Glubb's claim is nonsense fabricated to further his arguments. He gives a very limited set of examples from basically just Europe and western Asia and it's still riddled with holes, like including the Roman empire (almost 500 years even if you don't include the eastern half, which lasted another 1,000) and Alexander the Great's empire (which famously fell to pieces upon his death). It's not even clear how he chose the start and end for several of them
I'm not meaning to come across as mad at you or anything, I don't even know of you got the claim directly from Glubb's work or heard it elsewhere
Oh I didn't mean it sincerely, just by gut feeling I'd assume the lifetime of empires is something like an exponential distribution, so talking about the mean gives really no insight as to how long any given empire will last.
I just think its funny (with a solid dose of gallows humor) that this number is being floated so often, just as the US is sliding into fascism, 248 years after it's founding