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the branch of mathematics that deals with the mathematical aspects of problems from science and engineering: applied analysis, numerical mathematics, applied statistics etc. (For applications of mathematics in general, cf. also the [applications] tag.)

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name for $\underset{x}{\operatorname{argmin}} \displaystyle\sum\limits_{i=1}^n |x_i - x|$

The value of $x$ that satisfies this is the median of $x_i$. It minimizes $L_1$ loss. Note that the mean of $x_i$ is the value of $x$ minimizing $\sum(x_i - x)^2$, the $L_2$ loss.
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