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In the docs for function quantile_cont
:
https://duckdb.org/docs/sql/functions/aggregates.html#quantile_contx-pos
It mentions that it returns an interpolated quantile, but doesn't describe the method that is used to interpolate, nor does it allow controlling it.
See for example the docs for R's quantile
for examples of potential definitions for the interpolation:
https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/quantile