Find a row closest to the mean of a DataFrame column

Question

I am working with pandas using a small dataset and I am stuck somewhere.

Here is the data after merging:

Using this data, the code below give the minimum area of each region and complete with the corresponding country name on the same line in the Dataframe obtained.

Area_min=Africa.groupby('Region').Area.agg([min])
Area_min['Country']=(Africa.loc[Africa.groupby('Region').Area.idxmin(), 'Names']).values
Area_min

And this one give the maximum population of each region and complete with the corresponding country name on the same line in Dataframe obtained.

Pop_max=Africa.groupby('Region').Population.agg([max])
Pop_max['Country']=(Africa.loc[Africa.groupby('Region').Population.idxmax(), 'Names']).values
Pop_max

Now I am trying to get the average population of each region and complete with the name of country having the population closest to the average of the corresponding group, on the same line in the Dataframe obtained.

The code below give the average population of each region but I am stuck on corresponding with the country name.

Pop_average=Africa.groupby('Region').Population.agg(['mean'])

I am thinking about .map() and .apply() function but I have tried without success. Any hint will be helpful.