I'm an undergraduate majoring in economics, and I am deciding whether or not to take real analysis. My plan is eventually to get a Master of Science in data analytics, similar to this program:http://analytics.ncsu.edu/?page_id=1799. Given my course load, I may be able to make it fit, but I may not. This will be the last time I am able to take it. The course description reads: "Studies continuity, convergence of sequences and series, differentiability and integrability. Introduces appropriate topological concepts. How helpful will this class be in pursuing a master's in data analytics?
"The curriculum is a carefully calibrated mix of applied mathematics, statistics, computer science, and business disciplines."
Based on this taken from the link you provided, and my personal experience with data mining and statistical machine learning, I would say it would not be worth your efforts. It seems like the program you are interested in is much more applied and would not go into the mathematical rigor that would require a prerequisite knowledge of real analysis. Could it be useful for understanding the fundamentals of calculus, sequences, and series? Sure, but you could learn this without necessarily needing to learn how to rigorously prove everything. I would spend more time with programming and linear algebra to prepare you for data mining. Unless you want to go into acedemic research in data mining at the Phd level and beyond, I would not take real analysis.
Based on the description of the program in the link, I would say that it is not the most important thing.
If your plan is to stop at the masters level, then real analysis may not be important. However, if you are considering a future PhD that may officially fall into a statistics or mathematics department, then it might well be worth your time to take it. Departments like these do require real analysis--I have been associated with several universities (U.S.), I do not know any programs that do not require it. The masters level focuses more on practical skills than theory, and real analysis is more important for theoretical work, deriving methods, and bracketing results. Just to be clear, I'm saying it may be important for coursework, not necessarily for actual work.
I agree with other posters that programming skill may be more practically useful specifically for data mining. Though I am a big supporter of sound theoretical understanding.
If you want to get a master degree and eventually go to industry, I don't think you need take real analysis course. It is kind of too theoretical and far away from practical data mining techniques. On the contrary, multivariable calculus, linear algebra, statistics and optimization knowledge of undergraduate level is more helpful to appreciate almost all algorithms.
However, if someone wants to do Phd in related area, e.g., machine learning or learning theory, it is totally recommended, even necessary.