You could groupby on StationID and then take mean() on BiasTemp. To output Dataframe, use as_index=False
In [4]: df.groupby('StationID', as_index=False)['BiasTemp'].mean()
Out[4]:
StationID BiasTemp
0 BB 5.0
1 KEOPS 2.5
2 SS0279 15.0
Without as_index=False, it returns a Series instead
In [5]: df.groupby('StationID')['BiasTemp'].mean()
Out[5]:
StationID
BB 5.0
KEOPS 2.5
SS0279 15.0
Name: BiasTemp, dtype: float64
Read more about groupby in this pydata tutorial.