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Averaging across subjects' thresholds using Staircase

Hi all,
This is more of a psychometric question than a Psychopy one, so apologies if that’s inappropriate. I’m using Psychopy to collect people’s thresholds between two sound categories using a staircase analysis. I want to use the average of their answers in this experiment to determine a “generally ambiguous across subjects” sound to use for another experiment (in other words I want to find the average threshold across subjects and use that average sound in another experiment). Is it appropriate to simply take the mean (add up the average thresholds and divide by number of subjects)? Or is there some more nuanced method that should be used?
Thanks,
Mark