Parameters for models of biological systems are often obtained by averaging over experimental results from a number of different preparations. To explore the validity of this procedure, we studied the behavior of a conductance-based model neuron with five voltage-dependent conductances. We randomly varied the maximal conductance of each of the active currents in the model and identified sets of maximal conductances that generate bursting neurons that fire a single action potential at the peak of a slow membrane potential depolarization. A model constructed using the means of the maximal conductances of this population is not itself a one-spike burster, but rather fires three action potentials per burst. Averaging fails because the maximal conductances of the population of one-spike bursters lie in a highly concave region of parameter space that does not contain its mean. This demonstrates that averages over multiple samples can fail to characterize a system whose behavior depends on interactions involving a number of highly variable components.