Explain why the properties of a pure substance do not vary from sample to sample.

When you take a sample of something—a dirt sample from an archaeological site, a sap sample from a tree, an ice sample from the Arctic—you are taking a statistical sample of the substance's compositional atoms in the process. So if a certain region of Arctic ice is 95% water and 5% air bubbles on average, then on average your sample will match that, but there's no guarantee that you won't hit a patch that has a particularly thick or thin concentration of air. You must take multiple samples to determine the average across the entire region.
In contrast, if a pure substance is truly pure—100% unadulterated concentration of whatever you're sampling—then there is no need to worry about the properties changing. Unless you taint the substance in the sampling process, its properties cannot change, because every sample will be equally as pure as the source from which you are sampling.