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The phrase "about every fourth" is correct and usable in written English.
It can be used to indicate a frequency or occurrence that happens approximately every fourth instance in a series.
Example: "In the survey, we sampled about every fourth participant to gather diverse opinions."
Alternatives: "approximately every fourth" or "roughly every fourth".
Exact(12)
Although these results are not directly comparable due to methodological differences in the assessment of pain intensity (VAS versus faces) and pain frequency (one month versus one week recall period), these results indicate that about every fourth or fifth adolescent back problem might be serious.
You can say that about every fourth quarter so far".
"In the wild, on average, about every fourth gray squirrel born will be black".
Somehow I managed to approximate the proper movements on about every fourth or fifth stroke.
"Race fans for McCain," however, is stuck on about every fourth person here.Gary Mozingo is wearing one.
"This is about every fourth person you see," said Mr. Weiss, pointing at the Casablanca, a tousled look reminiscent of Mick Jagger circa 1973.
Similar(47)
We talked for ages about Pine Gap except I was only catching about every ninth word.
About every sixth biopsy contained lymphoid aggregations with germinal center-like morphology.
Like just about every fourth-year medical student, Nicole Fanarjian recently made the rounds of hospitals in search of a residency program that would train her for her specialty: obstetrics-gynecology.
About every third day, he's clean-shaven.
About every third sentence began with "By the way".
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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