Pandas BUG: in describe() result, mean is to NaN or Inf, when change float64 to float32 or float16

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Reproducible Example

df = pd.DataFrame({"a": range(1000)})
df.a = 1.2345678 * df.a
df["b"] = df.a.astype("float16")
df.describe()

    a   b
count   1000.000000 1000.0000
mean    616.666616  inf
std 356.567176  inf
min 0.000000    0.0000
25% 308.333308  308.4375
50% 616.666616  616.7500
75% 924.999924  924.8750
max 1233.333232 1233.0000

Issue Description

when change the column to low float format, the mean or std will calc wrong. In this case mean ,616 to inf. and in some case will result NaN. such as (but there is no NaN value in the column): count 674522.000000 mean NaN std 0.000000 min -17.359375 25% -1.610352 50% -0.280029 75% 1.049805 max 19.984375

Expected Behavior

same as normal mean or std

Installed Versions

/home/terry/.local/lib/python3.8/site-packages/_distutils_hack/init.py:30: UserWarning: Setuptools is replacing distutils. warnings.warn("Setuptools is replacing distutils.") Output exceeds the size limit. Open the full output data in a text editor

INSTALLED VERSIONS

commit : 87cfe4e38bafe7300a6003a1d18bd80f3f77c763 python : 3.8.10.final.0 python-bits : 64 OS : Linux OS-release : 5.15.0-46-generic Version : #49~20.04.1-Ubuntu SMP Thu Aug 4 19:15:44 UTC 2022 machine : x86_64 processor : x86_64 byteorder : little LC_ALL : None LANG : en_US.UTF-8 LOCALE : en_US.UTF-8

pandas : 1.5.0 numpy : 1.22.4 pytz : 2022.1 dateutil : 2.8.2 setuptools : 62.1.0 pip : 22.2.2 Cython : 0.29.30 pytest : 7.1.2 hypothesis : None ... xlrd : 2.0.1 xlwt : None zstandard : None tzdata : 2022.1

Comment From: rhshadrach

Thanks for the report! NumPy converts float16 to float32 for the sum when computing the mean, and I think it makes sense for pandas to do the same. I also found https://github.com/pandas-dev/pandas/pull/10172#discussion_r30620986 where there is the comment "float32 should stay float32" for the sum. I'm not sure why the sum shouldn't be computed with float64, but at least float32 would help in many cases.

As a side note, one can also implement mean in an overflow-safe way (so the tracking sum never exceeds the largest input value), but I'm guessing this would mean a performance hit.

Comment From: ruifeng96150

Yes, I totally agree with you. In my case, I use Lightgbm to train a model. If I use lower float format data, the model is worse, while the data value is same. The reason for not using float64 is to save memory.