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The phrase "a cross section of each" is correct and usable in written English.
It can be used when referring to a representative sample or a portion of different items or groups being analyzed or compared.
Example: "In our study, we collected a cross section of each demographic to ensure our findings were comprehensive."
Alternatives: "a representative sample of each" or "a sample from each".
Exact(3)
A cross section of each tooth was made 5 mm from the apex, and the samples were prepared for microscopic analysis.
This visual interpretation is confirmed by graphing the color change measurements of a cross section of each of the 12 strips both before and after immersion into water (Supporting Information, Figures S2 and S3).
Although a quota was not formally applied, care was taken to ensure that these key people represented a cross section of each community by including a range of different Afghan ethnic groups (Hazara, Tajik, Uzbek etc) and religious affiliations (Sunni, Shi'a etc) who move in different social circles [ 8].
Similar(57)
a A cross section of the graft.
"[They] represent a cross section of experience, but each [has] proven talent," said coach Warren Gatland.
The microreactor consists of eight microstructured compartments, each with a cross section of 2.28 mm×10.18 mm and 40 mm in length.
For each subsample, a cross section of the data is flagged for use as the validation set, and a new model is created by training on the remaining data which are the training set and not in the subsample.
The book's characters are a cross section of Hispanics.
But it was not a cross section of Israeli society.
Figure 8 shows a cross section of a heterojunction FET.
"I bought a cross section of 10 independent oil companies".
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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