2 ms·

While I loved this post, could have also been helpful to include more info about Pythagorean Means (geometric mean and harmonic mean). Worth looking into depend

While I loved this post, could have also been helpful to include more info about Pythagorean Means (geometric mean and harmonic mean). Worth looking into depending on the type of variability seen in your data. EDIT: just saw this was mentioned in one of the comments...

no_identd 9y ago
I agree. I'd also like to add that I think that generalizations of the median for higher dimensions should get explicit coverage, as well as a few related (and often neglected) concepts. Since the Wikipedia articles on this constitute a hot mess of not linking to each other in a sane way, I'll provide a list of articles on this topic here: https://en.wikipedia.org/wiki/Fr%C3%A9chet_mean https://en.wikipedia.org/wiki/Fr%C3%A9chet_mean https://en.wikipedia.org/wiki/Mode_(statistics)#Use https://en.wikipedia.org/wiki/Mode_(statistics)#Use https://en.wikipedia.org/wiki/Central_tendency#Measures https://en.wikipedia.org/wiki/Central_tendency#Measures https://en.wikipedia.org/wiki/Nonparametric_skew#Relationships_between_the_mean,_median_and_mode https://en.wikipedia.org/wiki/Nonparametric_skew#Relationshi... https://en.wikipedia.org/wiki/Geometric_median https://en.wikipedia.org/wiki/Geometric_median https://en.wikipedia.org/wiki/Weber_problem#Definition_and_history_of_the_Fermat,_Weber,_and_attraction-repulsion_problems https://en.wikipedia.org/wiki/Weber_problem#Definition_and_h... https://en.wikipedia.org/wiki/Centerpoint_(geometry) https://en.wikipedia.org/wiki/Centerpoint_(geometry) https://en.wikipedia.org/wiki/Trimean https://en.wikipedia.org/wiki/Trimean https://en.wikipedia.org/wiki/K-medians_clustering https://en.wikipedia.org/wiki/K-medians_clustering https://en.wikipedia.org/wiki/Medoid https://en.wikipedia.org/wiki/Medoid https://en.wikipedia.org/wiki/Generalized_mean https://en.wikipedia.org/wiki/Generalized_mean https://en.wikipedia.org/wiki/Quasi-arithmetic_mean https://en.wikipedia.org/wiki/Quasi-arithmetic_mean https://en.wikipedia.org/wiki/Lehmer_mean#Special_cases https://en.wikipedia.org/wiki/Lehmer_mean#Special_cases https://en.wikipedia.org/wiki/Logarithmic_mean#Generalization https://en.wikipedia.org/wiki/Logarithmic_mean#Generalizatio... https://en.wikipedia.org/wiki/Stolarsky_mean#Special_cases https://en.wikipedia.org/wiki/Stolarsky_mean#Special_cases https://en.wikipedia.org/wiki/Facility_location https://en.wikipedia.org/wiki/Facility_location See Also: https://en.wikipedia.org/wiki/Problem_of_points https://en.wikipedia.org/wiki/Problem_of_points https://en.wikipedia.org/wiki/Chebyshev%27s_inequality https://en.wikipedia.org/wiki/Chebyshev%27s_inequality https://en.wikipedia.org/wiki/L-estimator https://en.wikipedia.org/wiki/L-estimator https://en.wikipedia.org/wiki/M-estimator https://en.wikipedia.org/wiki/M-estimator
- twic 9y ago
  I just came across the Stolarsky mean in a completely separate context. It seems like a really useful framework for unifying different kinds of central measures, similar to the idea in the original article here.

no_identd 9y ago

I agree. I'd also like to add that I think that generalizations of the median for higher dimensions should get explicit coverage, as well as a few related (and often neglected) concepts. Since the Wikipedia articles on this constitute a hot mess of not linking to each other in a sane way, I'll provide a list of articles on this topic here: https://en.wikipedia.org/wiki/Fr%C3%A9chet_mean https://en.wikipedia.org/wiki/Fr%C3%A9chet_mean https://en.wikipedia.org/wiki/Mode_(statistics)#Use https://en.wikipedia.org/wiki/Mode_(statistics)#Use https://en.wikipedia.org/wiki/Central_tendency#Measures https://en.wikipedia.org/wiki/Central_tendency#Measures https://en.wikipedia.org/wiki/Nonparametric_skew#Relationships_between_the_mean,_median_and_mode https://en.wikipedia.org/wiki/Nonparametric_skew#Relationshi... https://en.wikipedia.org/wiki/Geometric_median https://en.wikipedia.org/wiki/Geometric_median https://en.wikipedia.org/wiki/Weber_problem#Definition_and_history_of_the_Fermat,_Weber,_and_attraction-repulsion_problems https://en.wikipedia.org/wiki/Weber_problem#Definition_and_h... https://en.wikipedia.org/wiki/Centerpoint_(geometry) https://en.wikipedia.org/wiki/Centerpoint_(geometry) https://en.wikipedia.org/wiki/Trimean https://en.wikipedia.org/wiki/Trimean https://en.wikipedia.org/wiki/K-medians_clustering https://en.wikipedia.org/wiki/K-medians_clustering https://en.wikipedia.org/wiki/Medoid https://en.wikipedia.org/wiki/Medoid https://en.wikipedia.org/wiki/Generalized_mean https://en.wikipedia.org/wiki/Generalized_mean https://en.wikipedia.org/wiki/Quasi-arithmetic_mean https://en.wikipedia.org/wiki/Quasi-arithmetic_mean https://en.wikipedia.org/wiki/Lehmer_mean#Special_cases https://en.wikipedia.org/wiki/Lehmer_mean#Special_cases https://en.wikipedia.org/wiki/Logarithmic_mean#Generalization https://en.wikipedia.org/wiki/Logarithmic_mean#Generalizatio... https://en.wikipedia.org/wiki/Stolarsky_mean#Special_cases https://en.wikipedia.org/wiki/Stolarsky_mean#Special_cases https://en.wikipedia.org/wiki/Facility_location https://en.wikipedia.org/wiki/Facility_location See Also: https://en.wikipedia.org/wiki/Problem_of_points https://en.wikipedia.org/wiki/Problem_of_points https://en.wikipedia.org/wiki/Chebyshev%27s_inequality https://en.wikipedia.org/wiki/Chebyshev%27s_inequality https://en.wikipedia.org/wiki/L-estimator https://en.wikipedia.org/wiki/L-estimator https://en.wikipedia.org/wiki/M-estimator https://en.wikipedia.org/wiki/M-estimator

twic 9y ago
I just came across the Stolarsky mean in a completely separate context. It seems like a really useful framework for unifying different kinds of central measures, similar to the idea in the original article here.