It's a fixed memory size but gets released when you move into the recursive part. Increasing the fixed part will give you a better starting estimate.

See here for quantiles: https://stackoverflow.com/questions/1058813/on-line-iterator...

The P^2 algorithm used in creme is interesting. For the median it would give a 2 sided median deviation. Maybe this could be changed slightly to be symmetric and give Median and MAD. I'll look into.