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Discover Ludwig"varied by" is correct and can be used in written English
You can use it when you want to describe something that has been changed or modified in some way. For example, "The design of the new model is varied by the addition of some unique features."
Exact(58)
Diet varied by species.
The outlook varied by region.
Responses varied by education, too.
The results varied by race.
The findings varied by service.
The actions varied by region.
The rankings varied by state.
Regrets also varied by level of education.
The numbers varied by race as well.
Contraceptive use also varied by race.
But here, too, attitudes varied by ethnicity.
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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