Earlier quoted context omitted.
You're talking about reduction in statistical variance due to replication of measurement (and then averaging). I'm talking about what happens when they extrapolate from that value by a huge factor (which is what they've done, and the silly article does egregiously). 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…
I think there is some kind of mixup, you can not scale up the variance percentages quadratically: 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 un…
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?