How to apply jensen's/the smoothing concept

Question

Given real numbers x1, . . . , xn, what is the minimum value of |x − x1| + · · · + |x − xn|?

I think i have an idea on how to use jensen's with this but the absolute value is tripping me up, Would you just assume without loss of generality an ordering of xi's ... and? I really don't know. I know it's elementary but can someone please explain the function of the absolute signs, I believe it's to take whichever absolute value gives you the smallest value in this case but I am not certain. I'd also like to confirm that this question is not asking for a numerical minimum.

Answer 1

It really isn't clear what your question is (to me at least) but you should think about what this function looks like for x in \[x\_i,x\_{i+1}\] (assuming the values x\_i are ordered from small to large).