Spoiler: TLDR (click to show/hide) Doesn't look like an approximated integral (using trapezoid rule) doesn't yield me any difference in results than from an initial minmax transform.



DT uses a slight variant from a minmax transform, and puts the mean at 50% by doing a minmax transform around the mean for 0 to 50% and 50% to 100%.



Then a similar transform is done again to recenter on the median.



Resulting in [more or less] a nicely distributed set of values.



I was hoping that by approximating "integral's" I would be able to find a better "curve". It appears that the concept of using the trapezoid rule to approximate integrals produces %'s that are exactly the same as a minmax transform. I was struggling with why my integral's 50% point did not represent the mean, but rather the midrange: (max - min) /2.



However, I know why [now], because that's what a minmax transform is, and an approximated integral based on the trapezoid rule produces the same #'s.

but has a perfect even average of 0.

Since we end up doing a final transform on the outputted data, and it seems that the #'s on the backend never really add up to 0 or 100% (hence why the new drawing method is used). We can still work with these #'s, albeit in a slightly better mean adjusted approach.

So turns out all my work on s transform and integral's has lead me full circle.So I just wasted a whole lot of time going full circle.However, what I would like to focus on. Is how to deal with datasets whose overall average doesn't = 50%.I fear that combining them together will slightly skew the overall weighted average of values.The data is already normalized <>50% on a 50/50 split. (except for extremely skewed datasets that contain a lot of null values: skills/preferences, but there mean is ~.5)So I was thinking, since the drawing method has been updated to draw from min/max of weighted average outputs, and 50% = median.Why not do something similar, but instead of adding up the %'s as if they are 0 to 100%.Subtract .5 from each %and get a set of values that are~-50% to ~+50%you know what, I don't think that would do anything. One would have to subtract from the datasets mean, and that would have a different issue