Intuitively, why is the median special in this case of minimizing the sum?
7740
The median minimizes the sum of absolute deviations (the $ {\ell}_{1} $ norm)
153949
Is there a "smallest" divergent sum?
10013
A problem that I'm not sure whether to use Weierstrass Approximation Theorem
20471
Evaluating a slow sum
34758
Cancellation Law for Direct Sums - What is wrong with this argument?
69392
How can I prove mathematically that the mean of a distribution is the measure that minimizes the variance?
98101
why this product is no more than the product of the two mean values?
144138
k-means vs k-median?
66913
Why does the maximum/minimum of linear programming occurs at a vertex?
129693
An interesting problem with "decomposing" natural numbers.
130996
Find the median of an array
158704
How to minimize $\sum_{i=1}^p (y_i-x_i)^2$ with constraints $\sum_{i=1}^p y_i - 1 =0$ and $\forall i=\overline{1,p}:-y_i \le 0$?
120182
For what (symmetric) distributions is sample mean a more efficient estimator than sample median?
78468
Understanding Dirichlet regularization in Sum
28596
Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces?
95084
What is the expected value of $\min\{|X|,|Y|\}/\max\{|X|,|Y|\}$ assuming $X$ and $Y$ are independent?
111075
Deriving of formula for finding the length of median