# Math Help - Average Absolute Deviation (find the minimum)

1. ## Average Absolute Deviation (find the minimum)

$S_n(x)=\frac 1n\sum_{i=1}^n|x_i-x| \Longleftrightarrow f(x)=nS_n(x)=\sum_{i=1}^n|x_i-x|$
Prove that it has the minimum when $x$ is the median.

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