BUG: Groupby median on timedelta column with NaT returns odd value

[goto-loop]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

import pandas as pd

df = pd.DataFrame({"label": ["foo", "foo"], "timedelta": [pd.NaT, pd.Timedelta("1d")]})

print(df.groupby("label")["timedelta"].median())

Issue Description

When calculating the median of a timedelta column in a grouped DataFrame, which contains a NaT value, Pandas returns a strange value:

import pandas as pd

df = pd.DataFrame({"label": ["foo", "foo"], "timedelta": [pd.NaT, pd.Timedelta("1d")]})

print(df.groupby("label")["timedelta"].median())

label
foo   -53376 days +12:06:21.572612096
Name: timedelta, dtype: timedelta64[ns]

It looks to me like the same issue as described in #10040, but with groupby.

Expected Behavior

If you calculate the median directly on the timedelta column, without the groupby, the output is as expected:

import pandas as pd

df = pd.DataFrame({"label": ["foo", "foo"], "timedelta": [pd.NaT, pd.Timedelta("1d")]})

print(df["timedelta"].median())

1 days 00:00:00

Installed Versions

INSTALLED VERSIONS

commit : bdc79c1
python : 3.12.2.final.0
python-bits : 64
OS : Linux
OS-release : 6.5.0-26-generic
Version : #26-Ubuntu SMP PREEMPT_DYNAMIC Tue Mar 5 21:19:28 UTC 2024
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.2.1
numpy : 1.26.4
pytz : 2023.3.post1
dateutil : 2.8.2
setuptools : 68.2.2
pip : 23.3.1
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.3
IPython : 8.20.0
pandas_datareader : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.12.2
bottleneck : 1.3.7
dataframe-api-compat : None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : 3.8.0
numba : None
numexpr : 2.8.7
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 15.0.1
pyreadstat : None
python-calamine : None
pyxlsb : None
s3fs : None
scipy : 1.12.0
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
zstandard : None
tzdata : 2023.3
qtpy : None
pyqt5 : None

[rhshadrach]

Thanks for the report, confirmed on main. Further investigations and PRs to fix are welcome!