Here’s one: Which of the following statements might be true?

1) Two-thirds of those enrolled never showed up

2) More than half of the students earned a passing grade

It’s obviously a trick question since the answer is “both.” The apparent contradiction is entirely dependent on another, perhaps bigger question, one that is often phrased as a challenge—if not to to the idea of MOOCs, to the idea of their value: What good is a class where only 2 percent of the students bother to finish?

Or, to put it a little more quantitatively: What denominator should we use in computing student participation, engagement, and completion in a course like this, when the numerator is going to be the number who passed (in my case, 1,196)?

While there are plenty of ways to answer that, the one I decided to try—in keeping with the modality of a MOOC—was asking the students.

So, halfway through “Understanding Media by Understanding Google,” my Northwestern course on Coursera, that’s what I did. And though the 302 students who replied didn’t entirely agree, the preponderance of the evidence pointed me to a different answer than any of those I first offered as possibilities. Should it be, I asked them, based on the number of people who watched even one lecture—or all the lectures? How about the number who tried the first quiz? Or should we just stick with that great big enrollment number?

None of the above, they told me. Just count the ones who were at least trying to pass. And if that’s the standard, perhaps this chart shows how to get to “more than half” with a straight face, even though 55,412 people were enrolled at one time or another.

So, back to my opening pair of answers. The “two-thirds who never showed up” are the 36,378 people who never encountered any course content after enrolling. That number is 66 percent (or 55,412 enrolled minus 19,034, the number who actually at least started to watch one lecture).

And the “more than half” who passed? Since a student had to turn in at least two homework assignments to have a mathematical chance to earn 70 points, that denominator would be 2,385. And 1,196 is indeed a little more than half that total. (You could get marginally higher percentages by using just the students who remained registered throughout, represented in the chart by the blue segments of the bars.)

There is, of course, sample bias at work in the students’ definition: Most who weighed in were still doing the work halfway through the six-week course. Several of the 302 responses, however, did come from people who said they never intended to earn a grade. They reported they would think of themselves as having completed the course if they watched all of the video lectures. In fact, they assigned themselves the well-established label of “auditors.”

Still, why do the numbers seem to shrink so?

Let’s move from our idea of “auditors” to another staple of academia, the course catalog. And let’s do a little comparing and contrasting.

I’ll start with the people I could call MOOC-omores, 55,000 people who happen to sign up for a free course that sounds interesting. Then I’ll create a completely theoretical population of second-year students at Bricks and Mortar U. who at the same are trolling for enjoyable on-campus electives—why, let’s call them sophomores. And I’ll set the second population size at 100 for ease of math.

How do these two groups proceed?

Admittedly, we don’t have many four-person elective classes here at Northwestern’s Medill School, where I teach journalism in some of those bricks-and-mortar buildings, so the comparisons do finally break down somewhat. But then again, the sophomore has limited tuition dollars as well as limited choices. The MOOC-omore has limited time and attention, but hundreds of choices, whether among other online courses or other life activities.

It’s also a factor that, as recently noted in the New York Times, signing up for a MOOC “takes less time than signing up for an iTunes account,” and that it then takes even less time simply to disappear from a crowd of 55,000.

For now, as I work on evaluating how much the 1,196 learned en route to the finish line, I think I have one helpful way to think about the 54,000 who didn’t get there. (Soon, I’ll have results of my post-course survey of students both who passed and who didn’t, perhaps allowing me to further refine my thinking—and my choice of metaphors.)

This is what I say for now: Sure, the entire population of the Chicago suburb of Mount Prospect can sign up for a course. But when it’s over, we can hold graduation in the same auditorium on Northwestern’s campus that we use for the journalism school.