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  Statistical Techniques and 6 Sigma
  Range

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Author Topic:   Range
Don Winton
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Posts: 498
From:Tullahoma, TN
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posted 13 February 1999 10:00 AM     Click Here to See the Profile for Don Winton   Click Here to Email Don Winton     Edit/Delete Message   Reply w/Quote
Found this interesting:

-------Snip-------
I am taking my first ever statistics course. However as an elementary teacher, I did teach such concepts as mean, median, mode and range. In this course we learned that range is the highest score/data minus the lowest then add 1 to the difference. I had taught that the way to figure out the range was to simply subtract the lowest score/data from the highest. This is also the way it is done in the statistics program I have. My husband (a statistician) agrees with my method. Which method is correct? If the first method is correct, please explain the reason one adds 1 to the difference. Thanks!

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=B-A. To obtain an unbiased estimate of R, you need to multiply r by (N+1)/(N-1), 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:
In this course we learned that range is the highest score/data minus the lowest then add 1 to the difference. I had taught that the way to figure out the range was to simply subtract the lowest score/data from the highest.

Thoughts,

Regards,
Don

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John C
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Posts: 134
From:Cork City, Ireland
Registered: Nov 98

posted 16 February 1999 09:50 AM     Click Here to See the Profile for John C   Click Here to Email John C     Edit/Delete Message   Reply w/Quote
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. 10-5 = 5. 5+1 = 6.
rgds, John C

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Kevin Mader
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Posts: 575
From:Seymour, CT USA
Registered: Nov 98

posted 16 February 1999 01:44 PM     Click Here to See the Profile for Kevin Mader   Click Here to Email Kevin Mader     Edit/Delete Message   Reply w/Quote
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 n-1 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.

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Don Winton
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Posts: 498
From:Tullahoma, TN
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posted 16 February 1999 09:38 PM     Click Here to See the Profile for Don Winton   Click Here to Email Don Winton     Edit/Delete Message   Reply w/Quote
quote:
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. 10-5 = 5. 5+1 = 6.

Agreed. I believe the response cited was probably considering this example. Or rather, see below.

quote:
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 n-1 is normally used.

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,
Don

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