Sample Grades

These are not real grades, just an incredible simulation.

 SSN    TEST1  HMWK1  FINAL  TOTAL  
         50.8   73.9   66.7
         20.8   27.4   14.9
 1234     85    100     83    87  
         100     99     91   95.4
 2345     14     85     72    57  
          48     85     80   71.7
 3456     55     70     58    60  
          78     71     66   70.8
 4567     42     79     39    48  
          69     80     47   60.1
 5678     19      0     53    32  
          52      0     61   46.2
 6789     56     84     62    65  
          79     84     70   75.6
 1357     71     92     73    76  
          90     92     81   85.8
 2468     49     81     57    59  
          74     81     65   71.0
 3579     67     55     79    71  
          87     58     87   81.2
 9876     50     93     91    79  
          74     92     99   90.5
TOTAL GRADES:   A     B     C     D     F
                2     2     4     1     1
Class Average = 74.8

The information in top two rows is the average and standard deviation for each test/assignment. Records for the students are in totally random order with a randomly assigned number in the "SSN" column. {In the beginning, I used alphabetical order by last name, identified by (the traditional) last four digits of the ssn; later, based on some objections, it changed to numerical order by ssn; now its super secure). The first line in each record is your unadjusted score (right off the page). The second line is the score adjusted by a rough curve.

The curve is very simple:

 ((Score - Ave) * (DSDEV/RSDEV)) + DAVE = Curved Grade
 
where 
	Score = what you got
	Ave   = class average
        DSDEV = the standard deviation I'm creating
        RSDEV = the class's standard deviation
        DAVE  = the average I'm creating

and assuming you actually took the test or handed in the
assignment (if not, your curved grade is also a zero).

Note that occasionally, the curve will tend to lower certain individual grades (especially if they were dramatically above average). My expectation is that pairs of grade-sets (curved and not) would have a strict mathematical relationship, but not necessarily that they be totally-ordered. If this distresses you, the option of basing your grade on all of the uncurved values is always available (but picking and choosing is not allowed).

The most important number (i.e. your final grade) is the last (fixed point) number in the second line. It will be the primary (but not only) number used in the computation of your letter grade.

ASSIGNING LETTER GRADES

The numbers at the bottom (after "TOTAL GRADES") are simply the counts of folks in the 90s, 80s, 70s, 60s and below respectively. They are only a rough measure of the grade distribution in the class, since other factors will be considered. Consequently, letter grades are never officially estimated during the course of the semester.

At the end of the semester, however, the registrar obliges me to assign grades to all the students. I start by making your curved average (under the usual 90+ -> A mapping) act as a minimum final grade. Then I look for factors in my experience that would lead me to believe that a higher grade is appropriate:

Did you have one really off night (like on a test)?
Did you make constant improvement?
Does your final test grade show a marked improvement?
Did your verbal contributions in class show a higher level of understanding than you demonstrated on written tasks?

If there is sufficient evidence, you will receive a higher grade than that indicated by your final average.

Consider the following example:

Student 1 gets a curved 70% up till the final, then gets an 85% on the final.
Student 2 gets a curved 77% up till the final, then gets a 77% on the final.

Other factors being equal, Student 1 will get a B (despite having a 76% average), while Student 2 will get a C (with a 77% average). Invariably this leads to Student 1 being happy, and Student 2 feeling upset. (Of course, if I didn't do this, Student 1 would feel like they had wasted all the effort required to make the big improvement, while Student 2 would have little reaction.)

Why assign grades this way? Well, remember the grading policy stated on the first night of class: "Your job is to learn the material by the end of the semester." Although Student 1, performed weakly for most of the semester, at the end, this individual has clearly demonstrated superior understanding. Student 2 also gets a final grade consistent with the level of understanding demonstrated at the end semester (it just so happens that this is the level maintained for the duration).

In general, no grading system will satisfy all the students (one of my professors--after I had explained why I deserved a better grade--once told me that he had learned more statistics from students trying to justify grades than any other source), so I try to stick to a grading system which I feel reflects the point of the class: achieving a thorough understanding of the course material.