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"mean standard deviation" is a correct and usable phrase in written English.
You can use this phrase to refer to the average amount of variation from the mean in a set of data. For example, "The mean standard deviation of the test scores was 7.2."
Exact(7)
Error bars mean standard deviation.
M (SD), mean (standard deviation).
Quantitative variables: mean (standard deviation).
aCells show mean (standard deviation).
Mean Standard deviation Min.
aArithmetic mean (standard deviation).
Similar(50)
Value = mean ± standard deviation, n ≥ 3.
Values denote mean ± standard deviation.
b mean ± standard deviation.
aValues represent mean ± standard deviation.
All data mean ± standard deviation.
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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