Earlier quoted context omitted.
I didn't find the source URL unreadable. It's here: https://climatereanalyzer.org/clim/sst_daily/?dm_id=nino3.4 The lowest ones were 1988 and 1989.
Fair, I had to click into the full size (I pinch zoomed on my phone). But now the fact that 1988/1989 are outliers raise a few more questions about the variance calculation. In particular, the title suggests that those weren't included in the variance calculation. A 3.5-sigma event is a 1-in-1000 chance. Yet we have 2 of them in our data set that goes back only 40ish years? Something is suspect. Maybe I'm not account…
The event in this case is a daily observation, so in the last 45 years there have been 16k events. Under Gaussian assumption, 3.5 sigma outliers in positive direction are 1 in ~4,000 events, in either direction 1 in ~2,000, so approx. 8 days would be outliers in the recorded period. Judging by the looks, it's pretty close. And the data is absolutely not Gaussian: at best it's the result of a Gaussian process, as the daily recordings are not independent, but dependent on the previous day.