Median and interquartile range stay scale-invariant where means fail

Evidence

Only the median and the interquartile range preserve their location relative to the data points when arranged on different scales; arithmetic and even geometric mean does not. — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 148

Categorization

• XREF: Directly extends the scale-transformation point of location 144 — together they establish that psychoacoustic data analysis should default to median-based statistics.