(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let [itex]f(a)=\frac{1}{n-1}\sum_{i=1}^{n}(x_{i}-a)^{2} [/itex]

Find the value of a that minimizes f(a) by replacing [itex](x_{i}-a)[/itex] by [itex]((x_{i}-\bar{x})+(\bar{x}-a))[/itex].

2. The attempt at a solution

[itex]f(a)=\frac{1}{n-1}\sum_{i=1}^{n}((x_{i}-\bar{x})+(\bar{x}-a))^{2}=\frac{1}{n-1}\sum_{i=1}^{n}((x_{i}-\bar{x})^{2}+(\bar{x}-a){}^{2}+2(x_{i}-\bar{x})(\bar{x}-a))=\frac{1}{n-1}[\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}+\sum(\bar{x}-a){}^{2}+\sum2(x_{i}-\bar{x})(\bar{x}-a)][/itex]

I'm a little stuck here. Any ideas?

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# Minimizing a function

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