In this case, the positioning of the adverb makes a significant difference to what is modified, and the polyseme involved.
Using the adverb after the main verb
- Data can be arranged arbitrarily
dictates that the main verb is modified ( ... arranged in an arbitrary as opposed to a set fashion) and virtually dictates that, as indicated, the 'random' / 'up to the arranger' sense/s are in play:
- 1 Based on random choice or personal whim, rather than any reason or system.
- his mealtimes were entirely arbitrary
But using 'arbitrarily' right after the modal gives the sense that the decision to implement the action (spelled out by the verb) has been taken arbitrarily, this time with the default sense peremptorily, without discussion:
arbitrary [adjective] ...
- 1.1 (of power or a ruling body) unrestrained and autocratic in the use of authority.
- arbitrary rule by King and bishops has been made impossible
- Congress can arbitrarily prohibit the interstate transportation of all intoxicating liquors
[Congressional Record: Proceedings and
Debates of the ... United States
Its use in the given sentence (2) might be considered unusual. You might find that someone / something has arranged the data.