We weren’t too surprised that most people didn’t know the exact jobless rate; most people aren’t economists. What was truly intriguing was that so many people answered in the completely wrong direction.

We set out wanting to learn about people’s perceptions of the value of college, now nearly seven years after the recession, when a big supply of college graduates and low demand for work had made the case for college seem weaker. Late last year, we asked Google Consumer Surveys to ask Americans about college costs, wages after college, and unemployment rates of college graduates and nongraduates.

The really interesting result was how people answered the jobless rate questions.

We asked: “What would you guess is the current unemployment rate for four-year college graduates between the ages of 25 and 34?” We also asked the same question, phrased the same way, but about high school graduates.

Initially, people were way off. The most common answers for college graduates were between 20 and 30 percent. Perhaps an understandable mistake: The question was open-ended, and maybe lots of people don’t know exactly how an unemployment rate is defined (it doesn’t include people who aren’t looking for jobs). But what surprised us was that the majority of people thought that unemployment rates for those with college degrees were higher than for those without.

We were so surprised that we thought we had done something wrong. Maybe we asked the question unclearly, or perhaps people weren’t thinking about unemployment rates consistently. So we ran the survey again, this time with a point of reference to anchor them. Our focus this time was figuring out whether people were completely mistaken about the effect of a college degree on one’s chances of having a job.

Can this really be true?

We asked: “The unemployment rate for 24-to-34-year-olds without a four-year college degree is 7 percent. What do you think it is for 25-to-34-year-olds with a four-year college degree?” More than half of the respondents thought that the jobless rate for college graduates was higher.

We were becoming convinced that this was a real misunderstanding, not a flaw in the surveys, each of which was run by Google, each with over 1,000 respondents. A report by the Pew Research Center found that the results from Google’s surveys are typically quite similar to the results from Pew’s telephone surveys.

We posed the same question to our friends and parents. Many have college degrees themselves; some are educators. They, too, mostly guessed that college graduates would be more likely to be unemployed than nongraduates. Their reasoning? College graduates would be pickier, overeducated or lacking practical skills.

We ran the quiz one last time with the same question and anchor, structured as a multiple-choice quiz.

This time, nearly half of the people in the survey guessed that college graduates had higher unemployment rates. We had to concede that we weren’t witnessing a mirage.

Are we — the news media — to blame? Many articles have been written in recent years questioning the value of college: about unemployed college graduates living at home, technological change replacing the demand for college graduates and overeducated college graduates who end up being either unemployed or underemployed. Our survey results suggest that articles like these have really taken hold with the public.

Here’s the thing about college degrees...

There is some evidence that having a college degree doesn’t guarantee a good job, but the alternative is much worse. Young people who have earned a college degree have substantially lower unemployment rates than those who haven’t. Since 2000, young college graduates, on average, have an unemployment rate that is 5.5 percentage points lower than those of nongraduates. And this gap typically widens during recessions; it expanded to 10 percentage points at the depths of the Great Recession.

College graduates also make more money. A typical college graduate can expect to make over half a million dollars more than a nongraduate over a lifetime. Much of this has to do with differences in wage growth during the midcareer of a college graduate versus a nongraduate.

And that’s not even trying to put a price on the social and intellectual benefits of college-level courses in Shakespeare, world history and modern literature (if you’re into that).

But most people have probably heard these statistics before. Vaguely, somewhere. What’s remarkable is that this story has been unseated by a more emotional narrative. One that could be very costly to young people and society.