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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 7, 17:36 +0200

Good to hear that the explanations helped to understand the difference between the two standard deviations (sample and population). At this point it may be helpful to add further the following two important "details" which the contributions from Richard B. Langley and Robert Bernecky actually already indicated:

Normal distribution:

The two standard deviation functions on the calculator or in the spread sheet are only correct if the population of measured data (and the infinite number of data they belong to) are normal distributed. The standard deviation function is generally used by *assuming* that this is the case. For the scattered values when measuring a certain parameter, i.e. the "noise" in measurements (and for many other applications), this assumption may indeed be reasonable. It is however quite common that one deals with data which are actually not normal distributed (search e.g. Google for: Non-Normal Distributions). For non-normal distributed data the two functions produce wrong results, it would require a different approach. However, depending on the reason for calculating the standard deviation, the wrong value may eventually still serve as some sort of approximate estimate.

Accuracy and Precision:

When dealing with scattered data these two terms have special meanings which are important to distinguish. This Web-page here http://celebrating200years.noaa.gov/magazine/tct/tct_side1.html explains well what the two expressions really mean. Note that the standard deviation (SD) is a measure for the Precision of the data: Small SD high precision and large SD low precision. The mean and the standard deviation of a data set contain however no information at all on the Accuracy (of the mean). The Accuracy of a data set can only be evaluated by comparison with results from other measurements.

Hopefully all these explanations allow you now to use the standard deviation function more conscious.

Marcel

Normal distribution:

The two standard deviation functions on the calculator or in the spread sheet are only correct if the population of measured data (and the infinite number of data they belong to) are normal distributed. The standard deviation function is generally used by *assuming* that this is the case. For the scattered values when measuring a certain parameter, i.e. the "noise" in measurements (and for many other applications), this assumption may indeed be reasonable. It is however quite common that one deals with data which are actually not normal distributed (search e.g. Google for: Non-Normal Distributions). For non-normal distributed data the two functions produce wrong results, it would require a different approach. However, depending on the reason for calculating the standard deviation, the wrong value may eventually still serve as some sort of approximate estimate.

Accuracy and Precision:

When dealing with scattered data these two terms have special meanings which are important to distinguish. This Web-page here http://celebrating200years.noaa.gov/magazine/tct/tct_side1.html explains well what the two expressions really mean. Note that the standard deviation (SD) is a measure for the Precision of the data: Small SD high precision and large SD low precision. The mean and the standard deviation of a data set contain however no information at all on the Accuracy (of the mean). The Accuracy of a data set can only be evaluated by comparison with results from other measurements.

Hopefully all these explanations allow you now to use the standard deviation function more conscious.

Marcel