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The phrase "a balanced sum of" is correct and usable in written English.
It can be used when discussing a combination of elements that are equal or proportionate in some way, often in contexts like finance, mathematics, or philosophy.
Example: "The project requires a balanced sum of creativity and practicality to succeed."
Alternatives: "an equitable total of" or "a proportional combination of".
Exact(3)
Groups would be assembled to combat the problem, ensuring that the scientific record reflected a balanced sum of the evidence.
The goal is to determine open service facilities and their service capacities, and to assign customers to primary and backup facilities in order to maximize an aggregated performance measure, which is a balanced sum of the customers' and the system owner's criteria.
A simple way to heuristically combine prior information is to multiply the contribution of each prior by a constant α p that measures the belief in the quality/relevance of each prior S p and consider a balanced sum of all self-informations.
Similar(57)
However, this is actually the balanced sum of favorable and unfavorable terms, whose values are much larger – about +60% and −55%, respectively, of the total score (see Figure 6B).
Culled litters contained a balanced amount of males and females.
Eat a balanced amount of protein every day.
Eat a balanced diet of meat and vegetables.
A balanced discussion of the issues.
A balanced view of China's trade.
A balanced range of interests, from photography to scuba diving.
I have a balanced way of hating everyone [laughs].
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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