It relies on a quantity being defined which happens to be equal to the mean, but that value can be arrived at without having defined the mean a priori. The mini

It relies on a quantity being defined which happens to be equal to the mean, but that value can be arrived at without having defined the mean a priori. The minimizers of (7,11) with respect to the 1-norm defined in the post include all values between 7 and 11. You need not have defined the mean to state this optimization problem. I suppose which median you pick can be considered a heuristic. I think "removing outliers" is also snugly in the camp of practical heuristics. A mathematical definition might not want to automatically eliminate outliers when "outlier" is also subject to a choice of definition.