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The phrase "more evenly distributed" is correct and usable in written English.
It can be used to indicate the spreading out of something (ex. income, resources, etc.) over a larger area or to a greater number of people. For example, "The company implemented a policy to ensure that profits were more evenly distributed among its employees."
Exact(60)
Female age distribution is more evenly distributed.
Population distribution in Kisii was more evenly distributed than that in Kwale (Figure 1a).
Also the potential distribution of the entire pipeline becomes more evenly distributed.
Playing minutes are more evenly distributed.
Here Wagner more evenly distributed the vocal demands on his ill-fated hero and heroine.
Some producers have noted that the Tony Awards were more evenly distributed than in years past.
It is therefore unlikely to pass until the country's population is more evenly distributed geographically.
Dramatic increases in longevity and health coincided with rising and more evenly distributed prosperity.
He has changed education funding so that it is more evenly distributed.
Comparable victories in the past have shown a more evenly distributed swing.
Britain would be a better place if growth were more evenly distributed around the country.
More suggestions(15)
more fairly distributed
more regularly distributed
more evenly dispersed
more universally distributed
more smoothly distributed
more evenly distribute
more evenly balanced
more evenly split
more evenly contested
more evenly spread
more evenly matched
more evenly fought
more evenly shared
more evenly poised
more evenly written
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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