We have measured both the current-voltage ($I_\mathrm{SD}$-$V_\mathrm{GS}$) and capacitance-voltage ($C$-$V_\mathrm{GS}$) characteristics of a $\mathrm{MoS_2-LiNbO_3}$ field effect transistor. From the measured capacitance we calculate the electron surface density and show that its gate voltage dependence follows the theoretical prediction resulting from the two-dimensional free electron model. This model allows us to fit the measured $I_\mathrm{SD}$-$V_\mathrm{GS}$ characteristics over the \emph{entire range} of $V_\mathrm{GS}$. Combining this experimental result with the measured current-voltage characteristics, we determine the field effect mobility as a function of gate voltage. We show that for our device this improved combined approach yields significantly smaller values (more than a factor of 4) of the electron mobility than the conventional analysis of the current-voltage characteristics only. ; Comment: to appear in Applied Physics Letters