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why do the properties of a mixture vary

A mixture is simply various compound mixed together. Vary the  amount of one compound in the mixture and the properties, such as  density, can be changed. For
example, salt and water can be  combined to make a mixture of salt water. If more salt is added the  density of the mixture increases. If you add more water, then the  density decreases.

While pure salt, a compound, will always have  the same density because it is governed by forces at the atomic  level, not simply the amount of sodium and chlorine that is  combined. The properties of a pure substance do not vary from sample to sample because there is no reason for them to.

Why would they? Water is water, and if you take any sample of water from any stream, lake or ocean and remove all the "stuff" in it to leave only the water, all the samples will behave the same way physically and chemically. The chemical properties of a substance (and the physical ones, too) are set by what the substance is.

And these properties define the way the substance behaves in the universe as a whole. There is no reason for any water found on, say Mars, to behave any differently than any water here on Earth - or anywhere else in the universe.

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