The Large High Altitude Air Shower Observatory (LHAASO) has accomplished comprehensive and precise measurements of very-high-energy cosmic ray air showers. For the first time, the logarithmic shower muon number has been employed to derive the mean logarithmic mass ($\langle \ln A \rangle$) of cosmic rays, while fluctuations in the logarithmic shower muon number have been utilized to construct the variance of the logarithmic mass ($\sigma_{\ln A}^{2}$). The analysis provides a clear depiction of the cosmic ray mass composition evolution with energy and explicitly illustrates the energy-dependent trend of $\sigma_{\ln A}^{2}$. The reliability of this parameterization method has been validated by employing simulations based on three different hadronic interaction models (QGSJET-II-04, EPOS-LHC, and SIBYLL 2.3d) with various cosmic ray compositions. The results demonstrate excellent consistency between the simulated input values of $\langle \ln A \rangle$ and $\sigma_{\ln A}^{2}$ and those derived from the parameterization, thus confirming the robustness and accuracy of this approach.