Part III of the reasons to avoid zeros in grading…
For folks who don’t or won’t buy into Doug Reeves’s arguments about the futility and just plain wrongness of putting zeros in a grade book and dumping them into a mean average, here are some words of wisdom from a statistics textbook author who apparently also had issues with at least one of his teachers.
“One of the most useful ideas in statistics is the representation of a collection of measures by a measure of central tendency, that is, a single value chosen in such a fashion as to by typical of the collection…
…Just what constitutes a typical (or average) measure will depend to a large extent on the level of measurement and the manner in which the measures are dispersed throughout the collection.” (Fundamental Research Statistics, John T. Roscoe, Holt, Rinehart, Winston, Inc., New York, 1969.)
The above paragraph tells us that a grade, as in report card grade, needs to be an alpha or numeric indicator of a collection of scores (marks or grades) that is truly representative of the scores.
“[The mean] is the only one of our three [measures] that is dependent upon the value of every measure in the collection. This latter characteristic is usually a valuable one, but not always, as the mean is much affected by extreme scores… (Yes, that would be a zero. — Hugh)
…Thus, the mean would not be very typical of a student’s work if the teacher makes a practice of awarding zeros when the student is absent or other wise unproductive.” (Italics mine.) (Fundamental Research Statistics, John T. Roscoe, Holt, Rinehart, Winston, Inc., New York, 1969.)
So what’s a poor teacher to do? For starters, face up to the fact that zero is just wrong for a lot of reasons. (See The Responsibility Paradox.) Zero’s not a score, or a mark, or a grade. It can’t legitimately be included in a mean average.
There’s more to this story, but for now, consider abandoning zero altogether, and give some thought to going to median averages for that part of the grade that you feel the need to calculate.
Tip: If your gradebook mean and median averages are close, you’re in good shape. If the mean is significantly off the median, you’ve probably included the forbidden “outliers” or extreme scores in the mean, which render it invalid.