Variance

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math

Are measures of the spread or dispersion of a set of data. For example consider the data sets \( 100, 200, 300 \) and \( 199, 200, 201 \). The first data set is more variable than the second.

We define the variance of a population as:

\begin{align} \sigma^2 &= \frac{\sum (x i \mu^2)}{n} \label{eq:variance} \\

  &= \frac{\sum x^2}{n} - \mu^2

\end{align}

Note: the variance is written using the square of the \( \sigma \) symbol, meaning we denote variance in-terms of the standard deviation. There isn't a separate symbol for variance and standard-deviation. And we can equivalently define the standard-deviation as

\begin{align} \sigma = \sqrt{\frac{\sum x^2}{n} - \mu^2} \label{eq:std-dev} \end{align}