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The phrase "a big deviation" is correct and usable in written English.
It can be used to describe a significant difference or departure from a standard, norm, or expected outcome.
Example: "The results of the experiment showed a big deviation from the predicted values, prompting further investigation."
Alternatives: "a significant deviation" or "a large discrepancy."
Exact(3)
Mr. Shiokawa suggested last month that the government might break the cap, though it wanted to "avoid a big deviation" from the 30 trillion yen limit.
A fitting model implied that the diffusion coefficient had a big deviation of Fick's law and greatly influenced by the pore structure of hollow fibers.
The results show that there exists a big deviation between the actual offloading volume and the demanded volume of the fifth batch at 4 OS, in accordance with the real situation.
Similar(57)
There is a big difference between deviations in stories and outright fabrications.
This deviation can make a big difference in how well marketers can execute their plans, especially in crowded cities where a small distance can change the consumer's physical state, as well as their state of mind.
But in fact, this minor deviation can make a big difference: it means that the Earth's distance from the Sun changes over its orbit to the tune of over 5 million kilometers!
Don't get me wrong, this is a good story, but for Byron it would be considered sensational and a pretty big deviation and frankly, not quite up to snuff.
Which would make it a pretty big deviation from the past R-rated film translations of the character Frank Castle.
A slight deviation in pronunciation will make a big difference.
Even a deviation of a quarter of a mile can make a big difference, he added.
What a big difference.
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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