BUG: Groupby.median returns absurd results for complex

[debnathshoham]

• 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 master branch of pandas.

Reproducible Example

import pandas as pd
import numpy as np

data = pd.Series(np.arange(20).reshape(10, 2).dot([1, 2j]))
print(data)
data.groupby(data.index % 2).median()

0    0.00+2.00j
1    2.00+6.00j
2     4.0+10.0j
3     6.0+14.0j
4     8.0+18.0j
5    10.0+22.0j
6    12.0+26.0j
7    14.0+30.0j
8    16.0+34.0j
9    18.0+38.0j
dtype: complex128
/Volumes/SD/pandas-debnathshoham/pandas/core/groupby/ops.py:192: ComplexWarning: Casting complex values to real discards the imaginary part
  values = ensure_float64(values)
Out[14]: 
0     8.0
1    10.0
dtype: float64

Issue Description

groupby.median() returns absurd result with complex numbers.
xref - #43756

Expected Behavior

Two possibilities:

1. raise with something like "median not defined for complex"
2. calculate the median separately for real and complex components (which happens on df.median)

In [11]: data
Out[11]: 
0    0.00+2.00j
1    2.00+6.00j
2     4.0+10.0j
3     6.0+14.0j
4     8.0+18.0j
5    10.0+22.0j
6    12.0+26.0j
7    14.0+30.0j
8    16.0+34.0j
9    18.0+38.0j
dtype: complex128

In [12]: data.median()
Out[12]: (9+20j)

Installed Versions

INSTALLED VERSIONS

commit : 619cbf8
python : 3.8.10.final.0
python-bits : 64
OS : Darwin
OS-release : 20.6.0
Version : Darwin Kernel Version 20.6.0: Mon Aug 30 06:12:21 PDT 2021; root:xnu-7195.141.6~3/RELEASE_X86_64
machine : x86_64
processor : i386
byteorder : little
LC_ALL : None
LANG : None
LOCALE : None.UTF-8

pandas : 1.4.0.dev0+771.g619cbf8b3e
numpy : 1.21.0
pytz : 2021.1
dateutil : 2.8.1
pip : 21.1.3
setuptools : 49.6.0.post20210108
Cython : 0.29.23
pytest : 6.2.4
hypothesis : 6.14.1
sphinx : 3.5.4
blosc : None
feather : None
xlsxwriter : 1.4.4
lxml.etree : 4.6.3
html5lib : 1.1
pymysql : None
psycopg2 : None
jinja2 : 3.0.1
IPython : 7.25.0
pandas_datareader: None
bs4 : 4.9.3
bottleneck : 1.3.2
fsspec : 2021.05.0
fastparquet : 0.6.3
gcsfs : 2021.05.0
matplotlib : 3.4.2
numexpr : 2.7.3
odfpy : None
openpyxl : 3.0.7
pandas_gbq : None
pyarrow : 4.0.1
pyxlsb : 1.0.8
s3fs : 0.4.2
scipy : 1.7.0
sqlalchemy : 1.4.20
tables : 3.6.1
tabulate : 0.8.9
xarray : 0.18.2
xlrd : 2.0.1
xlwt : 1.3.0
numba : 0.53.1

[attack68]

see mne-tools/mne-python#8879 (comment)

They mention np.median on complex is unsafe since it sorts by real part and returns result without consideration of complex.
The linked package use the marginal approach which I believe takes the median separately over real / imag.

I am inclined to use the same marginal approach, but document it, like the link so calculation is clear.

[debnathshoham]

Little confused about the use-case of calculating median for complex numbers.

Also, df.mean() calculates the median the same way as numpy (i.e. just the real part ignoring complex part).

In [25]: data
Out[25]: 
0    0.0+1.0j
1    1.0+4.0j
2    2.0+3.0j
3    3.0+2.0j
4    4.0+0.0j
dtype: complex128

In [26]: data.median()
Out[26]: (2+3j)

[jbrockmendel]

raise with something like "median not defined for complex"

I lean towards raising.