I think you're forgetting there have to be quotes round the string in the query.
So I think it's like this:

Code:
$result = mysql_query("DELETE FROM '" . $data[0] ."'  WHERE ID IN '" .$data[1] . "'");
I added the single quotes... (if ID is a number in your database, you can delete the single quotes there)

I hope it works, it's my first post here on the forum, and i just know the basics of PHP/MySQL, so don't shoot me if I'm wrong.