There are different techniques for normalizing scores, and the topic of how to do so properly belongs in a class on statistics. The best-known normalization formula, and the one I use for exams and other situations where the number of scores above and below the average are likely to be equal, is the "z-score":

z = (x - avg)/sd

where x is the student's score, avg the class average, and sd is the class standard deviation (a measure of how widely spread the class scores have been). More information on this score and why it is useful can be found in any statistics book.

For programming assignments, where experience has shown that the scores tend to be skewed, I have found that the formula

z = 1 - (max - x)/sd

where max is the largest score achieved by the class, provides a more appropriate normalization.