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The phrase "a population of around" is correct and usable in written English.
It can be used when discussing estimates or approximations of the number of individuals in a specific group or area.
Example: "The city has a population of around 500,000 residents, making it one of the largest in the region."
Alternatives: "approximately a population of" or "an estimated population of".
Exact(60)
The capital, Nuuk, has a population of around 15,000.
Belfast has a population of around 600,000.
South Ossetia is a piece of mountainous land with a population of around 70,000.
Tunis is a manageable size for a capital city, with a population of around 700,000.
The antelope has a Mongolian subspecies that until recently had a population of around 12,000.
Today there are 3,000-odd of them, out of a population of around 100,000.
Oak Island is a small resort town with a population of around 7,000.
All in an area where the big city has a population of around 16,000.
Sassuolo is the smallest town to boast a team in Serie A, with a population of around 41,000.
A year ago, her proposed relocation effort attracted just three families out of a population of around 2,000 people.
It has a population of around 5,200.
More suggestions(16)
a minority of around
a proportion of around
a density of around
a group of around
a demographic of around
a community of around
a village of around
a region of around
a bailout of around
a profit of around
a fall of around
a target of around
a circulation of around
a payment of around
a diameter of around
a thickness of around
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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