5. Descriptive Spatial Statistics
Mean Center
[latexpage]$\overline{X}=\dfrac{\sum x}{n}, \; \;\; \overline{Y}=\dfrac{\sum y}{n}$
The mean center applies the same notion of statistical mean to a spatial plane. In a given plane of x, y coordinates, mean center is the average x and y coordinates of all the points on the map.
Weighted Mean Center
$\overline{X}_w=\dfrac{\displaystyle\sum ^{n}_{i=1}w_{i}x_{i}}{\displaystyle\sum ^{n}_{i=1}w_{i}}, \; \;\; \overline{Y}_w=\dfrac{\displaystyle\sum ^{n}_{i=1}w_{i}y_{i}}{\displaystyle\sum ^{n}_{i=1}w_{i}}$
Weighted mean center is similar but each x and y coordinate is weighted by a particular variable, such as population. The mean population center, for example, would thus be the center of a set of points weighted by population.
Standard Distance
$SD=\sqrt{{\dfrac{\displaystyle\sum ^{n}_{i=1}\left( x_{i}-\overline{X}\right) ^{2}}{n}}+\dfrac{\displaystyle\sum ^{n}_{i=1}\left( y_{i}-\overline{Y}\right) ^{2}}{n}}}$
Standard distance, also known as standard distance deviation, is similar to standard deviation but applied to a spatial plane. It measures the degree of dispersion around a mean center point. It is generally plotted on a map as a circle with the radius equal to the standard distance.
