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The study of fast radio bursts (FRBs) is of great importance, and is a topic that has been extensively researched, particularly in recent years. While the extreme nature of FRBs can serve as a tool for researchers to probe the intergalactic medium and study exotic aspects of the Universe, keeping track of FRB properties is challenged by the frequent detection of new bursts. We introduce the FRBSTATS platform, which provides an up-to-date and user-friendly web interface to an open-access catalogue of published FRBs, along with a statistical overview of the observed events. The platform supports the retrieval of fundamental FRB data either directly through the FRBSTATS API, or in the form of a CSV/JSON-parsed database, while enabling the plotting of parameters and their distributions, for a variety of visualizations. These features allow researchers to conduct population studies and comparisons with astrophysical models, describing the origin and emission mechanism behind these sources. So far, the inferred redshift estimates of 813 bursts have been computed, providing the first public database that includes redshift estimates inferred from dispersion measure entries for nearly all observed FRBs, as well as host redshifts (where available). Lastly, the platform provides a visualization tool that illustrates associations between primary bursts and repeaters, complementing basic repeater information provided by the Transient Name Server. In this work, we present the structure of the platform, the established version control system, as well as the strategy for keeping such an open database up to date. Additionally, we introduce a novel, computationally-efficient, clustering-based approach that enables unsupervised classification of hundreds of bursts into repeaters and non-repeaters, resulting in the discovery of one new FRB repeater.