I have a theory that can explain situational anomalies such as this in classroom that's as situationally accurate as I have time to puzzle out.
To simplify the mathematics of the problem, I'm omitting some scale factors from my math which serve as little more than visual clutter.
Let an ideal bell curve be defined by
Your set of students is
S, and you have a magical function
s ∈ S which yields the "quality" of a student's work.
Now consider a test. The test consists of a set of problems (call this set
T). Each problem
p ∈ T has a difficulty, given by
D(p). The probability of a student
s correctly answering a problem is defined:
Pcorrect(s, p) =
It then follows that a student of higher
Q than the
D of the problem will be more than likely to solve it, and one with a lower
Q will be less than likely.
Let's define the ideal score of a student taking a test to be
Si(s, T) = Σ Pcorrect(s, p), p ∈ T
If you were to take the ideal score on a particular test for each student in your classroom, you would get an ideal distribution, and chances are that if your students actually took the test, you'd get a distribution that at least roughly approximated the ideal one.
The important thing to take away from what we have so far is that, for an population of students taking a test, the difficulty of the problems on the test mathematically affects the grade distribution you're likely to have.
For example, assuming your student population is roughly bell-curved, you might see a grade distribution like your observations if your test questions have roughly these difficulty levels:
[2, 2, 5, 6, 6, 7, 7, 8, 10, 10+, 10+]
A large number of students would get the 2 easy questions right, but since there are few questions of low-intermediate difficulty, some of the students on the lower end of the curve wouldn't be able to get any harder ones right. On the very high end, there are some questions that might be extraordinarily difficult for the skill level of the students (this can happen for a number of reasons) that most of the class got wrong (assuming the grade is out of 10 points total).
Assuming your class distribution is something like this,
3 | 1
4 | =2
5 | ===4
6 | ====5
7 | ====5
8 | ===4
9 | =2
10 | 1
Their ideal distribution (as defined previously, rounded a bit to reduce clumping) would look something like this:
2 | ===4
3 | ===4
4 | ===4
5 | ===4
6 | ==3
7 | =2
8 | 1
Which resembles, in a muted way, the observed curve you experimentally observed.
Also, realistic situations won't have such elegant mathematical solutions (like a student's probability of getting a question correct), so this model should only be viewed as a reasonable, educated approximation.
TL;DR It's possible the questions on this one test were more difficult and less comprehensive than you thought when you handed it out.