Table 1‑4 provides a list of common measures (univariate statistics) applied to datasets, and associated formulas for calculating the measure from a sample dataset in summation form (rather than integral form) where necessary. In some instances these formulas are adjusted to provide estimates of the population values rather than those obtained from the sample of data one is working on.

Many of the measures can be extended to two-dimensional forms in a very straightforward manner, and thus they provide the basis for numerous standard formulas in spatial statistics. For a number of univariate statistics (variance, skewness, kurtosis) we refer to the notion of (estimated) moments about the mean. These are computations of the form

When r=1 this summation will be 0, since this is just the difference of all values from the mean. For values of r>1 the expression provides measures that are useful for describing the shape (spread, skewness, peakedness) of a distribution, and simple variations on the formula are used to define the correlation between two or more datasets (the product moment correlation). The term moment in this context comes from physics, i.e. like ‘momentum’ and ‘moment of inertia’, and in a spatial (2D) context provides the basis for the definition of a centroid — the centre of mass or centre of gravity of an object, such as a polygon (see further, Section 4.2.5).

Table 1‑4 Common formulas and statistical measures

This table of measures has been divided into 9 subsections for ease of use. Each is provided with its own subheading:

·         Counts and specific values

·         Measures of centrality

·         Measures of spread

·         Measures of distribution shape

·         Measures of complexity and dimensionality

·         Common distributions

·         Data transforms and back transforms

·         Selected functions

·         Matrix expressions