Knowing how the Bureau of Labor Statistics calculates its numbers, including the fact that a survey of business establishments and of households are done each month, can go a long way toward understanding how there can be seeming anomalies in the results, especially in one month. Understanding math can help, too. Of course, some people don't care about how the numbers are actually derived.

Ezra Klein gets it exactly right:

Let’s get one thing out of the way: The data was not, as Jack Welch suggested in a now-infamous tweet, manipulated. The Bureau of Labor Statistics is set up to ensure the White House has no ability to influence it. As labor economist Betsey Stevenson wrote, “anyone who thinks that political folks can manipulate the unemployment data are completely ignorant of how the BLS works and how the data are compiled.” Plus, if the White House somehow was manipulating the data, don’t you think they would have made the payroll number look a bit better than 114,000? No one would have batted an eye at 160,000. [...]