Curving Tests

The average score on an AP Physics exam is usually pretty low.  In fact on recent exams, raw scores of only 65% have earned 5's (and college credit).  On the AP exam, the top 20% of all students taking the exam earn 5's, the next 20% earn 4's, then 3's, etc.  I cannot curve in-class exams this way, because this basically means that 20% of my students will be earning F's on all their tests (when they are working diligently and undeserving of such a score).  Also, since the AP classes aren't very large, I would have to decide if borderline students will receive a B or C, or worse, a D or F. 

 

Instead of breaking scores down into chunks of 20%, I have decided to curve so that the average score on the test is an 75% (a typical average in a college level course), and the highest score is a 100% using the statistical method described below. 

 

  1. Find the average score for the exam.

 x = Sx / N

  1. Find the standard deviation for scores on the exam. 
    This will basically determine the "spread" of the scores. 

s = {S[(x - x)2 / (N - 1)]}1/2

  1. Find the 'z-score' for each student. 
    This will determine how far each score is from average in terms of standard deviation.   

 z = (x - x) / s

  1. Choose a new average score. 
    This requires no calculation - I've chosen 75% - a common average for a college physics course. 

  1. Calculate a curved score using the equation to the right. 
    This equation will ensure that the top score will earn a 100%, and the average will be a 75%. 

xnew = 25·(z / zmax) + 75