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
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