BUG: pivot_table calculates incorrect standard deviation when np.std passed to aggfunc

[dcsaba89]

• I have checked that this issue has not already been reported.

• 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.

---

`
import numpy as np
import pandas as pd

df = pd.DataFrame({'A': ['a', 'a'], 'X': [2.8597, 2.8503]})
pivot = pd.pivot_table(df, index='A', values='X', aggfunc=(np.mean, np.std))
my_std = np.std(df.X) # 0.0047000000000001485
pivot_std = pivot.loc['a', 'std'] # 0.006646803743153757
`

Problem description

pivot_table calculates incorrect standard deviation when np.std passed to aggfunc.

Expected Output

Numpy calculates the correct std in the given example.

[dsaxton]

pivot_table is using the unbiased estimate of variance where we divide by n - 1 instead of n:

import numpy as np

np.std([2.8597, 2.8503], ddof=1)                                                                                                                                                               
# 0.006646803743153757
np.std([2.8597, 2.8503], ddof=0)                                                                                                                                                              
# 0.0047000000000001485

[mroeschke]

Going to close as a usage question.

[dcsaba89]

This difference is unexcepted:

df = pd.DataFrame({'A': ['a', 'a'], 'X': [2.8597, 2.8503]})
pivot = pd.pivot_table(df, index='A', values='X', aggfunc=(np.std, lambda x: np.std(x)))
lambda_std = pivot.loc['a', '<lambda_0>'] # 0.0047000000000001485
std = pivot.loc['a', 'std'] # 0.006646803743153757

In the above example, standard deviation is calculated twice, in the first case, np.std function directly passed to aggfunc, on the other hand in the second case, a lambda function is passed to aggfunc which uses the same np.std function to calculate standard deviation. The results in these cases must equal.