This work reports a novel graphene electrolyte-gated field-effect transistor (EGFET) array architecture along with a compact, self-contained, and inexpensive measurement system that allows DC characterization of hundreds of graphene EGFETs as a function of VDS and VGS within a matter of minutes. We develop a reliable graphene EGFET fabrication process capable of producing 100% yield for a sample size of 256 devices. Large sample size statistical analysis of graphene EGFET electrical performance is performed for the first time. This work develops a compact piecewise DC model for graphene EGFETs that is shown capable of fitting 87% of IDSvs. VGS curves with a mean percent error of 7% or less. The model is used to extract variations in device parameters such as mobility, contact resistance, minimum carrier concentration, and Dirac point. Correlations in variations are presented. Lastly, this work presents a framework for application-specific optimization of large-scale sensor designs based on graphene EGFETs.