[pfortuny]

I do not get it: if variance is too large, a random sample is very little representative of the mean. As simple as that?

Now the specific formula may be complicated. But otherwise I do not understand the “paradox”? Or am I missing something?

[hcks]

In the 1D case the single point will be the best estimator for the mean no matter what the variance is

[pfortuny]

OK, this is a good reply, and very informative, many thanks. Now I understand why the thing is paradoxical.