Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Measures of statistical dispersion ▷ Sample standard deviation

Definition: Let $x = \left\lbrace x_1, \ldots, x_n \right\rbrace$ be a sample from a random variable $X$. Then, the sample standard deviation of $x$ is given by

\[\label{eq:var-std} \hat{\sigma} = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2}\]

and the unbiased sample standard deviation of $x$ is given by

\[\label{eq:var-samp-unb} s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}\]

where $\bar{x}$ is the sample mean.

 
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Metadata: ID: D214 | shortcut: std-samp | author: JoramSoch | date: 2025-01-10, 17:44.