I would like to convert these numbers to a ranking so that the lowest one is assigned the number 1 and the highest 7368. Unfortunately I cannot just sort them and I need an equation that would take a number in the first group and give the number in the second group.

I have tried converting the initial raw scores into z scores and then converting them to a new scale with a mean of 3684 and SD of 2126.81 (which would be the mean and SD of a set of numbers going from 1 to 7368) but the results are nothing close to the linear relationship I want. The numbers start around 3200 and go up to 44,000.

Does anyone know how I can do something like this, even if it is not perfect? More generally, how I convert other distributions into a ranking using mathematical formulas? I am willing to read and study what I need to if someone can point me in the right direction.

Thanks!