Summary statistics by category using Python
IIUC:

In [80]: df.groupby("Category")['Score'].describe().reset_index()
Out[80]:
  Category  count       mean        std   min    25%    50%     75%    max
0     AAAA    3.0   1.666667   1.154701   1.0   1.00    1.0    2.00    3.0
1     BBBB    3.0  86.666667  79.839422   1.0  50.50  100.0  129.50  159.0
2     CCCC    2.0  -0.500000  13.435029 -10.0  -5.25   -0.5    4.25    9.0