I recently learned that if you minimize these functions with respect to "a", you get the mean and the median respectively:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\sum (y_i - a)^2[/tex]

[tex]\sum |y_i - a|[/tex]

What would you get if you minimized an expression like [tex]\sum |y_i - a|^n [/tex] for various n's? Do the resulting expressions have any use, or are they just a slightly different, more complicated mean?

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# Generalization of mean, median

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