What is a statistic? Does it mean something like a "secretary" or "accountant"?

No. There isn't a lot of context here but the person is most likely referring to becoming just another ____.

E. g. statistics are actually numeric representations of probability, numerical facts (this is not a great definition, by the way). The idea is, you show probabilities of occurrences/incidences.

Usually the context is one of crimes, e. g. if the statistics say that 15% of all single women will be robbed, and the writer was robbed, she might say "I became a statistic". That is, she also became a victim and therefore is one of the 15% in the example.

I'm sure someone will explain it more eloquently, but that's the general idea.

As one of three secretaries in the Applied Mechanics and Engineering Science Department at the University of Michigan, I helped six professors help their students make their dreams become reality. Every day for two long years I watched other young adults make their way through college.
Within a few short years following high school, I had become a statistic.
At the age of twenty, I married my high school sweetheart and started my family.

Here is more context.

As Jespah points out, a statistic is an expression of the probability of an event occuring. One probability is that a woman will marry someone from the town in which she grew up (a "high school sweetheart") and begin to have children. In that respect, she had become a statistic. That she might have worked as a secretary or an accountant is not relevant to her having become a statistic.

So can I take it as "I fellowed the general trend"?

How about, "I followed the general trend" . . .

It really depends on the rest of the article to see what "statistic" the author is refering to. You could use this type of statement if you got robbed in a parking lot (you just became a crime statistic) or if you lost your job (economic statistic). I take it to mean "I joined a group you often hear about in the news", in this case maybe women who give up there careers to start families.

Miss Nancy has provided the context. The first person narrator speaks of working as a secretary, and then marrying her high school sweetheart and starting a family--at which point she becomes a statistic.

I saw that, but there are lots of "statistics" she could have become a part of. Women marrying young? Women giving up budding careers? Stay at home moms? I thought this was more of a throw-away statement personally, but if I had the entire article, it might have more meaning for me.

A statistic sometimes refers to a person becoming unemployed, a number or part of a percentage. So in this case, not having read the rest of the story...
She was part of a team that educated a new generation of workers and then she was no longer working, no longer part of the workforce when she became wife and mother. She was (for example) one of the 10% unemployed in the USA or whatever the relevant stat was at the time.