You say you are not a mathematics teacher. The word “statistics” strikes fear in your heart. I will try to simplify this subject for you.

We all know a little bit about statistics, right? Average? Okay, that is a good place to start. What is the average grade your students earned on the last test? What is the average grade your students are earning for the course? Does it seem reasonable? If the average works out to a B or C, things may be in order. Or, they may not be. This is where grade distribution comes into play.

If ¼ of your students are averaging 98 percent (high A’s) and ¾ of them are averaging 66 percent (mid D range), the average grade is (trust me on this) 74 percent (mid C range). The fact that a significant number of students get very good grades does not necessarily mean that the other students deserve the poor grades they are earning. It is all too easy to rationalize that if some students do well, you are doing well as an instructor. However, more likely than not, you have a problem you need to address.

### Why Would the Majority of Students Fail?

If you graph your students’ grades on a simple bar chart, some interesting information may emerge. Look at Grade Distribution 1 on the right. What conclusions would you draw?

Perhaps you have had classes like this. If so, did you conclude that 25 percent A’s was a good thing? Did you question why so many students failed? Why might that be?

Some of the reasons why a large number of students got A’s while twice that number failed are:

• There were two different groups of students – those who worked hard and studied and those who did not apply themselves.
• One fourth of your students could teach themselves. You only needed to tell them what they needed to learn, and they did the rest.
• Half of the students could not learn in your class. You may not have appealed to their diverse learning styles. You may not have answered their questions in a way they could understand. You may not assessed their learning “on the run.” We call that formative assessment.

My point is this. You may have missed the opportunity to help many of your students. If you care about your students, this is definitly an aspect of teaching that you want to focus on.

### Grades – The Normal Distribution

Those of you who have taken a statistics course remember the normal distribution. If not, you probably remember the term “bell shaped curve.” Those of you who went on to major in statistics may remember that “technically” this is a Gaussian distribution. Okay, far too technical. Let’s move on!

The “perfect” normal distribution is a symmetrical bell shaped curve. Grade Distribution 2 is not perfectly symmetrical, but it is close. Here is another statistics term – “mode.” The mode is the value that occurs most frequently. So, the mode for Grade Distribution 2 is …? Sure, it is a grade of “C.” If the number of A’s equaled the number of F’s and the number of B’s equally the number of D’s this would have been the symmetrical bell shaped curve that is indicative of a normal distribution.

Are you an instructor who grades on the curve? Then you shift all the grades to make sure that the mode (a.k.a. the majority of students) earn C’s. I am not saying this is a bad practice, but it can be in some situations. If you realize that your grading criteria exceeded the requirements for assessing the learning objective a curve is in order.

What did I just say? If you students actually acheived the learning objectives but your grading policy was “too tough” you should, by all means, curve the final grades. In other words, were your tests too tough?

There is nothing necessarily wrong with Grade Distribution 2. But wouldn’t you want more of your students to succeed? Or, do you fear that you will be judged as an easier grader?

Grade distribution 3 is more desireable that Grade Distribution 2. The reason should be obvious.

The grades depicted in the graph at the right show that 83 percent of the student passed this course (or this test or assignment). Isn’t that your goal – to guide students to passing?

If this were the distribution for your students, only 18 percent would have earned D’s and F’s. That means fewer students are likely to lodge grade appeals than in the previous two situations. (Keep in mind, your primary goal is not to avoid grade appeals, but it is relatively high on the list.)

If your students’ grades are distributed like this, you are almost certainly doing a decent job. The majority of your students are passing. In fact 82 percent of your students are getting the C or above that they need to graduate. This does’t mean there is not room for improvement, but there this distribution provides no indication that you are doing something.

### Why Should Any Students Fail?

In the grade distribution at the right you can see that every student passed with a grade of C or better. Wait! Shouldn’t grades be normally distributed? Shouldn’t some students be expected to fail in a well run, challenging, high quality college course? Isn’t something wrong if everyone passes?

Statistically, the answer is NO. The normal probability distribution is representative of random chance. If the grades your students get are random and not representative of what they learning, you have a problem.

There is no reason that any student should fail other than the student himself or herself. Some students don’t put in the effort. Some don’t know how to study. Some have test anxiety. Some have personal life issues that do not allow them to do their best. Some have learning disabilities. The list goes on!

There are only some many things you can do as a college teacher. You cannot intervene in a student’s personal life. You cannot erase a learning disability. You cannot force students to put in the time and effort necessary to do well. However, there are several things you can do. For example, in no particular order you can:

• present material in a variety of ways that appeal to diverse learning styles;
• demonstrate enthusiasm for your subject;
• display confidence in your students;
• make sure your students take advantage of college resources such as tutoring;
• give your students study tips;
• review before tests;