Grades, like as not, are an important aspect of most forms of structured learning. Inevitably, teachers and professors have to rely on some kind of objective system to assess the performance of individual students. Since the range of performances in any class of significant size tends be be wide regardless of subject, both on individual assignments and end-of-term final grades.

Most teachers assign a certain low percentage of very high and very low grades, a modest percentage of "okay" grades between the extremes and the class average, and a large cluster around the class average. In the U.S. system, these grades usually range from **A to F**. But numerical scores vary wildly across academic situations. How can graders account for this?

Grading on a curve and dividing the student performances into **class intervals** based on time-tested statistical criteria helps make this conversion a standard process and can iron out some of the effects of overly difficult or easy exams and other unwanted situations.

## How Are Grades Assigned?

A typical grade percentage chart in the United States will show letter grades ranging from F to A in order of improving performance, typically with the grades other than F given sub-gradations, e.g., B+ and C−. "E" is skipped; F is a failing grade and thus does not require further scoring.

An alternative (and sometimes complementary) system involves GPA, or grade-point average. This ranges normally from 0.00 to 4.00, with each interval number corresponding to a letter grade. That is, 0.00 is F, 1.00 is D, 2.00 is C, 3.00 is B and 4.00 is A. Getting to "+" and "−" gradations requires moving up and down in increments of 0.33.

Both of these systems map onto percentage systems in a fairly consistent way. The range of 1.67 to 2.33 is the range of C grades, and also corresponds to percentile scores between 70.0 and 79.9. These percentile scores, however, are often *scaled scores* rather than *raw scores* because of the phenomenon of grading on a curve.

## Grading on a Curve

If you and your classmates all took a 25-question quiz asking you to write a different letter of the alphabet in each space, chances are excellent that almost everyone would get 25/25 right. On the other hand, if you were asked to name 25 galaxies besides the Milky Way, the class average (the sum of the individual scores divided by the number of test-takers) would likely hover close to zero.

Because tests of knowledge are imperfect means of assessing learning progress for a host of reasons, many instructors **grade on a curve** to establish a fixed ratio of A, B, C, D and F grades between tests, regardless of the raw percentages achieved. The reason the "curve" is mentioned is that graphs of the number of students getting a given score is normally distributed symmetrically on either side of the average or mean, yielding the proverbial "bell-shaped curve."

This grading is accomplished by running a statistical analysis on the data to determine the standard deviation (SD) of the mean, which is a measure of how closely clustered (small SD) or widely ranging (large SD) the data are. See the Resources for a grade percentage calculator that assigns letter grade ranges based on raw data using this statistical principle.

## What Is a Class Interval?

Your instructor may assign grades based instead on fixed class intervals, with or without scaling the raw scores of a given test first. For example, in a class with 25 students and scores ranging from 55/100 to 98/100 on an exam, the instructor may choose to use six intervals of 10 points "wide" each and then assign grades based on this alone.

For example, if the number of students in each ascending 10-point, whole-number interval from 50 to 59, 60 to 69, etc. up to 90-99 is 2, 6, 11. 4 and 3, then the teacher might choose to assign F to the 2 in lowest range, D to the next 6 and so on, since the raw scores in this instance are suggestive of a normal distribution with a mean in the mid-70s.

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Resources

About the Author

Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Formerly with ScienceBlogs.com and the editor of "Run Strong," he has written for Runner's World, Men's Fitness, Competitor, and a variety of other publications. More about Kevin and links to his professional work can be found at www.kemibe.com.