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GEOGRAPHICAL STATISTICS GE 2110 ZAKARIA A. KHAMIS Spatial Descriptive Statistics 2 Descriptive measures of spatial data are important in understanding and evaluating such fundamental geographic concepts accessibility and dispersion E.g. it is important to locate public facilities so that they are accessible to defined populations Spatial measures of centrality applied to the location of individuals in the population will result in geographic locations that are in some sense optimal with respect to accessibility to the facility Zakaria Khamis 5/24/2017 Spatial Descriptive Statistics Similarly, it is important to characterize the dispersion of events around a point It is useful to summarize the spatial location of individuals around a hazardous waste site Are the individual with a particular disease less dispersed around the site than are people without the disease? If so, this could indicate that there is increased risk of disease at location near the site Mean Center This is the most common used spatial measure of central tendency For point data, x and y coordinates of the mean center are found by simply finding the mean of the x coordinates and the mean of y coordinates For areal data, the mean center can be found by using the centroids of each area. It is often useful to attach weights to the x and y coordinates Mean Center For instance, to find the center a population, the weights are taken as the number of people living in each subregion The weighted mean of x coordinates and y coordinates then provides the location of the mean center of population n n wi xi wi yi x i 1n y i 1n wi wi i 1 i 1 Mean Center Where the wi are the weights (e.g. population in region i) and xi and yi are the coordinates of the centroid in region i Conceptually, this is identical to assume that all individuals living in a particular sub-region live at a pre-specified point centroid E.g. the mean center of population in the USA has migrated west and south over time Standard Distance Aspatial measures of variability, such as variance and standard deviation, characterize the amount of dispersion of data points around the mean Similarly, the spatial variability of locations around a fixed central location may be summarized The standard distance is defined as the square root of the average squared distance of points to the mean center (Bachi 1963) Standard Distance n sd d i 1 2 ic n Where dic is the distance from point i to the mean center The square root can be taken out from the equation because, distance is absolute