Definition: Sample variance

Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Variance ▷ Sample variance

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

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

and the unbiased sample variance of $x$ is given by

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

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

 

Sources:

• Wikipedia (2021): "Variance"; in: Wikipedia, the free encyclopedia, retrieved on 2020-04-16; URL: https://en.wikipedia.org/wiki/Variance#Sample_variance.

Metadata: ID: D143 | shortcut: var-samp | author: JoramSoch | date: 2021-04-16, 12:04.