Get a value to a lambda function from another DataFrame

Question

I have the following DataFrame, every month numbers are not duplicates, it's from different years.

print(df)

    Month  Deviation
0   1      10   
1   2      20   
2   3      30 
3   1      3
4   2      6
5   3      9
6   1      20
7   2      40
8   3      50

I need to get a mean value of 'Deviation' of a particular Month numbers from different years. I have only 3 months types (1,2,3), so only 3 mean values should be in df. Expecting the following:

    Month  Deviation  Avrg
0   1      10         7.6
1   2      20         22
2   3      30         29.6
3   1      3          7.6
4   2      6          22
5   3      9          29.6
6   1      20         7.6
7   2      40         22
8   3      50         29.6

I'm trying to group by months and then get this mean value to a lambda function:

gr = df.groupby('Month')['Deviation'].mean().reset_index()

df.assign(Avrg=lambda x: gr.loc[df.loc[x, 'Month'],'Deviation'])

this is not working