# What statistics should I disclose when giving grades to students?

When giving grades to students, I often find it interesting to disclose some information about the grades distribution. I imagine that it helps to know where one is situated in comparison to others.

I usually don't want to disclose the maximum grade and the minimum grade, the latter obviously for keeping the students that didn't perform well motivated.

I usually end up giving the mean (or the median, should they be significantly different).

Can one do better? Information about quartiles maybe? What are your practices?

If relevant, I am teaching in France where the grades range from 0 to 20. I am interested in different situations: small class (~20) or whole group of students (~200), regular assignments or final exams.

--- EDIT ---

I am interested in keeping the students motivation high. Are there any (research backed-up) studies about that question?

• @Buffy Many students ask for it so I suppose it is useful to them in a way. Of course, a relevant answer would be "none". Feel free to elaborate in an answer if it is your experience. May 28 '20 at 15:35
• @Buffy Knowing rudimentary statistics about an exam can give a better idea of the difficulty level, which I think some students can take encouragement from. May 28 '20 at 15:46
• Numerous reasons: 1. you learn that you did do better than others, 2. you learn that you are in a better position than at the last evaluation, etc. May 28 '20 at 15:58
• I am not at all suggesting competitive grading. May 28 '20 at 16:03
• @Buffy Let's say I get a 50% on a quiz. If everyone else did in the 80s-90s then I realize I need to study harder. If everyone got between 50-60 then I know it was a hard (or bad) quiz and maybe my effort is reasonable. People differ, and personally, I don't see how distributions are harmful. May 28 '20 at 16:08

I would suggest a mean, a standard deviation and some bands, e.g. Fail (<10), 10 - 15, 15 -20. Quartiles would also help, but two quartiles below the mean are not helpful. That should be more than enough. Personally, I discuss but do not report the percentage that fails and the maximum.

I can't speak to whether disclosing the minimum or maximum grade motivates or demotivates anyone, but Canvas, a learning management system (LMS) common in the US, displays a boxplot with mean, IQR and upper/lower bounds.

(Image credit to St. Mark's School)

• Thank you. Precisely, the question is about motivating the students. Should I rephrase? May 28 '20 at 15:38
• I wish I could claim my students can all read box plots... May 28 '20 at 15:40
• @bela83 You asked what statistics to disclose, I gave a common practice that my peers and I had no issue with. If you want to ask about whether giving mean/maximum scores is good/bad for motivating your students, you should ask a new question, now that you've received answers for the question as asked. May 28 '20 at 15:40

First, as to the overall question about posting information about grade distributions on assignments: I do not do it. More below.

Can one do better? Information about quartiles maybe?

One problem that you may be trying to solve to give better information to students on how to map a score to a true course grade. In other words, you may be trying to avoid the anxiety of a "hidden" curve grading system from the perspective of the students. Taken to an extreme, you are wanting to avoid the case where your students don't really know where they stand against your grading metrics until you post their final course grades.

Is this is where you are trying to do better? If so, perhaps you should just post the equation that says directly:

Assignment Score --> Assignment Grade

When this is still unknown for some reason, then at least post a statement to the effect:

Assignment Score --> AT LEAST this Grade

This is NOT the grade distribution of the students in the class at that point on that assignment/exam. This is how you will map any given score to a likely future grade going forward.

Perhaps better still, fix the curve on the assignment grades before you report/return the score on the assignment. Add offsets or rescale. For example, rather than returning an exam with a 50% "hidden curve" grade and having to report that 50% --> B, rescale the exam scores so that 50% becomes 85% up front on the exam.

In short, when you are trying to avoid causing undue anxiety in students because the truth in your curve grading system is "hidden" to them, then stop using an after-the-fact curve grading and start reporting a "truth in grading" score.

Another improvement that you hint that you are trying to make is in your approach to motivate individual students to do better. Let's presume that you are solving this problem separately from the above problem. In other words, let's presume that, when a student gets a score of 85% on you exam, that student knows unambiguously that they have a B on the assignment. Correspondingly, a student who gets a score of 67% on your exam knows unambiguously that they have a C- on that exam. Let's presume that both students know that these grades are not subject to any future "hidden" curve grading (leaving aside case-by-case benefit of the doubt situations for borderline scores).

