La Fuenfría Hospital (LFH) operative parameters such as: hospitalised patients; daily admissions and discharges were studies for the hospital as a whole, and per each Hospital's service unit (just called "service" here). Data were used to build operative parameter value series and their variation. Conventional statistical analyses and fractal dimension analyses were performed on the series. Statistical analyses indicated that the data did not follow a Gauss (i.e. "normal") distribution, thus nonparametric statistical analyses were chosen to describe data. The sequence of admitted daily admissions and patients staying on each service were found to be a kind of random series of a kind called random walks (Rw). Rw are sequences where what happens next ($ y_{t+Δt}$), depends on what happens now ($ y_{t}$) plus a random variable ($ ε$), $ y_{t+Δt}= y_t + ε$. Rw analysed with parametric or non parametric statistics may simulate cycles and drifts which resemble seasonal variations or fake trends. Globally, admitted patients Rws in LFFH, were found to be determined by the time elapsed between daily discharges and admissions. The factor determining LFH Rw were found to be the difference between daily admissions and discharges. The analysis suggests discharges are replaced by admissions with some random delay and that the random difference determinants LFH Rws. The daily difference between hospitalised patients follows the same statistical distribution as the daily difference between admissions and discharges. These suggest that if the daily difference between admissions and discharges is minimised, i.e., a patient is admitted without delay when another is discharged, the number of admitted panties would fluctuate less and the number of unoccupied beds would be reduced optimising the Hospital service.