BUG: groupby.std() casts to float64

[debnathshoham]

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

• (optional) I have confirmed this bug exists on the master branch of pandas.

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This came out of #43213 (comment)

Code Sample, a copy-pastable example

In [1]: import pandas as pd

In [2]: pd.__version__
Out[2]: '1.4.0.dev0+532.g9bf09adcda'

In [3]: df=pd.DataFrame([[1,2]]*3, columns=["a","b"], dtype="Int64")

In [4]: df.groupby("a").std().dtypes
Out[4]: 
b    float64
dtype: object

In [5]: df=pd.DataFrame([[1,2]]*3, columns=["a","b"], dtype="Float64")

In [6]: df.groupby("a").std().dtypes
Out[6]: 
b    float64
dtype: object

Problem description

With Float64 as input, should return Float64 and not float64

Output of pd.show_versions()

INSTALLED VERSIONS

commit : 9bf09ad
python : 3.8.10.final.0
python-bits : 64
OS : Darwin
OS-release : 20.6.0
Version : Darwin Kernel Version 20.6.0: Wed Jun 23 00:26:31 PDT 2021; root:xnu-7195.141.2~5/RELEASE_X86_64
machine : x86_64
processor : i386
byteorder : little
LC_ALL : None
LANG : None
LOCALE : None.UTF-8

pandas : 1.4.0.dev0+532.g9bf09adcda
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

[phofl]

See #37494

[debnathshoham]

I don't think this behaviour is specific to nullable dtypes. I think it is always cast to float64

In [17]: df=pd.DataFrame([[1,2]]*3, columns=["a","b"], dtype="float32")

In [18]: df.groupby("a").std().dtypes
Out[18]: 
b    float64
dtype: object

[phofl]

Does this happen also with other functions except var? I think this is on purpose for std and var

[debnathshoham]

var is working as expected..

In [4]: df=pd.DataFrame([[1,2]]*3, columns=["a","b"], dtype="Int64")

In [5]: df.groupby("a").var().dtypes
Out[5]: 
b    Float64
dtype: object

In [6]: df=pd.DataFrame([[1,2]]*3, columns=["a","b"], dtype="float32")

In [7]: df.groupby("a").var().dtypes
Out[7]: 
b    float32
dtype: object