We propose a novel measure of statistical dispersion of a positive continuous random variable: the entropy-based dispersion (ED). We discuss the properties of ED and contrast them with the widely employed standard deviation (SD) measure. We show that the properties of SD and ED are different: while SD is a second moment characteristics measuring the dispersion relative to the mean value, ED measures an effective spread of the probability distribution and is more closely related to the notion of randomness of spiking activity. We apply both SD and ED to analyze the temporal precision of neuronal spiking activity of the perfect integrate-and-fire model, which is a plausible neural model under the assumption of high input synaptic activity. We show that SD and ED may give strikingly different results for some widely used models of presynaptic activity.