Centrography is the establishment of trends and laws of the distribution of phenomena based on the relationships and migrations of their centers of gravity . Measures of center are geographical techniques for locating the position of a point (or area) that represents the average location of the entire population sampled. This population is applicable to a host of variables including species populations, manufacturing, natural resources, epidemics, agriculture, education, etc.
Centrographic measures can be used to describe two features of discrete distributions: (1) central tendency, and (2) dispersion. The former is a point which is found by applying at least one averaging criterion. Since there exist several averaging criteria, there are several such points. The most common are the center of gravity (mean center), median center, and the point of minimum aggregate travel. The latter feature, dispersion, depicts the degree of scatter from a point of central tendency.
In the two dimensional case, there are numerous techniques and figures which demonstrate the scatter of points: the standard radius, the standard deviational ellipse, the standard deviational bicircular quartic and several versions of the sectogram.
Mean center calculations are divided into two methods of use. The first method is called the spatial mean or mean center. According to Wong (2005), the mean center is “a central or average location of a set of points.” The calculation of the mean center involves the summation of the X coordinates, the summation of the Y coordinates, then finally dividing each sum by the number of sample points. This produces an average X,Y coordinate pair (an average point) of all the sample points. For example, the mean center of the U.S. would be found using all 50 state center coordinates in the calculation. The second method is actually the more robust of the two calculations for mean centers, when “the points or locations have different frequencies or occurrences of the phenomenon being studied” (Wong, 2005). When these point locations have different frequencies, a “weight” is then applied by multiplying that weight with each coordinate during the summation of each X and Y dataset. An example of a weight would be the number of residents in a parcel. Parcels with more people would have a higher weight in the mean center calculation of population for parcels in a defined area (like a city). This weighting of variables then affects the resultant mean center point because the points with higher weights (like more people) effect the calculation more “pulling” the center more than lesser weighted points. This effect is known as a “sensitive center”.
There are a number of ways to calculate centers, including the median point calculation, quartilides, decilides and centrilides. The median point method involves finding “the point of intersection of two orthogonal lines each of which divides the population into two equal groups” (Sviatlovsky, 1937). One major downside to the median point method is that its results may vary radically with small changes in populations because it does not have what Sviatlovsky calls a “sensitive center”. This lack of a sensitive center causes the median point to shift erratically with certain changes to the population, whereas, the mean center will not. This occurs because the median center is calculated based on the position of orthogonal lines, not a statistical operation like the mean center calculation. When populations move only slight distances (over an orthogonal), they can cause major shifts in the median point location. The opposite is true when a large population migrates but does not pass over an orthogonal. Quartilides, decilides and centrilides are similar to the median point method in that they involve lines that divide the population into equal portions, however, the number of dividing lines is higher. This produces divisions of populations in quarters, tenths and hundredths. According to Sviatlovsky, this method is advantageous in regional analysis because it allows for “a greater degree of refinement…than ordinarily profitable”.
Wong, David, W.S.; Lee, Jay (2005): Statistical Analysis of Geographic Information, John Wiley and Sons.
Sviatlovsky, E. E.; Eells, Walter Crosby (1937): The Centrographical Method and Regional Analysis, Geographical Review, Vol. 27, No. 2.
Poulsen, Thomas M. (1959): Centrography in Russian Geography, Annals of the Association of American Geographers, Vol. 49, No. 3.
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