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The phrase "a circumscribed proportion" is correct and usable in written English.
It can be used when discussing a limited or defined part of a whole, often in contexts related to statistics, mathematics, or analysis.
Example: "In the study, we focused on a circumscribed proportion of the population to ensure accurate results."
Alternatives: "a defined portion" or "a limited fraction".
Exact(1)
In agreement with the findings of Lehrner et al. [18] significant improvement of neuropsychological performance was evident in a circumscribed proportion of patients (45%).
Similar(59)
He also continued his developments in mathematics; in 1681 he was concerned with the proportion between a circle and a circumscribed square and, in 1684, with the resistance of solids.
Alternatively, hospital specialisation is measured as the proportion of a hospital's total admissions during a circumscribed period that have a specific procedure (for example, hip replacement surgery) or fall into a single disease category, such as orthopaedics.
But this was a circumscribed revolutionary spirit.
Chess is a circumscribed world filled with mighty egos.
Driving to his class he realizes what a circumscribed life he has led.
Yet they also know that there's something inglorious about such a circumscribed existence.
She now lives a circumscribed existence in New York City and rarely sees her children.
The world of Acorn Lake in the 60's is a circumscribed one.
Critics say such a circumscribed electoral process is not the answer.
They're trashy, selfish, catchy and often hilarious — smart pop storytelling in a circumscribed realm.
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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