As the minimum age to become president is 35, you should exclude people under 35 from the statistics. I can believe that 55 is close to the median age of people 35 and older.
The population of the U.S. has grown considerably since 1985. The median age of the entire population does not seem like a good metric. What's the median age of people qualified to run for president today? It appears to be 50-60.
No, there’s no doubt in my mind that the median age of a president is greater than the median age of the general population, but that in no way implies that old age “runs deep” among presidents, which I take to mean that it’s a common thing.
About half are less than 55 and half are more than 55. Most are somewhere near 55 (since the distribution conforms to a bell curve). 55, in my opinion, is not “old age”, but your mileage may vary.
Extra context: a 55-year-old who gets elected for president twice would finish at 63, about 3-4 years short of retirement age (66-67 depending on birth year).
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[0]: https://www.census.gov/library/stories/2019/06/median-age-do...
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