How do I punctuate this sentence? A machine breaks down on average three times per day
I am confused about whether it should be
A machine breaks down - on average - three times per day.
or
A machine breaks down on average, three times per day.
No punctuation is necessary. You can swap in a different adverb to see:
A machine breaks down about three times per day.
Here are some more examples of on average in action:
Corpus of Contemporary American English: on average
If you want to make on average nonessential—an aside—then use punctuation (commas, em dashes, parentheses) on both sides of it:
A machine breaks down, on average, three times per day.