I am an inveterate and incorrigible Mathematica user, as most of my “real work” deals with what might be best described in layperson’s terms as “symbolic math”.

Even though Wolfram has not (yet? hope always dies last!) released a version of Mathematica for the iPad (meaning, a frontend notebook coupled to an actual onboard computing kernel) they have released a client for “Wolfram Online” (often referred to as “Cloud Mathematica”) offering. This isn’t quite what I would like, as there’s a significant range of circumstances where I cannot rely on network access (such as when flying) but for most other situations it suits the purpose.

Other mathematics-inclined apps allow even greater range of onboard functionality (Pythonista, MathSudio spring to mind).

Upshot: one can most definitely do significant amounts of data analysis on an iPad.