To choose the optimal combination of options over a lifelong career - 1. Is graduate school economically worthwhile, and up to what level of education? 2. Which academic subject should one pursue to study? TC: $245k
Wouldn’t recommend masters in Business analytics. They’re just cash cow programs. Source: I’m a graduate of one of those.
First you need to define, "Data Scientist." What kind of work do you actually want to do, and what are you optimizing for? Fulfillment? Achievement? Compensation? Impact? This title is even more overloaded than "Software Engineer." Most data scientists are just less highly paid developers who run SQL queries. Others build Tableau reports and timeseries visualizations for product managers. Some data scientists participate in greenfield quantitative research, or develop bespoke models.
I enjoy math, but need to make a living too. Intellectual fulfillment is the #1 priority. 70-90% of SWE pay is good enough. If I can choose to write my code in C++ for entertainment, I would do it even if that generates zero impact.
If intellectual fulfillment is truly your #1 priority and you're okay with 70 - 90% SWE pay (and the potential for significantly higher), then get a PhD. You'll end up going for applied research roles rather than what's usually meant by data science. Otherwise, don't bother getting any graduate degree (not even a Masters). Focus on building up creative and impactful data science experience through professional work and a personal portfolio.