How can I curve a test grade knowing only the average and the highest score? I am trying to get a raw score for my test grade, but I don't know anything about the distribution of test grades; all the information I have is the average and the highest score (and of course my own grade). Can I curve my grade based on this information? The method of curving doesn't matter, and the raw score doesn't need to be my "actual" grade. Here is the context: I am moderating a competition between me and my friends, and we are split into different teams. The teams get points based on their test averages, but since we are all taking different courses with different difficulties I need a way to be able to fairly turn each grade into a raw score. Again, the curving method doesn't matter; all that matters is that it's constant for everyone. Does anyone know how to do this?

You don't have the right kind of data to construct a uniform measure of difficulty that would normalize the different results on one scale. One needs the relative difficulty of tasks to be calibrated by a large number of cases where the same individual does multiple tasks, with enough cases and enough overlaps to quantify all the tasks in relation to each other.

If you pretend that every class has a test-result distribution that is from a 2-or-fewer parameter family of distributions, such as Gaussians, then you can use the two given pieces of information (and possibly also the number of students in the class, if that is available) to place everyone's results as points on one model distribution, and take those as the normalizations.