By applying the statistical definition of a depolarizing Mueller matrix we formally derive and physically interpret the differential matrix of a depolarizing homogeneous medium. The depolarization phenomenon being a direct consequence of the fluctuations of the six elementary polarization properties of the medium, the differential matrix contains the mean values and the variances of the properties, thus fully describing those from a statistical viewpoint. Similarly, the reduced coherency matrix associated with the G-symmetric component of the differential matrix has an immediate physical interpretation as being the covariance matrix of the three basic groups of polarization properties. The formal developments are illustrated on experimental examples.