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The mean center refers to the central point of data points distributed on a two-dimensional plane. In general statistics, the mean is calculated by dividing the sum of all data values by the number of observations.
Since spatial data consists of two dimensions, X and Y coordinates, the mean center is calculated by dividing the sum of all X coordinates and the sum of all Y coordinates separately by the number of data points. This can be expressed with the following formula:$$ \bar{X} = \frac{\sum_{i=1}^{n} x_i}{n}, \quad \bar{Y} = \frac{\sum_{i=1}^{n} y_i}{n} $$
where ${x_i}$ and ${y_i}$ are the X and Y coordinates of each data point, respectively.
Characteristics of the Mean Center
- All points are equally weighted in the calculation.
- When the spatial distribution is symmetrical, the mean center lies at the center.
- The mean center is easily shifted by outliers (points located far from the cluster).
- It serves as the basis for calculating measures such as the Standard Distance or Weighted Mean Center.
Thus, the mean center is useful for identifying the central area where spatial phenomena occur, and it can be applied, for example, to determine service facility locations for businesses or public institutions.
Application Examples
- Identifying the center of crime occurrences by calculating the mean center of incident locations
- Selecting a location for a new store by identifying the center of customer distribution within a commercial area
- Establishing a central logistics hub based on the mean center location