on average vs roughly

on average

prep
  • Expressed as a measure of central tendency (usually the arithmetic mean). 

  • Usually, typically; as a rule; as often as not. 

roughly

adv
  • Unevenly or irregularly. 

  • Without precision or exactness; imprecisely but close to in quantity or amount; approximately. 

  • In a rough manner; without kindness, softness, or gentleness. 

How often have the words on average and roughly occurred in a corpus of books? (source: Google Ngram Viewer )