Pandas : mean/median precedent rows having the same ID

I have the following ordered Dataframe

Index  ID  Amount
1      A   10
2      A   15
3      A   17
4      A   12
5      A   10
6      B   20
7      B   15
...

What I want is to add a column indicating the median of all the precedent Amounts for the same IDs in the dataframe

The result must be the following

Index  ID  Amount  (PastElements)   MedianOfPastElements
1      A   10      ()
2      A   15      (10)             10
3      A   17      (10;15)          12.5
4      A   12      (10;15;17)       15
5      A   10      (10;12;15;17)    13.5  
6      B   20      ()              
7      B   15      (20)             20
...

I don’t have to keep the PastElements column in my result, I just added it to clarify my problem.
Does someone see any way to do so ? Thanks in advance

>Solution :

Use groupby.transform with shift and expanding.median:

df['MedianOfPastElements'] = (df.groupby('ID')['Amount']
                                .transform(lambda s: s.shift().expanding().median())
                             )

Output:

   Index ID  Amount  MedianOfPastElements
0      1  A      10                   NaN
1      2  A      15                  10.0
2      3  A      17                  12.5
3      4  A      12                  15.0
4      5  A      10                  13.5
5      6  B      20                   NaN
6      7  B      15                  20.0