On: Eastern Antarctica sees record temperatures 70 degrees above normal

[FabHK]

The probability that an observation is beyond 5 standard deviations is < 1/25 = 4%, according to Chebyshev's inequality, provided the variance of the distribution is finite (which, as you say, is not guaranteed, eg. for Cauchy distributed random variables).

https://en.wikipedia.org/wiki/Chebyshev's_inequality

https://en.wikipedia.org/wiki/Cauchy_distribution

[tomrod → FabHK]

An observation bound below by 5 standard deviations is at best a one in a million on a standard normal distribution.

[FabHK → tomrod]

Yes, for a normal, which is known to have extremely thin tails (decaying with a squared exponential!). Chebyshev's bound holds for any possible distribution (with finite variance).

[FabHK → FabHK]

Not squared exponential (that's just an exponential), but exponential of a square, even. Anyway.

[WinterMount223 → FabHK]

If the observed variable is “the mean temperature in a given day”, 4% can be expected to occur relatively frequently.

Anyway until we know the probability distribution, and my intuition says that it’s definitely not Normal for wide periods of time, we can’t say if it’s significant or not.

[lanstin → WinterMount223]

Five standard deviations is not four percent, it is in the 1 in 3 Million range.

[FabHK → lanstin]

Yes, for a normal, which is known to have extremely thin tails (decaying with a squared exponential!). Chebyshev's bound holds for any possible distribution (with finite variance).

[ianai → WinterMount223]

You’re the only one introducing the normal distribution here.

[nobodyandproud → ianai]

When discussing standard deviations, what meaning is there for non-normal distribution?

https://stats.stackexchange.com/questions/108578/what-does-s...

[zmgsabst → FabHK]

4% would imply that we should expect about two weeks of such weather every year, in total.

Which would make this article somewhat clickbait — nothing more than “wowza, July 15th is another hot one in California!”

Since it’s currently summer, in the Southern Hemisphere.

[cma → zmgsabst]

That's a bound not an expectation.