Context: The quiet Sun magnetic field probability density function (PDF) remains poorly known. Modeling this field also introduces a magnetic filling factor that is also poorly known. With these two quantities, PDF and filling factor, the statistical description of the quiet Sun magnetic field is complex and needs to be clarified. Aims: In the present paper, we propose a procedure that combines direct determinations and inversion results to derive the magnetic field vector and filling factor, and their PDFs. Methods: We used spectro-polarimetric observations taken with the ZIMPOL polarimeter mounted on the THEMIS telescope. The target was a quiet region at disk center. We analyzed the data by means of the UNNOFIT inversion code, with which we inferred the distribution of the mean magnetic field α B, α being the magnetic filling factor. The distribution of α was derived by an independent method, directly from the spectro-polarimetric data. The magnetic field PDF p(B) could then be inferred. By introducing a joint PDF for the filling factor and the magnetic field strength, we have clarified the definition of the PDF of the quiet Sun magnetic field when the latter is assumed not to be volume-filling. Results: The most frequent local average magnetic field strength is found to be 13 G. We find that the magnetic filling factor is related to the magnetic field strength by the simple law α = B_1/B with B1 = 15 G. This result is compatible with the Hanle weak-field determinations, as well as with the stronger field determinations from the Zeeman effect (kGauss field filling 1-2% of space). From linear fits, we obtain the analytical dependence of the magnetic field PDF. Our analysis has also revealed that the magnetic field in the quiet Sun is isotropically distributed in direction. Conclusions: We conclude that the quiet Sun is a complex medium where magnetic fields having different field strengths and filling factors coexist. Further observations with a better polarimetric accuracy are, however, needed to confirm the results obtained in the present work. Based on observations made with the French-Italian telescope THEMIS operated by the CNRS and CNR on the island of Tenerife in the Spanish Observatorio del Teide of the Instituto de Astrofísica de Canarias. Present address: Instituto de Astrofísica de Canarias, vía Láctea s/n, 38205 La Laguna, Tenerife, Spain.