Urdu, I'm told by someone who speaks the language, is Hindi written in Arabic script.
Could well be true! I'm not qualified to speak about that. Looking it up, seems like I mis-spoke when I said Urdu was Dravidian. But there are a lot of Indian languages that are (e.g. Kannada), so the overall point stands that the "averaging" comment is a bit misleading.
Incidentally, your comment led me to this http://en.wikipedia.org/wiki/Hindi–Urdu_controversy which you may find interesting.
> This could explain the result for Hindi - it is a standard language that 'averages' a large number of other Indian languages.
I think this is a little misleading; a lot of Indian languages come from a completely different language family to Hindi (Hindi is Indo-European, but a lot of Indian languages are Dravidian, e.g. Tamil and Urdu), though I'm not qualified to speak about this.