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[Solution] Suppose you have N data points: x_1, x_2, ..., x_N . Give formulas for the sample average and sample standard deviation of these data. Also, let

Question: Suppose you have \(N\) data points: \(x_{1}, x_{2}, \ldots, x_{N} .\) Give formulas for the sample average and sample standard deviation of these data. Also, let \(\bar{x}\) represent the sample average and prove that

\[\frac{1}{N} \sum_{i=1}^{N}\left(x_{i}-\bar{x}\right)^{2}=\left(\frac{1}{N} \sum_{i=1}^{N} x_{i}{ }^{2}\right)-\bar{x}^{2}\]

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