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Description: Human infants learn object names by mapping heard names to perceived things. The key challenge to this learning is referential uncertainty: for any heard name, there are many candidate referents with variable perceptual properties. Previous experimental research on how infants solve this problem has been based on different assumptions about the nature of this uncertainty. The present study is the first to quantify the degrees of referential uncertainty by measuring infants’ real-time attention to the potential referents when parents name unfamiliar objects. We discovered an unexpected bimodal distribution of infant attention to the intended referents in parent speech during everyday parent-infant interactions, which redefines the century-long puzzle of referential uncertainty as problem in the sampling of data for learning.