Why do data scientists use R and Python, as opposed to other languages like C#?

As a “proper” programmer, used to programming in heavy duty, compiled languages like C# (and before that C++ and C), my reaction on discovering during my Data Science journey that R and Python are heavily used by data scientists was: why??

Why would anyone use an interpreted language, which is therefore bound to be slower, and why would anyone go to the trouble of using yet another language when there are perfectly good compiled languages around like C#, F# and VB.net?

The answer seems to be partly that R and Python are free (open source), and also because R and Python have excellent visualisation tools, which the other languages currently lack.