Not exactly what was asked in the question, but if you wanted to avoid NaN values, calculate the population standard deviation, specified with std(ddof=0):

>>> print(df.groupby('Category').std(ddof=0))
                 A         B         C         D         E         F
Category                                                            
A         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
B         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
C         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
D         0.248192  0.195198  0.275101  0.194955  0.190215  0.052423
E         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
F         0.288417  0.127854  0.065012  0.110096  0.354885  0.191643
G         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000
H         0.000000  0.000000  0.000000  0.000000  0.000000  0.000000

Note the different defaults for ddof (Delta Degrees of Freedom):

• Pandas: DataFrame.std has default ddof=1 for sample standard deviation (divisor: N − 1)
• NumPy: numpy.std has default ddof=0 for population standard deviation (divisor: N)

pd.DataFrame.std assumes 1 degree of freedom by default, also known as sample standard deviation. This results in NaN results for groups with one number.

numpy.std, by contrast, assumes 0 degree of freedom by default, also known as population standard deviation. This gives 0 for groups with one number.

To understand the difference between sample and population, see Bessel's correction.

Therefore, you can specify numpy.std for your calculation. Note, however, that the output will be different as the calculation is different. Here's a minimal example.

import pandas as pd, numpy as np

df = pd.DataFrame(np.random.randint(0, 9, (5, 2)))

def std(x): return np.std(x)

res = df.groupby(0)[1].agg(['size', 'sum', 'mean', std])

print(res)

   size  sum  mean       std
0                           
0     2   13   6.5       0.5
4     1    3   3.0       0.0
5     1    3   3.0       0.0
6     1    3   3.0       0.0

Alternatively, if you require 1 degree of freedom, you can use fillna to replace NaN values with 0:

res = df.groupby(0)[1].agg(['size', 'sum', 'mean', 'std']).fillna(0)

I think you need convert column to float64/float32, because no hardware support for float16 on a typical processor:

df[col].astype('float64').mean()
df[col].astype('float32').mean()