Matthew West

Curving Exam Scores

Linear curving function

We use a curving function that satisfies the following three properties:

  1. The curving function is linear.
  2. A perfect score of 100 will map to 100.
  3. The current median score M0 will increase to the new median value of M1.

These three requirements uniquely determine the curving function. It maps the old score S0 to the new score S1 by:

S1 = 100 - (100 - S0) × (100 - M1) / (100 - M0)

As an example, if the old median was M0 = 60 and the new median is M1 = 80, then the function is:

The advantages of the above curving function are:

The disadvantages of the above curving function are:

Piecewise-linear curving function

One choice for a curving function that deals with low-scoring students is to map a score of 0 to the new score Z1 (typically in the range 20 to 50), using a piecewise linear function of the form:

S1 = 100 - (100 - S0) × (100 - M1) / (100 - M0), if S0 > M0
S1 = Z1 + S0 × (M1 - Z1) / M0, if S0M0

With the median values from the previous example and Z1 = 20, this gives the function: