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is it possible to derive the standard deviation from data described with mean and 95% confidence interval? If I have a distribution with a mean of 2.5 (1.5-4.0), what would be the standard deviation?

Thank you

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It is not possible with only those data.

With some reasonable assumptions, the length of the confidence interval for the mean depends on:

  • Confidence level.
  • Standard deviation.
  • Sample size.

Given the confidence interval and two out of that three parameters, we could get the third one. However, in your question both standard deviation and sample size are unknown. Therefore, we would need to know how large was the sample to compute standard deviation.

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