Not for me- if you have an article, you should usually have a noun with it- on an average day, etc.
Where I come from, we say "on average" in this context - on average.Thank you. I have searched online and a few native speakers share the same view as yours. But one dictionary seems to say: on the average=on an average and can be used independently to mean 'usually':
Average | Definition of Average at Dictionary.com:
—Idiom 15.on the or an average, usually; typically: She can read 50 pages an hour, on the average.
Where I come from, we say "on average" in this context - on average.
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