The calculation results of the Population Representation Index for county-level units in Mainland China in 2010 and 2020.

To quantitatively assess the capacity of POI in representing demographic data, this study proposes the Population Representation Index (PRI), defined as the population size mapped by per unit of POI.This index reveals the population base corresponding to each unit of POI, directly reflecting the relationship between population and POI. Furthermore, it measures the population service capacity per POI unit, indicating supply-demand between infrastructure and demographics need. A higher PRI value indicates that each POI unit corresponds to a larger population, suggesting a potential mismatch between POI and population demand in the area, thereby indicating weaker POI representativeness. A greater distribution range and higher dispersion of RPI values signify more pronounced regional variation in the representativeness of POI.