I have interviewed and worked with many programmers and DBAs. Most of them are not good at all, if not unqualified, in my opinion. It would be better that you study something else. The way they think shows that they could not be a good programmer or DBA. Definitely, they can find a job as programmer or DBA, but it doesn't mean they are good. It would become more and more difficult for them along the time. It may sound harsh, but it is the fact.
For example, I am a DBA. I interviewed many DBAs, including very senior ones. To my surprise, the majority of them are not clear on basic OS concepts and know little about hardware. They know how to write SQL queries. It is not enough, though. Enough more of the interview candidates know little about how the database engine works under the hood. Without the knowledge, you can never write the most optimized queries consistently. (One example, an very experienced DBA in my team wrote a query to search and aggregate a large amount of data. It gave the right results, but take 10 minutes. That query looks amazing to those who dont' understand it. But it shows that the DBAs have no idea how the engine's optimizer works and it wasted a lot of resources. I rewrote it and it takes only 5 seconds.) And if you don't understand some OS and hardware, you can never tune up database to get the best performance.
A side note on the hype on Data Analyst. It is true that you can write functional SQL queries in two months even if you had no background before. These positions are mostly in marketing team. If you have chance to touch the database servers, try to learn some DBA stuffs. DBA is just an OK job, not that good as touted here. It may, however, be a choice if you want to worry less about job security as a Data Analyst.
Also, no matter you are a DBA or a Data Analyst, make sure that you are 100% knowledge on the biz logic behind the data. If you know it and others don't, you are in a much better position even if the others are better in technical details.