To select the rows of your dataframe you can use iloc, you can then select the columns you want using square brackets.

For example:

 df = pd.DataFrame(data=[[1,2,3]]*5, index=range(3, 8), columns = ['a','b','c'])

gives the following dataframe:

   a  b  c
3  1  2  3
4  1  2  3
5  1  2  3
6  1  2  3
7  1  2  3

to select only the 3d and fifth row you can do:

df.iloc[[2,4]]

which returns:

   a  b  c
5  1  2  3
7  1  2  3

if you then want to select only columns b and c you use the following command:

df[['b', 'c']].iloc[[2,4]]

which yields:

   b  c
5  2  3
7  2  3

To then get the mean of this subset of your dataframe you can use the df.mean function. If you want the means of the columns you can specify axis=0, if you want the means of the rows you can specify axis=1

thus:

df[['b', 'c']].iloc[[2,4]].mean(axis=0)

returns:

b    2
c    3

As we should expect from the input dataframe.

For your code you can then do:

 df[column_list].iloc[row_index_list].mean(axis=0)

EDIT after comment: New question in comment: I have to store these means in another df/matrix. I have L1, L2, L3, L4...LX lists which tells me the index whose mean I need for columns C[1, 2, 3]. For ex: L1 = [0, 2, 3] , means I need mean of rows 0,2,3 and store it in 1st row of a new df/matrix. Then L2 = [1,4] for which again I will calculate mean and store it in 2nd row of the new df/matrix. Similarly till LX, I want the new df to have X rows and len(C) columns. Columns for L1..LX will remain same. Could you help me with this?

Answer:

If i understand correctly, the following code should do the trick (Same df as above, as columns I took 'a' and 'b':

first you loop over all the lists of rows, collection all the means as pd.series, then you concatenate the resulting list of series over axis=1, followed by taking the transpose to get it in the right format.

dfs = list()
for l in L:
    dfs.append(df[['a', 'b']].iloc[l].mean(axis=0))

mean_matrix = pd.concat(dfs, axis=1).T

Iterating through the rows doesn't take advantage of Pandas' strengths. If you want to do something with a column based on values of another column, you can use .loc[]:

dataFrame.loc[dataFrame['Dates'] == 'Oct-16', 'Score 1']

The first part of .loc[] selects the rows you want, using your specified criteria (dataFrame['Dates'] == 'Oct-16'). The second part specifies the column you want (Score 1). Then if you want to get the mean, you can just put .mean() on the end:

dataFrame.loc[dataFrame['Dates'] == 'Oct-16', 'Score 1'].mean()

You can specify a new column. You also need to compute the mean along the rows, so use axis=1.

df['mean'] = df.mean(axis=1)
>>> df
       Y1961      Y1962      Y1963      Y1964      Y1965 Region       mean
0  82.567307  83.104757  83.183700  83.030338  82.831958     US  82.943612
1   2.699372   2.610110   2.587919   2.696451   2.846247     US   2.688020
2  14.131355  13.690028  13.599516  13.649176  13.649046     US  13.743824
3   0.048589   0.046982   0.046583   0.046225   0.051750     US   0.048026
4   0.553377   0.548123   0.582282   0.577811   0.620999     US   0.576518

You can try via filter() select columns Named like 'Week' then find mean and store that into a variable(for good performance) and finally fill NaN's by using fillna():

cols=df.filter(regex='Week').columns
m=df[cols].mean(axis=1).round()
df=df.fillna({x:m for x in cols})

output:

    ID  Feature Paid    Week1       Week2   Week3   Week4
0   1       1       1       12      12.0    12.0    12.0
1   2       0       1       34      23.0    28.0    28.0
2   3       1       0       24      13.0    14.0    17.0