The experimental data from quasielastic electron scattering from $^{12}$C are reanalyzed in terms of a new scaling variable suggested by the interacting relativistic Fermi gas with scalar and vector interactions, which is known to generate a relativistic effective mass for the interacting nucleons. By choosing a mean value of this relativistic effective mass $m_N^* =0.8 m_N$, we observe that most of the data fall inside a region around the inverse parabola-shaped universal scaling function of the relativistic Fermi gas. This suggests a method to select the subset of data that highlight the quasielastic region, about two thirds of the total 2,500 data. Regardless of the momentum and energy transfer, this method automatically excludes the data that are not dominated by the quasielastic process. The resulting band of data reflects deviations from the perfect universality, and can be used to characterize experimentally the quasielastic peak, despite the manifest scaling violation. Moreover we show that the spread of the data around the scaling function can be interpreted as genuine fluctuations of the effective mass $M^* equiv m^*_N/m_N sim 0.8 pm 0.1$. Applying the same procedure we transport the scaling quasielastic band into a theoretical prediction band for neutrino scattering cross section that is compatible with the recent measurements and slightly more accurate.
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