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The phrase "a big variation" is correct and usable in written English.
It can be used when discussing differences or changes in size, amount, or degree in various contexts, such as statistics, research, or general observations.
Example: "There was a big variation in the test scores among the students, indicating differing levels of understanding of the material."
Alternatives: "a significant difference" or "a large discrepancy."
Exact(27)
A big variation.
But there is a big variation in weekly rents charged by different provider types.
There was a big variation in when and how people used brand names and generic names.
But early signs suggest a big variation from employer to employer.
Fingernails grow at an average rate of just shy of 4cm a year, though there is quite a big variation between individuals.
Four seats on the Great Barrier Reef are all key marginal seats but there was a big variation in the swings in these seats.
Similar(33)
The top one has a bigger variation.
There is a bigger variation in the cheese types without targets (18 500%); setting a target would narrow this variability.
When the prevalence or incidence of a common musculoskeletal disorder show a very big variation, as there also are examples of in the present review, one may suspect that this possibly could be an artifact due to different clinical criteria, making it even more difficult to compare prevalence or incidence figures.
Yes, we can see big variation for a Bit Coin.
"But an enduring mystery is the big variation in the declines of closely related species.
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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