### Two thoughts on the statistics quiz

Last week, Rudbeckia Hirta at Learning Curves posted a handful of definitions of the Pigeonhole Principle, as given by her students. Go read them if you haven’t already: they’re not only spectacularly incorrect, they’re also bizarre, incoherent, and could rival the output of The Random Sentence Generator. I was jealous. *My* students’ incorrect answers just make me cry, not laugh. I said as much in the comments, and RH replied, *You would get equally comic answers if you were able to ask this sort of question. Maybe you could try, “What is a function?”*

~~I have no qualms about designing quizzes with the singular purpose of acquiring fodder for entertaining blog posts, so~~ The opportunity presented itself this week, when I decided to check if my students really knew what the standard deviation measured, and not just how to evaluate it. “What characteristic of a data set does the standard deviation measure? Explain in a sentence or two,” I instructed, and tingled with anticipation as I collected the papers.

I sat down to grade them later that day, and…

I got nothin’ for you, folks. Apparently my students actually *know* what characteristic of a data set the standard deviation measures.

Hunh. I guess that’s okay, too.

One aspect of my job that never fails to surprise me: the strange and many *ways* in which my students don’t understand the subject. I’m still caught off guard by these, even after tutoring and teaching math for years. And I’m not referring to the sort of *dear God, why can’t they add fractions already* frustration that I experience on occasion and have chronicled in detail, but rather the very frequent *oh, they’re confused by THAT. I didn’t even realize that that could be confusing* realizations.

For instance: on the stats quiz, I asked students to write down the formula for the standard deviation, and also to specify what each of the variables represented. The question was, for the most part, quite well done: most got the formula right or close to right, and most were able to tell me that x-bar was the mean, the x_{i}’s were the data values, and n was the number of values.

…and then, half a dozen or so of them also went on to explain that the capital sigma meant to add stuff up, and that the symbol that looked like a checkmark with a horizontal tail meant to take the square root.

They don’t know the difference between variables and functions. I had no idea.

The charitable explanation is that they’re computer science students who program in some bizarre programming language where you can redefine standard functions. Maybe they thought they COULD define ∑ to mean “standard deviation” and √ to mean “logarithm”, but didn’t, and wanted to point out that they didn’t.

In some ancient programming languages (or some ancient and badly written compilers), you could actually redefine integers. “LET 3=4; PRINT 3+3″ would output 8. Or maybe 7.

Or less charitably, maybe they have poor reading comprehension and they are actually being very defensive, telling you everything they possibly can.

Jeff - wow, what a crappy programming language. But none of my students are CS majors.

Mitch - I gave full marks if they explained all of the actual variables, so no harm, no foul. It’s just that this was totally unexpected, y’know?