Why the last five months are hot means nothing

In an earlier POST  I discussed the broad dimensions of the lie that “this month was the 8th hottest ever”.   I discussed this earlier from a top-down perspective where I showed that the data is expected to show exactly that and that this data is obviously worthless in determining a trend.  In fact, as I showed, we would be SURPRISED to NOT find the hottest decade ever in the last decade.  Now I tackle the question from a statistical point of view.  Why is this a common and rather stupid mistake to make?

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