Medians, Quartiles, Quintiles, Deciles, Percentiles. Moreover these measures are reported grouped by any number of columns (and I have never seen this capability anywhere else). In this context, the use of a cursor is mandatory!

Median as a measure of central tendency is okay when calculated in SQL Server. But as the median alone is not terribly useful, I generally prefer the use of a specialized software called Prophet or simply download the data to Excel for any statistical stuff I do. Because, as you have implied the code will become messy and might require a cursor (actually I never have thought about calculating the things you've mentioned in SQL Server)

As for gdefi:

I agree, each one to his taste.