This paper considers the mixture fraction which is often used to quantify the turbulent mixing efficiency in fluid engineering devices. We contrast a volume-based approach, where the mixture fraction is quantified directly using the volume bounded by the interface between mixed versus pure fluid, to a surface-based approach that requires area integrals of all mixed-fluid interfaces. Experimentally, we investigate the resolution-scale robustness of the volume-based approach compared to the small-scale sensitivity of the surface-based approach. The difference in robustness between these approaches has implications for examining, modeling, and optimizing the turbulent mixing efficiency.