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.