Hello Mahmood. Why do you want to create low and high groups? What will you do with the groups? What is your research question? I ask because I wonder if there is a way to address your question without coarsening your variable. Thank you for clarifying.

Yes, it depends od high and low groups. Moreover the main concern is statistical signficance.

Hello again Mahmood. Carving quantitative variables into categories prior to analysis is rarely necessary, and rarely a good idea. For more info, see:

• https://discourse.datamethods.org/t/categorizing-continuous-variables/3402

So again, I wonder if you can address your question via models that treat the variables as they are rather than carving them into categories--especially if the cut-points between categories are arbitrary.

I completely agree with Bruce Weaver , but if are set on dichotomizing, then you might justify using 40 rather than the midpoint in several ways, all based on the sample distribution. If 40 is at or near the sample median, then 40 is a plausible cut-off because it yields Hi and Lo groups of the same size. Or maybe you have solid theoretical reason for wanting to distinguish "definitely low" from "close to average or above average". If 40 is at or near the first quartile, you define "definitely low" as the lowest 25% of cases; if 40 is at or near the first quintile, then "definitely low" is the lowest 20%, etc. Or, maybe there's a sharp gap in the frequency distribution at around 40 -- for example, plenty of cases evenly spread at 40 or below, and more cases evenly spread at, say, 45 and above, but few or no cases between 41 and 44. That would be another way to justify using 40 as the cutoff point. Or you could combine these justifications -- the median is 38, but there's a gap at 40, so use a cutoff of 40.