[myrmidon]

> What is the variance of the resulting sample distribution?

Relatively? The same. Yes it scales quadratically, but that is just because variance has such a weird unit.

Just consider standard deviation (which has the same physical unit as what you are measuring, and can be substituted for variance conceptually): This increases linearly when you scale up the sample.

An example: Say you take 20 blood samples (5 ml), and find that they contain 4.5 ml water, with a standard deviation of 0.1 ml over your samples.

From that, your best guess for the whole human (5 liters, i.e. x1000) has to be 4.5 liters water, with standard deviation scaled up to 0.1 liters (or what would you argue for, and why?)