It makes more sense than 2378. It makes much more sense that he graduated in 2278 than that he wasn’t familiar with humans. So no definite date was established by the 78 remark.Let’s do some math.
We know for a fact that TNG takes place in the 24th century, but we don’t know the exact year. Logically it would have to take place no earlier than January 1, 2301. So if Data graduated Starfleet Academy in 2278, his posting to the Enterprise-D would have been at least 23 years after that. There’s no way that could be accurate. Data’s unfamiliarity with humans would be nonexistent after 23 years serving with them.
And in later canon, he was discovered by a landing party from the USS Tripoli on Omicron Theta in 2338. He graduated in 2345. One of Data's first assignments after he graduated Starfleet Academy was aboard the USS Trieste. He spent three years as an ensign and twelve as a lieutenant before being promoted to lieutenant commander in 2360, so had 26 years familiarity by 2364. Even without the dates, it takes years to go to college and become a Lieutenant commander.
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