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"represents the norm" is correct and usable in written English.
You can use it when you want to talk about something that is typical or standard for a particular group. For example, "Despite his young age, his maturity level represents the norm for people in his profession."
Exact(18)
On the contrary, the company represents the norm.
The modes of digital delivery vary, but the method used by Technology Review fairly represents the norm.
The situation at Los Angeles Southwest, without question, more closely represents the norm among community colleges around the country.
If Shoppers is the best-case scenario for corner stores, a mile down the road, Simpson Food Mart represents the norm.
||.|| represents the norm operator.
Where ‖·‖ represents the norm Frobenius.
Similar(42)
These inaccurate forecasts more represent the norm than the exception.
When teenagers incorrectly assume that certain extreme behaviors represent the norm, it can influence the behaviors of the majority (pdf).
Andrew Newbury, head of the family department at Pannone Solicitors, said: "Those currently over the age of 60 are the last generation for whom marriage would have represented the norm.
Many of you will find these developments absurd or pathological, but let's not forget that the contemporary notion of relationships as romantic has not always represented the norm – in fact, love as we define it today is a fairly recent idea.
However, TAO foresees limited support for representing the norm concepts and the different agent architectures.
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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