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> The appearance of two 3.5-sigma events suggests that the data is no longer being randomly generated around that mean, but is instead drifting away from that mean.

Not if the two 3.5-sigma events are in opposite directions, as in this case.



> ... opposite directions ...

Yes, I'd forgotten that detail. Still, though, chaotic bifurcation could be present with Il Niño and La Niña driving high & low extremes. Same mean, maybe, but with a bimodal distribution?




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