In this case, I must say that, I have never heard nor believed in a philosophy that a posting a grade distribution does any good or even more good than harm to motivate an individual student to do better compared with other options. In some cases, e.g. small class sizes, I even fear that posting a grade distribution, even in part, gives enough information for students to reverse-engineer grades for other students in the course. Being in the US under the guidelines of FERPA, I tend then to just avoid any possible downside risks, in this case that Student Joe will be able to figure out the grade for Student Sally. I do not post the grade distribution at all. You asked about practices as a function of class sizes. Perhaps this counter thought will give you also some insights to the potential harm.

What are your practices?

My first practice is to follow a "truth in grading" philosophy. I post the grade metrics before the course. I state where the cutoffs are for the various grade levels. Finally, I state that all problems on exams will be graded for completeness using the given grading scale.

What happens in practice is interesting. At times, I give somewhat easy exams looking back. I leave the scores fall as they do. On the next assignment or exam, I may push the boundary a bit higher for performance. At times, I give rather difficult exams, in some cases perhaps to a degree beyond what was appropriate. At that point, before I return the exam, I rescale all exam scores for that exam. In class, I state that I rescaled the exam because, taken on a wider perspective, it was more difficult than appropriate. I do this also on individual problems on exams, dropping or adding points back because I realized that the specific problem was (in hindsight) too difficult.

The net result (after many years of practice) is an ability to grade assignments and exams with final scores that are not subject to a need for a "hidden" curve to be applied later. This practice still allows for benefit of the doubt considerations for borderline cases. However, again by truth in grading, I am adamant to tell students that they will never get a lower score than what they have directly calculated, although they may (in borderline cases) have shown initiatives to obtain a higher score.

My second practice is a message to students that they are not in competition with each other or anyone else but themselves in my course. By specific example, I state that an 85% is a mid-B grade and, should this score be the highest returned grade on a course exam, then that is what the highest grade on that exam will be. I also purposely turn off the ability for students to see the overall course grade distributions in our learning management system (Canvas).

My final practice is a message to students that individual initiatives matter. Along this line, I am apt in junior or lower level classes to give bonus points for office visits.

I am interested in keeping the students motivation high. Are there any (research backed-up) studies about that question?

I too would be curious to hear whether giving out grade distributions motivates students or not. I would especially be curious to hear in the case that "hidden" curve grading is removed as a factor in such studies.

• "If so, perhaps you should just post the equation that says directly: Assignment Score --> Assignment Grade" That applies if you know this equation in advance. Rather unlikely when you're teaching a class for the first time, or the material has changed significantly, or the audience has changed significantly. A more realistic option is to post an inequality saying Grade >= some function of Score and then only modify the grade upwards. Even that can be tricky when you are new to the line of work. May 28 '20 at 20:58
• @darijgrinberg Yes, inexperience is a factor. I account for your remedy with a "truth in grading" statement that you (a student) will never be awarded a final course grade that is lower than what I report. I would also invert this ... When inexperienced, be clear about the lower bounds, learn well what you need about your ability to grade fairly, and never post publicly what you don't know for certain. Finally, one disagreement: When a faculty is well-experienced, the preparation level of the audience is not a factor for/against making a change a course grading distribution after the fact. May 28 '20 at 21:16
• I strongly agree with this viewpoint... In any situation I've ever seen where students anticipate (rightly or wrongly) a "curve", they get into the frame of mind (like outrunning a bear when camping: you only need to be faster than at least one of your fellow campers?) that their goal is just to do no worse than some fraction of the other students. Then the material takes a back seat to grade-gaming. This approach appears to be so pervasive that I've had people (amazingly!) think their 35% is maybe ok, despite my explanation of "absolute" grade ranges where 65% or worse is a big problem... May 28 '20 at 22:50

Old question, but here's my \$0.02:

The distribution and other stats are useful for the instructor but counterproductive for students because it sends the message that their classmates are competitors. It doesn't matter that they ask for it.

As for providing feedback about performance, it's better to give a scale for what score ranges in absolute terms correspond to excellent, good, etc. as Jeffrey Weimer suggests. I cannot think of a single pedagogically valid reason to inform students of their relative ranking within a class.

I can only speak from a U.S. student's perspective, but I found the canvas model shown above to be motivating when I was a student. Granted, I was usually toward the top of the curve, but that can improve confidence and keep students motivated to perform their best. The students toward the low end are typically the ones who aren't putting any effort into the class and don't care if they're at the bottom. And if they do care, then seeing their rank may motivate them to study more or attend tutoring etc.

As long as you're not posting their names, it's okay to show the top and bottom score. Again, I think it has more benefits than drawbacks.

• For students who are struggling, seeing that you are near the bottom of the class is more often demotivating rather than motivating. Dec 5 '21 at 0:16