![arcmap point density arcmap point density](https://michaelminn.net/tutorials/arcgis-pro-points/2020-kernel-density.png)
The standard deviational ellipse is very useful in representing point patterns that follow a directional orientation (ESRI, 2018). The center of the ellipse is the mean center, the major elliptical axis follows the direction with the greatest dispersion, and the length of each orthogonal axis is determined by the corresponding standard distance along that direction (Figure 2). To this end, researchers use standard deviational ellipses to calculate separate standard distances for two perpendicular axes.
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In spatial statistics, median center is the location that minimizes the sum of distances traveled to all points in the study area, and it is calculated using an iterative procedure introduced by Kulin and Kuenne (1962). Where ( μ x, μ y) are the coordinates of the mean center, ( x i, y i) represent the coordinates of a given point i, and n is the total number of points. Mean center averages the ( x, y) coordinates of all points in the study area (Equation 1): Two commonly used measures of central tendency are mean center and median center (Gimond, 2019). Central tendency focuses on extracting the central or typical location from a point pattern, providing an estimate of the location around which all the points are spread (O'Sullivan & Unwin, 2010). In PPA, descriptive statistics provide a summary of the basic characteristics of a point pattern, such as its central tendency and dispersion. This entry reviews both types of methods in PPA and illustrates these methods based on a classic case study of the 1854 cholera outbreaks in London (Snow, 1855). Distance-based methods, on the other hand, consider the distance between point pairs and therefore measure second-order properties. In general, density-based methods, such as kernel density, mostly address first-order properties of point patterns.
![arcmap point density arcmap point density](https://i.imgur.com/LxN2wr3.png)
One example of second-order properties is the degree of dispersion (e.g., clustered, dispersed, or random) of a point pattern (Oyana & Margai, 2016). The former focuses on the characteristics of individual locations and their variations across space, whereas the latter focuses on properties that concern not only individual points, but also the interactions between points and their influences on one another. Generally, these properties can be divided into two categories: first-order properties and second-order properties. Previous studies have developed various methods and measurements, such as density-based methods and distance-based methods, to analyze, model, visualize, and interpret the properties of point patterns. Point pattern analysis (PPA) studies the spatial distribution of points (Boots & Getis, 1988).