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I think you're making potentially invalid assumptions about the about the relative scales of the numbers involved.

The issue is that if the small outlier leads to the product being less than 1, the degree of the root doesn't matter because the largest value possible of the n-th root approaches 1, which may be below whatever meaningful thresholds are relevant here.

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> The issue is that if the small outlier leads to the product being less than 1, the degree of the root doesn't matter because the largest value possible of the n-th root approaches 1, which may be below whatever meaningful thresholds are relevant here.

That is true, but I don't see the relevance given the context. If the geometric mean approaches 1 (i.e. after the n-th root), then you have too much lead. If all your samples have lead levels well below tolerance, then the n-th root of the product will not approach 1, but will be significantly smaller. Example: If all 10 samples are 0.01, the geometric mean is 0.01.

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