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## Main Question or Discussion Point

Hi,

How can I rigorously prove that the quantity

[tex]S = \sum_{i=1}^{n}|X_{i} - a|[/tex]

(where [itex]X_{1},\ldots,X_{n}[/itex] is a random sample and a is some real number) is minimum when a is the median of the [itex]X_{i}[/itex]'s?

Thanks.

How can I rigorously prove that the quantity

[tex]S = \sum_{i=1}^{n}|X_{i} - a|[/tex]

(where [itex]X_{1},\ldots,X_{n}[/itex] is a random sample and a is some real number) is minimum when a is the median of the [itex]X_{i}[/itex]'s?

Thanks.

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