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BUG: Pearson correlation outside expected range -1 to 1 #59652

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@madrjor02-bh

Description

@madrjor02-bh

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Reproducible Example

values = [{'col1': 30.0, 'col2': 116.80000305175781},
 {'col1': None, 'col2': None},
 {'col1': None, 'col2': None},
 {'col1': None, 'col2': None},
 {'col1': None, 'col2': None},
 {'col1': None, 'col2': None},
 {'col1': None, 'col2': None},
 {'col1': None, 'col2': None},
 {'col1': None, 'col2': None},
 {'col1': None, 'col2': None},
 {'col1': None, 'col2': None},
 {'col1': None, 'col2': None},
 {'col1': None, 'col2': None},
 {'col1': 30.100000381469727, 'col2': 116.8000030517578},
 {'col1': None, 'col2': None},
 {'col1': None, 'col2': None}]

data = pd.DataFrame(values)
data.corr(method='pearson')

Issue Description

In the code snipped I'm trying to calculate the correlation between a pair of columns. However, when using pearson correlation method for this particular example, the outputted correlation is outside the -1 to 1 expected range.

Expected Behavior

The output of the pearson correlation method should be inside the -1 to 1 range.

Installed Versions

INSTALLED VERSIONS

commit : d9cdd2e
python : 3.9.19.final.0
python-bits : 64
OS : Linux
OS-release : 5.10.223-211.872.amzn2.x86_64
Version : #1 SMP Mon Jul 29 19:52:29 UTC 2024
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : C.UTF-8
LANG : C.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.2.2
numpy : 1.26.4
pytz : 2024.1
dateutil : 2.9.0.post0
setuptools : 69.5.1
pip : 24.0
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.4
IPython : 8.18.1
pandas_datareader : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : None
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : 3.9.2
numba : None
numexpr : None
odfpy : None
openpyxl : 3.1.5
pandas_gbq : None
pyarrow : 14.0.1
pyreadstat : None
python-calamine : None
pyxlsb : None
s3fs : None
scipy : 1.10.1
sqlalchemy : 2.0.31
tables : None
tabulate : None
xarray : None
xlrd : None
zstandard : None
tzdata : 2024.1
qtpy : None
pyqt5 : None

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