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[Community Question] Calculus: Find a number that have minimum sum of distances between set of numbers

One of our user asked:

Lets say we have a set of numbers { 5, 7, 1, 2, 5, 100 }, I want to find a number x such that the sum of distances of every number from the set to x is minimal.

My first thought was that x is the average of the sum of all element of the set: (sum / n), but it's not true it fail the above example.

Any help or hint will be appriciated, thanks.


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