Statistically. The duality is due to our mathematical models based on probability. Via calculus and empirical observation, we don’t literally see wave-like particles, but rather theoretically understand particles as waves with a probable point of epicenter.
The counter-intuitive wave-particle duality is purely theoretical, and thus mathematical. It’s not known if – and not likely to be – that there is a “real” or true duality inherent to nature. There is inherently a duality in the statistical mathematical models we create.
The reason for this contrived duality is because in order to define a particle, it needs to be a “point” (or have a point it’s defined by), but in order to define it’s function and interaction, it needs to be a “wave” (or have a frequency set and range it’s defined by). Furthermore, we actually understand particles as spread out in their respective field, thus not being points but broader perturbations. So these are never going to be points acting like waves, but rather definable, minimum quantities of energy fluxes in the field. In this sense, it does not seem to be a very paradoxical duality after all.
The Broad Spectrum Life 