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The phrase "a relatively large number" is correct and usable in written English.
It can be used when discussing quantities that are significant in comparison to other numbers or amounts, but not excessively large.
Example: "In the survey, a relatively large number of participants expressed their satisfaction with the service provided."
Alternatives: "a considerable number" or "a significant number".
Exact(59)
A relatively large number of Saudis also come to the region for schooling, Professor Pizam said.
Inspections have confirmed the presence of a relatively large number of missile engines, some imported as late as 2002.
In the language of statistics, such a pattern has a "fat tail" -- a relatively large number of apparently unusual occurrences.
It also has 21 electoral-college votes, a relatively large number that could decide a tight presidential race.
Many African nations and India have, for this reason, a relatively large number of North American and European teachers.
Still, 1024 is a relatively large number causing excessive complexity.
Meanwhile the "worst" product line used fully depreciated equipment but a relatively large number of workers.
Variety of customer requirements leads to a relatively large number of distinct configurations.
The teleostean diencephalon contains a relatively large number of dopaminergic neurons compared to other vertebrates.
A relatively large number of migrants are observed along the border with fSU countries.
A relatively large number were more than 40 years of age (49%%).
More suggestions(16)
a relatively large coverage
a relatively large product
a relatively large fish
a relatively large downtown
a relatively large collar
a relatively large effect
a relatively large clay
a relatively large patch
a relatively large tax
a relatively large amount
a relatively large company
a relatively large swath
a relatively large brain
a relatively substantial number
a relatively narrow number
a relatively large population
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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