Give n floating point numbers **a1 , a2 … an** . Find **X** such that it minimizes maximum absolute difference (d)

d = [ for ( 1 <= i <= n) max ( abs ( ai - **X** ) ) ]

how to find **X** such that d is minimum ?

I have tried using some **Order Statistics**

X is any real number

Source : Unknown : (

is it ((max(ai)+min(ai) )/2) ?

# Minimizing maximum deviation

Here’s my idea:

So, if you view the numbers on the number line, you should realise that the problem asks you to find X so that the maximum distance from any number is minimised. Now, for any choice of X, you can show that you actually only need to care about distances from two points: the largest and the smallest. So yeah, X=(max(ai)+min(ai))/2 (the post was edited while I was writing this).

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yeah I’m thinking about proof