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Statistical Techniques and 6 Sigma Range

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Author  Topic: Range 
Don Winton Forum Contributor Posts: 498 
posted 13 February 1999 10:00 AM
Found this interesting: Snip In response to Range: {Not Mine, Don} Dona, you and your husband is right. The method you used of subtracting the smallest data value from the largest is the correct way of calculating the sample range. The only possible alternative I could think of would be if you wanted to construct an unbiased estimate of the population range. For example, suppose you have a uniform distribution between A and B, with both limits being unknown. You then calculate from the data, the sample range, r = largest minus smallest. This r necessarily is less than the population range, R=BA. To obtain an unbiased estimate of R, you need to multiply r by (N+1)/(N1), where N is the sample size. Note that this is a multiplicative factor, not an additive factor. In short, I can't think of any reason to add one to the sample range. End Snip
quote: Thoughts, Regards, IP: Logged 
John C Forum Contributor Posts: 134 
posted 16 February 1999 09:50 AM
Don, My statistical training was always sketchy and is now very rusty, so I offer this only as a possible clue to the problem. I canāt vouch for itās validity; For variables, the range is highest minus lowest. Thatās the way I was taught. eg measurement in inches; Highest 10, lowest 5. 10  5 = 5. For attributes, itās the number of consecutive attributes in the sample (or potential attributes, if all possible have not been observed) that gives the range, eg; marks on a screen; Highest sample had 10, lowest had 5. The range can be considered to include; 5, 6, 7, 8, 9 and 10. So thatās 6 levels of attributes. 105 = 5. 5+1 = 6. rgds, John C IP: Logged 
Kevin Mader Forum Wizard Posts: 575 
posted 16 February 1999 01:44 PM
Don, As part of figuring Sigma, finding the estimation and unbiased estimation is merely the result of data from a population or from a sample. As always, the sample always has potential error beyond the population estimate and n1 is normally used. Not sure why to add/subtract a 1 for the Range though. JC's explanation seems reasonable, but I can not confirm. IP: Logged 
Don Winton Forum Contributor Posts: 498 
posted 16 February 1999 09:38 PM
quote: Agreed. I believe the response cited was probably considering this example. Or rather, see below.
quote: It is also possible that the respondent was thinking sigma rather than range. I posted this in order to see what the responses would be. Many thanks, guys. Regards, IP: Logged 
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