureau since 1942, allows the government to estimate the number of people who are employed and calculate the unemployment rate.