Question
Given $n$ numbers $x_{1}, \ldots, x_{n},$ find the value of $x$ minimizing the sum of the squares:$$\left(x-x_{1}\right)^{2}+\left(x-x_{2}\right)^{2}+\cdots+\left(x-x_{n}\right)^{2}$$ First solve for $n=2,3$ and then try it for arbitrary $n$
Step 1
Step 1: We want to minimize the function $f(x) = \left(x-x_{1}\right)^{2}+\left(x-x_{2}\right)^{2}+\cdots+\left(x-x_{n}\right)^{2}$. Show more…
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