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Let $Z_{1}, \ldots, Z_{k}$ be distinct points in $\mathbb{R}^{n}$. Find a unique point $X_{0}$ in $\mathbb{R}^{n}$ at which the function
$Q(X)=\left\|X-Z_{1}\right\|^{2}+\cdots+\left\|X-Z_{k}\right\|^{2}$
achieves its minimum value by "completing the square" to obtain the identity
$Q(X)=k\left\|X-\frac{1}{k} \sum_{n=1}^{k} Z_{n}\right\|^{2}+\sum_{j=1}^{k}\left\|\left.Z_{j}\right|^{2}-\frac{1}{k}\right\| \sum_{j=1}^{k} Z_{j} \|^{2}$
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