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The phrase "were equally distributed" is correct and usable in written English.
It is commonly used to express the concept of something being divided equally across a group, or a proportion of something staying the same across different places or people. For example, "The resources were equally distributed among the people of the town."
Exact(60)
Males and females were equally distributed across GROUP and SIDE (χ2 = 0.79, P = 0.94).
So the votes were equally distributed among all the candidates, and the president was not re-elected.
We used forced-choice trials for this analysis, because they were equally distributed across the levels of these factors.
Patients were equally distributed for all demographic and intraoperative characteristics.
Additionally, the DIF items were equally distributed among the groups.
The 2448 samples were equally distributed (408 per class).
However, habitat qualities were equally distributed across the elevation gradient.
Shares were equally distributed in order to avoid ownership concentration among Russia's mafiosos and rich bureaucrats.
Low and high spatial ability participants were equally distributed in the visual and verbal groups.
Immigrants were equally distributed and came from Romania, Albania, Morocco, People's Republic of China, and Germany.
Patients were equally distributed in the infection and non-infection groups (five in each group).
More suggestions(12)
were equitably distributed
were similarly distributed
were also distributed
participated equally distributed
were simultaneously distributed
were uniformly distributed
were identically distributed
were fairly distributed
were equally dispersed
are likewise distributed
almost equally distributed
is similarly distributed
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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