You can simply:

df['avg'] = df.mean(axis=1)

       Monday  Tuesday  Wednesday        avg
Mike       42      NaN         12  27.000000
Jenna     NaN      NaN         15  15.000000
Jon        21        4          1   8.666667

because .mean() ignores missing values by default: see docs.

To select a subset, you can:

df['avg'] = df[['Monday', 'Tuesday']].mean(axis=1)

       Monday  Tuesday  Wednesday   avg
Mike       42      NaN         12  42.0
Jenna     NaN      NaN         15   NaN
Jon        21        4          1  12.5

Given this dataframe:

df = pd.DataFrame({
    "Gender": ["Male", "Female", "Female", "Male"],
    "Age": [28, 40, 23, 35],
    "Salary": [45000, 70000, 40000, 55000],
    "Yr_exp": [6, 15, 1, 12]
})

df
   Age  Gender  Salary  Yr_exp
0   28    Male   45000       6
1   40  Female   70000      15
2   23  Female   40000       1
3   35    Male   55000      12

Group by gender and use the mean() function:

df.groupby("Gender").mean()
         Age   Salary  Yr_exp
Gender                       
Female  31.5  55000.0     8.0
Male    31.5  50000.0     9.0

Edit: you may need to change the way you're indexing after groupby(): df['Age', 'Salary'] gives a KeyError, but df[['Age', 'Salary']] returns the expected:

   Age  Salary
0   28   45000
1   40   70000
2   23   40000
3   35   55000

Try changing

df.groupby("Gender", as_index=True)['Age', 'Salary', 'Yr_exp'].mean() 

to

df.groupby("Gender", as_index=True)[['Age', 'Salary', 'Yr_exp']].mean()

What have you tried so far?

You need to pass a list of the columns to groupby, what you passed was interpreted as the axis param which is why it raised an error:

In [30]:
columns = ['col1','col2','avg']
df = pd.DataFrame(columns=columns)
df.loc[0] = [1,2,3]
df.loc[1] = [1,3,3]

print(df[['col1','col2','avg']].groupby(['col1','col2']).mean())
           avg
col1 col2     
1    2       3
     3       3

Assuming that you have the data stored in separate dataframes, you can use a combination of pandas.concat and pandas.DataFrame.groupby to achieve what you are looking for:

import pandas as pd
import numpy as np

df1 = pd.DataFrame({
    "x": [0,0,5,1,0],
    "y": [2,1,3,1,2],
    "z": [2,3,0,0,0]
})

df2 = pd.DataFrame({
    "x": [1,1,0,0,0],
    "y": [0,1,4,2,2],
    "z": [2,3,2,0,1]
})

df3 = pd.DataFrame({
    "y": [2,1,2,0,0],
    "z": [0,0,0,1,3]
})

df = (
    # combine dataframes into a single dataframe
    pd.concat([df1, df2, df3])
    # replace 0 values with nan to exclude them from mean calculation
    .replace(0, np.nan)
    .reset_index()
    # group by the row within the original dataframe
    .groupby("index")
    # calculate the mean
    .mean()
)