Some functions implemented through reduction operation arise exceptions

[YarShev]

Describe the problem

Some functions (such as median, skew, std, var, sum, prod) arise an exception when level specified.

Source code / logs

import modin.pandas as pd
import pandas
arrays = [['1', '1', '1', '2', '2', '2', '3', '3', '3'], ['1', '2', '3', '4', '5', '6', '7', '8', '9']]
ps = pandas.Series([3,3,3,3,3,3,3,3,3], index=arrays)
ms = pd.Series([3,3,3,3,3,3,3,3,3], index=arrays)
ps.std(level=0)
1    0.0
2    0.0
3    0.0
dtype: float64
ms.std(level=0) # the same exception is arisen for median, skew, var, sum, prod
ValueError: Length mismatch: Expected axis has 3 elements, new values have 1 elements
arrays = [['1', '1', '2', '2'], ['1', '2', '3', '4']]
pdf = pandas.DataFrame([[1,2,3,4], [1,2,3,4], [1,2,3,4], [1,2,3,4]], index=arrays)
mdf = pd.DataFrame([[1,2,3,4], [1,2,3,4], [1,2,3,4], [1,2,3,4]], index=arrays)
pdf.std(level=0)
     0    1    2    3
1  0.0  0.0  0.0  0.0
2  0.0  0.0  0.0  0.0
mdf.std(level=0) # the same exception is arisen for median, skew, var, sum, prod
ValueError: Length mismatch: Expected axis has 2 elements, new values have 1 elements

[mvashishtha]

@YarShev

Should these functions be working? I noticed today that e.g. in this test, Modin defaults to pandas for median, skew, std, var, and sem. Taking the "median" version of that test:

import modin.pandas as pd
arrays = [["1", "1", "2", "2"], ["1", "2", "3", "4"]]
data = [[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]]
modin_df = pd.DataFrame(data, index=arrays)
modin_df.median(level=0)

UserWarning: `DataFrame.median` defaulting to pandas implementation.
To request implementation, send an email to [email protected].
FutureWarning: Using the level keyword in DataFrame and Series aggregations is deprecated and will be removed in a future version. Use groupby instead. df.median(level=1) should use df.groupby(level=1).median().
UserWarning: Distributing <class 'pandas.core.frame.DataFrame'> object. This may take some time.

[YarShev]

@mvashishtha , yes, they are working but in case level is specified we started defaulting to pandas for them in #2655. We should probably add a note in docs that we use default pandas implementation for the operations when level is specified. Would you get this done?

[mvashishtha]

@YarShev Yes, I created #3698 for that. Please take a look.