This should be straightforward, but the closest thing I\'ve found is this post: pandas: Filling missing values within a group, and I still can\'t solve my problem....
The featured high ranked answer only works for a pandas Dataframe with only two columns. If you have a more columns case use instead:
df['Crude_Birth_rate'] = df.groupby("continent").Crude_Birth_rate.transform( lambda x: x.fillna(x.mean()))