I would go for a BSc in Stats and a Ph.D in Computer Science (or an specialization course). Stats will give you the theory behind the techniques you use to analyse data. Some colleges are giving classes about programing in stats (which is a little bit different of what you do in Computer Science), so that will help you to have basis to program. Know how to program is important and we use it a lot, since data is getting bigger everyday and getting, cleaning and organizing data is EVERYTHING for a good analysis (and that is what Comp Science will help with).
The specialization (or Ph.D) will give you support to expand your programmer’s side and there are some of skills that you don’t need to know for analysis, but can help you to develop a plataform to offer your analysis easier to your clients 😉 But if you just want the BSc, you can go for Stats and take online classes (Coursera and DataCamp offers a lot of them) to improve your programming skills.