Self-amplified spontaneous emission (SASE) pulses delivered by free electron lasers (FELs) are inherently fluctuating sources; each pulse varies in energy, duration, arrival time and spectral shape. Therefore, there is strong demand for a full characterization of the properties of SASE radiation, which will facilitate more precise interpretation of the experimental data taken at SASE FELs. In this paper, we present an investigation into the fluctuations of pulse duration, spectral distribution, arrival time and pulse energy of SASE XUV pulses at FLASH, both on a shot-to-shot basis and on average over many pulses. With the aid of simulations, we derived scaling laws for these parameters and disentangled the statistical SASE fluctuations from accelerator-based fluctuations and measurement uncertainties.