Which Generalized Mean Best Approximates the Median?

[Gerenuk]

Which of the generalized means (like http://en.wikipedia.org/wiki/Generalized_mean and more general) do you think is most suitable to approximate the median?

 

[mathman]

The mean itself. Basically, the concept is a generalization of moments for non-integer cases (specifically the nth root of the nth moment).

 

[Gerenuk]

You can invent many different generalizations like
http://en.wikipedia.org/wiki/Generalized_f-mean
http://en.wikipedia.org/wiki/Lehmer_mean
http://en.wikipedia.org/wiki/Logarithmic_mean
Now I wonder if any of these means does better than the arithmetic mean!?