This is news to me - I have only ever heard the range defined as 'maximum - minimum' (and then usually wiped out as a mostly useless statistic......)
I usually point out to students that in everyday language the word 'range' is used for the interval - as in 'prices for cabbages ranged from $1 to $2.50', so the statistical usage is (another) one of these words with a different meaning in the field. For a continuous (numeric) variable, the range only makes sense using the max - min definition. If the min is 27.324 and the max is 33.654, the range is 6.333. For a discrete (numeric) variable, you can argue that the concept of 'range' requires continuity, so that we have to assume the values are rounded. So for exam marks, recorded to the nearest per cent, a max of 97 is assumed to be rounded from somewhere in the interval 96.5 to 97.5; a min of 35 is likewise considered to be rounded from 34.5 to 35.5. With this model, the max value may have been as high as 97.5 and the min as low as 34.5, so the range is calculated as 97.5 - 34.5. This gives you your +1 calculation - that is, it is a correction for continuity. Regards, Alan jeff rasmussen wrote: > > Dear statistically-enamored, > > There was a question in my undergrad class concerning how to define the > range, where a student pointed out that contrary to my edict, the range was > "the difference between the maximum & minimum". I'd always believed that > the correct answer was the "difference between the maximum & minimum plus > one"; and irrespective of what the students' textbook and also SPSS said > (when I ran some numbers through it) I thought that was the commonly > accepted answer. I favor the "plus one" account as I feel that it balances > out the "minus one" of degrees of freedom and thus puts the Tao correctly > in balance. I asked a colleague who also came up with the same answer. > Below in I and II are answers from internet sites that also agree. > > There are also however some sites that define it nakedly as "the > difference between the maximum & minimum"; my theory is that the Evil SPSS > Empire bought them off as part of their plan for world domination.... > > Finally, we have a waffler's answer in III below... > > Curious to hear what you think about this defining issue for our times. > > best, > > JR > > from http://www.cuny.edu/tony/edstat22.html > > I. Measures of Dispersion or Spread > > Range - is the difference between the highest and lowest values in a group > of values plus one. For example, the range of the following group of values > 60,70,80,90,100 is 41 and is calculated by subtracting the lowest value > (60) from the highest value (100) = 40 plus 1 = 41. > > from http://www.uwsp.edu/psych/stat/5/CT-Var.htm#II1 > > II. Range > > As we noted when discussing the rules for creation of a grouped frequency > distribution, the range is given by the highest score in the distribution > minus the lowest score plus one. > > R = XH - XL + 1 > > from http://luna.cas.usf.edu/~rasch/stat.html > > III. Measures of Dispersion > > Range: The Inclusive Range is the highest score minus the lowest score in a > distribution plus 1. If the highest score on an examination is 97 and the > lowest score 65, the range is 33. The plus 1 correction captures the values > from 97.49 to 64.50. The Exclusive Range is just the highest score minus > the lowest score. In the above example 32. > > Jeff Rasmussen > http://www.symynet.com > website & graphic design > quantitative software > spirit of tao te ching paperback & taoism > > ================================================================= > Instructions for joining and leaving this list and remarks about > the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ > ================================================================= -- Alan McLean ([EMAIL PROTECTED]) Department of Econometrics and Business Statistics Monash University, Caulfield Campus, Melbourne Tel: +61 03 9903 2102 Fax: +61 03 9903 2007 ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
