Standard Deviation

The standard deviation is a measure of the breadth of a distribution of numbers. For a set of numbers x₁, x₂, x₃, ... x_N, of any type except direction, Windographer calculates the standard deviation using the following equation:

The above equation gives the sample standard deviation, as opposed to the population standard deviation, whose definition is the same except that the N - 1 term changes to N.

Directional Values

For a set of directional numbers, Windographer instead uses the Yamartino method (Yarmartino, 1984), which produces an estimate of the standard deviation (in radians) using the following equation:

where:

Windographer reports standard deviations in many tables in the Tables window.