<standardDeviation>

<standardDeviation> is a Math Operator component that renders the standard deviation of a list of enclosed data values according to the equation:

$\sigma(x) = \sqrt{\frac{\sum_{i=1}^n (x_{i} - \bar x)^2}{n-1}}$

In this equation, $\bar x$ represents the mean of the sample and $n$ the number of data points. By default, the sample standard deviation is calculated. If instead, the population attribute is specified as “true”, the equation becomes:

$\sigma(x) = \sqrt{\frac{\sum_{i=1}^n (x_{i} - \bar x)^2}{n}}$

Attributes and Properties

Example: <standardDeviation> of a list of numbers

The <standardDeviation> component is used without any additional attributes. Data is directly entered in the form of a list of numbers separated by spaces within the opening and closing tags.

Attribute Example: population

The <standardDeviation> component is used with the population attribute and the population standard deviation is calculated according the second equation shown above.