average across vs average among vs. average over

I want to express that I take a mean over answers in a questionnaire. This is usually indicated as answers for specific items. Lets assume I have three items with the values 1, 2, and 3. The mean across/among/over the items would be 2.

What is the correct preposition here

Although use of "average over" in situations like the one you ask about seems to have grown somewhat more common in recent decades, and although I have noticed a rise in the popularity of "average across" in articles that I've edited in the past couple of years, these two forms are still nowhere near as common as "average of." The very large difference in frequency of "the average across" (blue line) vs. "the average among" (red line) vs. "the average of" (green line) vs. "the average over" (yellow line) in published works within the Google Books database for the period 1750–2008 is shown graphically in this Ngram:

It should be clear from this graph that the most common wording for your sentence would be the following:

The mean [value] of the items would be 2.