Well, it still tells us something. What are the upper and lower bounds of whole brain microplastic content, given that 25% variation?
The Smithsonian magazine article is garbage. Ignore it. The paper is saying that they see longitudinal trends in plastic bioaccumulation in various cadaver tissues, and this is plausible. But no, you don't have a plastic spoon in your head. That's just panic porn.
[1] Actually...I just asked Gemini and it reminded me that the expected variance of a draw from a distribution, scaled by factor C, should have a variance of the scaled sample distribution that grows with C^2. So, if we scale up the measurement by a factor of 10,000, we'd expect the variance of the scaled estimate to be proportional to 10,000^2.
And for what it is worth, the paper itself has plenty of other interesting findings that OP fails to discuss or rebut at all. OP asks an LLM some very basic statistics questions, putting into question their ability to credibly apply and interpret the LLM's findings.
My interpretation of that evidence is that OP, a random internet commenter, just doesn't think it is credible that plastics are harmful to humans, and is grasping at plastic straws with cherry picked evidence and poor rebuttals to reach that "fact based" conclusion.
So what? If some things haven't been discussed or rebutted, then just say that the argument is incomplete for those reasons and move on.
The paper isn't clear what they mean when they said "~25% within-sample coefficient of variation", so I can't directly address what you're asking, but it's tangential to the point I'm making. My naïve interpretation is that they did an ANOVA, and reported the within-group variance, or something similar.
All I'm saying in my footnote is that, whatever the final point estimate, scaling it by a factor of C will affect the variance of the final sample distribution by C^2. So for example, if you have an 8% variance on the measurement at ug/g, and you scale it by 1300 (for 1300g; what the interwebs tells me is the mass of a standard human brain), then you'd expect the variance of the scaled measurement to be 1300^2 * 8%.
That makes a ton of assumptions that probably don't hold in practice -- and I expect the real error to be larger -- but illustrates the point.
If you do a small-scale measurement, say you get result of 5g, with a standard deviation of 0.2g. That means the variance is 0.04 g^2.
If you then scale the setup up by 1000 (=> getting 5kg as expected value), then the variance scales to 1000^2 * 0.04 = 40000 g^2.
BUT the standard deviation is still 200g. The relative uncertainty is NOT increasing quadratically!
(another sanity check: if you change the units by a factor of 1000, your variance must not increase, relatively).
But maybe I misunderstood your point?
They didn't "scale the setup". They made a small-scale measurement, then extrapolated from that result by many orders of magnitude. They didn't grind up whole brains and measure the plastic content.
Imagine the experiment as a draw from a normal distribution (the distribution is irrelevant; it's just easier to visualize). You then multiply that sample by 10,000. 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?)