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"average of roughly" is grammatically correct and can be used in written English.
It is typically used when discussing a numerical average that is estimated or approximate. Example: The average of roughly 100 people attended the concert last night.
Exact(58)
Currently, workers are responsible for an average of roughly 20 families.
Home delivery prices went up an average of roughly 10percentt.
They have logged the fewest innings, an average of roughly five and a third per game.
The time-series trend is profound: from an average of roughly 0.2 in 1980 to 0.7 in 2017.
The average salary at Norilsk Nickel is $900 a month, compared with a national average of roughly $150.
This spring's oversupply has driven the price down to an average of roughly $100 a kilogram, according to Western diplomats.
Last week, Vox churned out an average of roughly 25 posts per weekday, according to this feed.
The N.H.L. records an average of roughly 75 concussions per year, a figure believed to be vastly underreported.
For example, the 5.1 mm samples underestimated the elastic modulus of the 10.6 mm samples by an average of roughly 20%.
For the past decade, an average of roughly eight million vehicles made by General Motors, Ford and Chrysler have been sold annually.
In the past, when the price of soda has risen by 10percentt, consumption has dropped by an average of roughly 8percentt.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com