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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Standard Deviation Question**

**From:**Marcel Tschudin

**Date:**2013 Jan 8, 11:15 +0200

Lars, you wrote: "I think the formula for (an estimated) standard deviation can be used on any distribution."

Sorry, Lars, but I do not agree with you. Yes, you can calculate the standard deviation (of an estimated normal distribution) for any distribution. The question is however whether the result makes really sense. What would this result mean if you calculate it for a data set without realising that the values in it are strongly asymmetric?

It looks like both of us have not described the limited validity of the standard deviation function the mathematical correct way. Within these general understandable explanations this was not my intention. I only wanted to make aware that the standard deviation function has limitations.

In practice one analyses often a small number of data where one only notices that they scatter around a mean value. One assumes then that these data are normal distributed and uses this concept to calculate the standard deviation. Depending on how the user interprets the result this may or may not be reasonable. In such cases the (one) standard deviation may be an indicative size useful for the purpose of comparison (e.g. as error bars). When analysing small data sets it would however be wrong to trust much the low probability values at the edges of the distribution. In order being able to recognise the "real" type of distribution in a histogram requires a large number of data. (Regarding this subject see e.g. the pdf-file from Richard B. Langley or/and the Web-page here http://www.isixsigma.com/tools-templates/normality/dealing-non-normal-data-strategies-and-tools/ )

Marcel

It looks like both of us have not described the limited validity of the standard deviation function the mathematical correct way. Within these general understandable explanations this was not my intention. I only wanted to make aware that the standard deviation function has limitations.

In practice one analyses often a small number of data where one only notices that they scatter around a mean value. One assumes then that these data are normal distributed and uses this concept to calculate the standard deviation. Depending on how the user interprets the result this may or may not be reasonable. In such cases the (one) standard deviation may be an indicative size useful for the purpose of comparison (e.g. as error bars). When analysing small data sets it would however be wrong to trust much the low probability values at the edges of the distribution. In order being able to recognise the "real" type of distribution in a histogram requires a large number of data. (Regarding this subject see e.g. the pdf-file from Richard B. Langley or/and the Web-page here http://www.isixsigma.com/tools-templates/normality/dealing-non-normal-data-strategies-and-tools/ )

Marcel