How does U.S. know 11 million Illegal immigrants

Politicians seem to give the same ballpark estimate of how many people are living in the U.S. illegally, 11 million, but how exactly do they get to this number in the first place?

It's not like people who are living in the U.S. illegally are jumping up and down to volunteer that kind of information.

Bring on the statisticians!

Number-crunchers dive deep into census data and other government surveys, make a bunch of educated assumptions and adjustments for people who may be left out, mix in some population information from Mexico and elsewhere and tend to arrive at similar figures.

The Homeland Security Department, for example, estimates there were 11.5 million unauthorized immigrants living in the U.S. in January 2011. The Pew Hispanic Center, a nonpartisan research organization, estimates there were 11.1 million living in the U.S. in March 2011. Other estimates are in the same neighborhood.

The demographers rely on what's called the "residual" method to tease out the data.

That is, they take estimates of the legal foreign-born population and subtract that number from the total foreign-born population. The remainder – or residual – represents those who are living in the country without legal permission.

It's a fairly simple concept, but there are lots of complex assumptions that go into the calculations: How much to adjust for an undercount of foreign-born residents in the census that's done once every 10 years? How many foreign-born residents are migrating out of the U.S.? How many die in the U.S.? And so on.

"All of these things tweak the numbers on the margins, but they don't change the story very much," says Randy Capps, a senior policy analyst at the nonpartisan Migration Policy Institute. "There's a pretty good consensus, and I think the numbers are generally accepted on all sides of the debate."

Pew demographer Jeffrey Passel, who's been calculating illegal immigration estimates for decades, says the underlying method isn't all that complicated, but there's a lot of number-crunching to be done to reach a solid estimate.

"I wouldn't argue that it's good to the last hundred thousand, but I think most people think it's within a half a million," says Passel.

He tries to clearly lay out how he gets his numbers to a point.

"My colleagues give me a hard time," he says, "because when I write a report the methodology section is longer than the report."