The orbit eccentricities of the Solar system planets are unusually low compared to the average of known exoplanetary systems. A power-law correlation has previously been found between the multiplicity of a planetary system and the orbital eccentricities of its components, for systems with multiplicities above two. In this study we investigate the correlation for an expanded data sample by focusing on planetary systems as units (unlike previous studies that have focused on individual planets). Our full data sample contains 1171 exoplanets, in 895 systems, and the correlation between eccentricity and multiplicity is found to follow a clear power law for all multiplicities above one. We discuss the correlation for several individual subsamples and find that all samples consistently follow the same basic trend regardless of e.g. planet types and detection methods. We find that the eccentricities of the Solar system fit the general trend and suggest that the Solar system might not show uncommonly low eccentricities (as often speculated) but rather uncommonly many planets compared to a 'standard' planetary system. The only outlier from the power-law correlation is, consistently in all the samples, the one-planet systems. It has previously been suggested that this may be due to additional unseen exoplanets in the observed one-planet systems. Based on this assumption and the power-law correlation, we estimate that the probability of a system having eight planets or more is of the order of 1 per cent, in good agreement with recent predictions from analyses based on independent arguments.