It's not really that straightforward though, is it? Firstly is it a mean or a median average? What counts as an empire? When do we date the rise and fall of specific empires? These are not questions with straightforwards answers. Would Hitler's Germany count as an empire? How many Roman empires were there?

Sure, we could also work out the average life expectancy of a mammal.

But, would it really be useful, predictive or meaningful, given the variety and variability of the conditions the data emerges from?

It being an average number, pulled out of it's context, doesn't necessarily mean anything beyond just the average

Average out of which number? There has not been enough empires in human history to get any kind of valid statistical conclusion.

Also, the ancient egyptian empire lasted over 3k years, for you to get an average of 250y with such outlier you would need to include what, several 10y "empires", or divide empires by ruler. Which would then make the conversation moot since each US president would be a new "empire".

The claim comes from John Glubb, and he used this chart to make the average out of... 11 data points!?! While missing tons of other ancient empires that lasted thousands of years?!

This is the book where he makes such claim

So to answer your comment, yeah math is easy. Impossible to reach such average number with all the data though, given that it was made with a wildly incomplete and incorrect data...