The result of the sklearn standardcaler result is different from the result of the manual

Question

I used the measure of the sklearn calculator (average removal and scaling of variance) to scale the data frame and compared it with the data framework, where I manually subtracted the average value and divided by the standard deviation. The comparison shows consistent small differences. Can anyone explain why? (I used this dataset: http://archive.ics.uci.edu/ml/datasets/Wine

import pandas as pd
from sklearn.preprocessing import StandardScaler

df = pd.read_csv("~/DataSets/WineDataSetItaly/wine.data.txt", names=["Class", "Alcohol", "Malic acid", "Ash", "Alcalinity of ash", "Magnesium", "Total phenols", "Flavanoids", "Nonflavanoid phenols", "Proanthocyanins", "Color intensity", "Hue", "OD280/OD315 of diluted wines", "Proline"])

cols = list(df.columns)[1:]    # I didn't want to scale the "Class" column
std_scal = StandardScaler()
standardized = std_scal.fit_transform(df[cols])
df_standardized_fit = pd.DataFrame(standardized, index=df.index, columns=df.columns[1:])

df_standardized_manual = (df - df.mean()) / df.std()
df_standardized_manual.drop("Class", axis=1, inplace=True)

df_differences = df_standardized_fit - df_standardized_manual
df_differences.iloc[:,:5]


    Alcohol    Malic acid   Ash         Alcalinity  Magnesium
0   0.004272    -0.001582   0.000653    -0.003290   0.005384
1   0.000693    -0.001405   -0.002329   -0.007007   0.000051
2   0.000554    0.000060    0.003120    -0.000756   0.000249
3   0.004758    -0.000976   0.001373    -0.002276   0.002619
4   0.000832    0.000640    0.005177    0.001271    0.003606
5   0.004168    -0.001455   0.000858    -0.003628   0.002421

Answer 1

scikit-learn np.std, ( ) pandas ( - 1) (. Wikipedia), (ddof). numpy scikit-learn ddof=0, pandas ddof=1 (docs).

DataFrame.std(axis = None, skipna = None, level = None, ddof = 1, numeric_only = None, ** kwargs)

.

N-1 . ddof

pandas :

df_standardized_manual = (df - df.mean()) / df.std(ddof=0)

:

        Alcohol    Malic acid           Ash  Alcalinity of ash     Magnesium
0 -8.215650e-15 -5.551115e-16  3.191891e-15       0.000000e+00  2.220446e-16
1 -8.715251e-15 -4.996004e-16  3.441691e-15       0.000000e+00  0.000000e+00
2 -8.715251e-15 -3.955170e-16  2.886580e-15      -5.551115e-17  1.387779e-17
3 -8.437695e-15 -4.440892e-16  3.164136e-15      -1.110223e-16  1.110223e-16
4 -8.659740e-15 -3.330669e-16  2.886580e-15       5.551115e-17  2.220446e-16