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"a random sample of" is a correct and usable phrase in written English.
It is typically used to describe a subset of data or objects that has been selected at random from a larger group. This phrase is commonly used in research studies and statistical analysis. Example: In order to accurately measure the effects of the new medication, a random sample of 100 patients was selected from the total population of 500 patients.
Exact(60)
The survey has a ±3.1 percentage-point margin of sampling error for a random sample of this size.
That was a random sample of low-income students.
We also surveyed a random sample of 236 customers.
"Try finding a random sample of Jews by phone," Rivers says.
ICM Research interviewed a random sample of 505 people by telephone on 15th April 2010.
That's what a random sample of people in our office consider the worst Halloween costume imaginable.
Population: A random sample of Estonian adult population (N=997).
Each dot represents a SNP from a random sample of 100,000 SNPs.
In the fall of 1968 we interviewed a random sample of 155 Phoenix House residents.
One asks a random sample of employers how many people are on their payroll.
The study involves a random sample of about 50,000 Union Army veterans.
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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