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Radial distribution functions (RDFs) are widely used in molecular simulation and beyond. Most approaches to computing RDFs require assembling a histogram over inter-particle separation distances. In turn, these histograms require a specific (and generally arbitrary) choice of discretization for bins. We demonstrate that this arbitrary choice for binning can lead to significant and spurious phenomena in several commonplace molecular-simulation analyses that make use of RDFs, such as identifying phase boundaries and generating excess entropy scaling relationships. We show that a straightforward approach (which we term Kernel-Averaging Method to Eliminate Length-Of-Bin Effects) mitigates these issues. This approach is based on systematic and mass-conserving mollification of RDFs using a Gaussian kernel. This technique has several advantages compared to existing methods, including being useful for cases where the original particle kinematic data have not been retained, and the only available data are the RDFs themselves. We also discuss the optimal implementation of this approach in the context of several application areas.