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The phrase 'big variation between' is correct and can be used in written English
You can use this phrase to describe a large difference between two things. For example: "There is a big variation between the average temperatures in the summer and winter."
Exact(4)
Fingernails grow at an average rate of just shy of 4cm a year, though there is quite a big variation between individuals.
The figures show however, that there is a big variation between hospitals.
The only big variation between the Mondeo wagon and what Jag might build is that the current X-Type has four-wheel drive and the Mondeo only gets juice to its front wheels.
The only large point on which the two analyses agree is that there is big variation between the most and least effective teachers in Los Angeles Unified.
Similar(56)
Firms like Jaguar and Mulberry have missed plans already.And the aggregate figures disguise big variations between sectors.
Analysis from the Institute for Government shows big variations between departments, with the Department for Business, Innovation and Skills, the Department for Environment, Food and Rural Affairs and the Department for Transport.
The value of donated objects such as paintings, fundraising campaigns and grants for projects such as new buildings or works of art cause big variations between years as well as between organisations.
There are big variations between the 53 countries, with a gap in life expectancy for men of 22 years between those who live in Spain and those who live in Turkmenistan.
While the impact of the worst recession since the second world war has been to push up joblessness in every continent and every country, the IMF reported big variations between countries.
When league tables of their results were first compiled in 1992, they highlighted the big variations between different schools—something that in the past parents had only guessed at.
Put another way, today's average world emissions per capita are nearly 7 tonnes of carbon-dioxide-equivalent each year, with big variations between countries: for instance, the United States emits about 24 tonnes per head while the figure for India is below 2 tonnes.
More suggestions(14)
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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