Various detection techniques are employed to study extensive air showers, with the fluorescence method—tracking the longitudinal development of the charged shower component—being the most reliable for cosmic ray composition analyses. Composition differences affect the interaction cross-section with atmospheric nuclei, influencing both the average depth of the shower maximum ($X_\mathrm{max}$) and its dispersion ($\sigma(X_\mathrm{max})$). This work presents an alternative approach that correlates $X_\mathrm{max}$ with a mass-sensitive observable, $V_b$, measured by underground muon detetctors. By utilizing the correlation coefficient instead of the observable, this method mitigates both the impact of the muon deficit and the dependence on high-energy hadronic interaction models. The correlation coefficient thus serves as an indicator of the spread of masses in the primary cosmic ray beam. Using simulations of air showers and detector responses we show that Kendall’s $\tau(X_\mathrm{max}, V_b)$ in the energy range $\log_{10}(E$/eV) $\in$ [17.3,18.6] is sensitive enough to distinguish between mixed and pure compositions while remaining only weakly dependent on the choice of high-energy hadronic interaction models.