Experimental magnetization curves for a polydisperse ferrofluid at various concentrations are examined using analytical theories and computer simulations with the aim of establishing a robust method for obtaining the magnetic-core diameter distribution function $p\left(x\right)$. Theoretical expressions are fitted to the experimental data to yield the parameters of $p\left(x\right)$. It is shown that the majority of available theories yield results that depend strongly on the ferrofluid concentration, even though the magnetic composition should be fixed. The sole exception is the second-order modified mean-field (MMF2) theory of Ivanov and Kuznetsova [Phys. Rev. E 64, 041405 (2001)] which yields consistent results over the full experimental range of ferrofluid concentration. To check for consistency, extensive molecular dynamics and Monte Carlo simulations are performed on systems with discretized versions of $p\left(x\right)$ corresponding as closely as possible to that of the real ferrofluid. Essentially perfect agreement between experiment, theory, and computer simulation is demonstrated. In addition, the MMF2 theory provides excellent predictions for the initial susceptibility measured in simulations.