Haroun Melgani,

You might look into using Jenks natural breaks optimization. It's implemented in the classInt package in R, among a few others methods, if you're an R user.

Best,

Caleb

The first question is, If you have a range of scores, why would you want to convert this to two categories, and lose all that valuable information?

In general, there's no standard way to dichotomize numeric data.

A kind of neutral way is to use a median split. That is, the top 50% of observations go to one group and the bottom 50% go to another group. But only you can decide if this makes sense for your data. If may make sense to use other quantiles, for example, maybe up to 90th percentile is "low/normal" and 90th percentile and above is "high". Again, only you can decide what makes sense for your data.

I think the more "statistical" methods referenced by Caleb A. Aldridge may be very useful. (classIntervals function in the R classInt package). But note here, too, there are different options for how the data are approached, and the results can be quite different. E.g., note the differences in results in the following. Again, it depends on what you think makes sense for your data.

if(!require(classInt)){install.packages("classInt")}

library(classInt)

A = c(1,2,3,3,4,4,5,5,6,7,9,10,11,12,100,101)

classIntervals(A, n=3, style="quantile")

# vs.

classIntervals(A, n=3, style="fisher")

# vs.

classIntervals(A, n=3, style="pretty")

Thank you so much Salvatore S. Magiafico & Caleb Ashton Aldridge