ghostiee-11 commented on issue #28985:
URL: https://github.com/apache/arrow/issues/28985#issuecomment-5295288970

   could this be reopened? it was closed by the stale bot rather than by a 
decision, and the last human comment was a deferral rather than a no.
   
   concrete impact: `hash_approximate_median` on a two element group returns 
the lower value instead of the mean.
   
   ```python
   import pyarrow as pa
   
   t = pa.table({"g": ["a", "a"], "v": [10.0, 20.0]})
   print(t.group_by("g").aggregate([("v", "approximate_median")]).to_pydict())
   # {'g': ['a'], 'v_approximate_median': [10.0]}   exact median is 15.0
   ```
   
   `hash_tdigest` returns 10.0 too.
   
   narwhals maps its `median()` onto these, so a grouped median is silently 
wrong there for small groups: narwhals-dev/narwhals#3853. the scalar path can 
be fixed with `quantile(q=0.5)` since that one is exact, but there is no 
`hash_quantile` to switch to for grouped.
   
   one data point on cost, scalar only: `pc.quantile(q=0.5, 
interpolation="linear")` measured 3 to 4x faster than `pc.approximate_median` 
from n=2 up to n=10M here. that says nothing about what a grouped 
implementation would cost, and the in memory accumulation concern from 2021 
still stands.
   
   pyarrow 23.0.1
   


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