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The phrase "a relatively narrow slice" is correct and usable in written English.
It can be used to describe a specific, limited portion or segment of a larger whole, often in contexts like analysis, research, or discussion.
Example: "The study focused on a relatively narrow slice of the population, specifically young adults aged 18 to 24."
Alternatives: "a limited segment" or "a small portion".
Exact(7)
The fighting has been confined to a relatively narrow slice of the country, along the western border.
But the larger point is still crucial: the modern American economy distributes the fruits of its growth to a relatively narrow slice of the population.
But those gains benefited a relatively narrow slice of the population: entrepreneurs, urban white-collar workers, foreign investors and some government officials who engaged in corrupt activities.
The Obama campaign does not need to convince everybody in order to have an effect on the voting outcome in key states, only a relatively narrow slice of the religiously motivated voters who supported Mr. Bush by substantial margins in 2000 and 2004.
Cruz: [T]he prior program only covered a relatively narrow slice of phone calls.
When you had a terrorist, you could only search a relatively narrow slice of numbers, primarily land lines.
Similar(53)
Those two are using a relatively narrow definition.
For Mr. Basescu, 60, it was a relatively narrow escape.
These are nifty, but deliver a relatively narrow frequency range.
That gave ABC a relatively narrow window of time.
The Apollo, celebrating its 75th anniversary this year, has a relatively narrow stage and a tiny backstage.
More suggestions(2)
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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