Using your code, you get the mean for all the solutionType's that you have.
You can use .loc
to get the attribute value for the fixed solutionType:
val = df.groupby('solutionType', as_index=False)['attribute'].mean().set_index('solutionType').loc['fixed','attribute']
df['attribue'] = val
Which prints:
solutionType attribute attribue
0 fixed 1 355.333
1 float 2 355.333
2 other 42 355.333
3 fixed 55 355.333
4 fixed 1010 355.333
5 float 2021 355.333
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