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If making use of standard statistical notions such as arithmetic mean, do peer reviewers still expect to see a formal definition such as μ = ( Σ Xi ) / N, or is the notion so common that it'd be redundant to define it this way?

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    Before you learn to write, you learn to read. Surely if you're writing a paper for a math journal you've hopefully read papers in math journals. What do those papers do?
    – Bryan Krause
    Dec 27, 2020 at 5:44
  • Thanks, did not say it was for a math journal though. Would you formally define the arithmetic mean for a neuroscience study, for instance? Or would that be perceived as redundant and boring?
    – Jamerson2
    Dec 27, 2020 at 6:09
  • In my experience people don't write formal anything outside of math (broadly interpreted) journals.
    – Bryan Krause
    Dec 27, 2020 at 6:23
  • A paper should have all relevant information for reproducing its derivations. You need to define all symbols. If you talk about an average, perhaps it is clear, but if there is any possibility of ambiguity, you need to resolve it. E.g. variance estimators could be biased or unbiased. Etc. Dec 27, 2020 at 9:24

2 Answers 2

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You do not need to define common "notions" such as the mean.

You do need to define common symbols, such as "μ", because they are common symbols for more than one thing.

These are just broad guidelines. Each research community has its own practices. If unsure, avoid ambiguity.

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Statistical journals (and other journals that commonly use statistical results) would not usually require you to define the arithmetic mean of the sample values (called the "sample mean"). However, mu is not the standard symbol for the sample mean. The standard symbol for the mean of data values labelled with x is an x with a bar over it (and possibly a subscript N if you need to keep track of sample size). The Greek letter mu is usually used for the mean parameter for the underlying probability distribution, which is a different thing.

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