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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:**Richard B. Langley

**Date:**2013 Jan 5, 12:27 -0400

;-) There's also Inside GNSS, whose editor is the former editor of GPS World: http://www.insidegnss.com/ On 5-Jan-13, at 12:14 PM, Thomas Sult wrote: > The thing of general use to me is ... WOW there is a GPS world > magazine! > > Tom Sult > Sent from my iPhone > > On Jan 5, 2013, at 8:10, "Richard B. Langley"wrote: > >> Warning: Slightly off topic; delete if not interested. >> >> Not wanting to muddy the waters, but for those interested, here is >> a link to an article on GPS precision and accuracy that appeared in >> my GPS World column a few years ago: >> http://gge.unb.ca/test/gpsworld.may10.pdf >> >> There may be something of general use that could also be considered >> when looking at the statistics of CN observations. >> >> -- Richard Langley >> >> On 5-Jan-13, at 6:24 AM, Marcel Tschudin wrote: >> >>> ... when should I be using stdDevPop and when should I be using >>> stdDevSamp? >>> >>> I try to explain the difference in a general understandable way. >>> >>> The calculation of the standard deviation requires to know the >>> mean value. The difference between the two functions results from >>> whether the mean value from the given data set represents the >>> exact mean or is an estimated mean. >>> >>> If the given data represent all of them, i.e. they represent the >>> complete population, then their mean value is exact and the >>> standard deviation is calculated on the basis of an exact mean >>> value. However, to have a complete population and know the exact >>> mean is rather the exception. It is more likely that we have some >>> selected (measured) values out of a greater population which is >>> assumed infinite and where the exact mean value is unknown; the >>> mean value of the given data set represents therefore an estimate, >>> and the standard deviation is calculated on the basis that the >>> mean value of the data set is an estimate. >>> >>> The difference between stdDevPop and stdDevSamp is therefore: >>> stdDevPop() calculates the standard deviation understanding that >>> the entered data are all of the population and that the mean value >>> of the entered data is the exact mean value. >>> stdDevSamp() calculates the standard deviation understanding that >>> the entered data represent a sample from an infinite population >>> and that the mean value of the entered data represents therefore >>> an estimation for an infinite population. >>> >>> Now, what does the standard deviation mean? This is a measure for >>> a probability that an other data (an other measurement taken under >>> the same condition) will be within (or outside) certain limits. If >>> we look at Greg's last data and designate with the mean value >>> = 0.575' and with Sx = 0.159' the standard deviation of his >>> sample with 20 measurements, then >>> >>> +/- 1Sx (+/- one standard deviation) >>> means that 68% or about 2 out of 3 other measurements of the same >>> type are expected to be within (or about 1 out of 3 outside) the >>> range between 0.416' and 0.734'. >>> >>> Generally the results provide the mean and one standard deviation >>> as above. However, these values allow representing the result also >>> related to other probabilities, like e.g. >>> >>> +/- 2Sx (+/- two standard deviation) >>> means that 95% other measurements of the same type are expected to >>> be within (or about 1 out of 20 outside) the range between 0.257' >>> and 0.893'. >>> >>> +/- 3Sx (+/- three standard deviation) >>> means that 99.7% other measurements of the same type are expected >>> to be within (or 3 out of 1000 outside) the range between 0.098' >>> and 1.052'. >>> >>> I hope it helps. >>> >>> To those of you who are familiar with the subject: Please feel >>> free to improve or even correct these general explanations where >>> necessary. Thank you. >>> >>> Marcel >> >> ----------------------------------------------------------------------------- >> | Richard B. Langley E-mail: >> lang---.ca | >> | Geodetic Research Laboratory Web: http://www.unb.ca/GGE/ >> | >> | Dept. of Geodesy and Geomatics Engineering Phone: +1 506 >> 453-5142 | >> | University of New Brunswick Fax: +1 506 >> 453-4943 | >> | Fredericton, N.B., Canada E3B >> 5A3 | >> | Fredericton? Where's that? See: http:// >> www.fredericton.ca/ | >> ----------------------------------------------------------------------------- >> >> >> >> > > > ----------------------------------------------------------------------------- | Richard B. Langley E-mail: lang---.ca | | Geodetic Research Laboratory Web: http://www.unb.ca/GGE/ | | Dept. of Geodesy and Geomatics Engineering Phone: +1 506 453-5142 | | University of New Brunswick Fax: +1 506 453-4943 | | Fredericton, N.B., Canada E3B 5A3 | | Fredericton? Where's that? See: http:// www.fredericton.ca/ | -----------------------------------------------------------------------------