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I am an ESL editor and I came across a manuscript where the authors mentioned a mean Health Assessment Questionnaire score of 0.47±0.64. This seemed odd to me because the (-) part would go into negative. It is possible that the number of data elements is small and the author used the sample formula rather than the population formula for standard deviation.

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  • Please link your sources.
    – Thomas
    Oct 30, 2020 at 13:23
  • My apologies. I cannot. It is a manuscript I am editing. Unpublished.
    – sciencejedi
    Oct 31, 2020 at 2:01

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It's common for people to use mean and standard deviation in situations where it doesn't make a lot of sense. Sometimes it's okay, but yes it can lead to weird behavior like you've described. You should not interpret "+/-" here to mean that the values range from 0.47-0.64 to 0.47+0.64, just that the standard deviation is 0.64. Whether it makes sense to think of a standard deviation for these data is another matter.

This doesn't have anything to do with sample vs population standard deviation. Imagine your data are six 0s and two 2s:

[0 0 0 0 0 0 2 2]

The mean is 0.5. The standard deviation is about 0.9. You could report that as 0.5 +/- 0.9 but that doesn't really describe the data very well.

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  • Thank you very much. That really answered my question perfectly!
    – sciencejedi
    Oct 31, 2020 at 2:00

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