William B. Ware said on 10/5/01 8:58 AM:
>I don't think I understand your argument... Are you saying that the
>"descriptive statistic" should be invariant over scale?
>
>Anyway, more to the point... the "add one" is an old argument based on the
>notion of "real limits." Suppose the range of scores is 50 to 89. It was
>argued that 50 really goes down to 49.5 and 89 really goes up to
>89.5. Thus the range was defined as 89.5 - 49.5... thus the additional
>one unit...
>
>Personally, I don't subscribe to this position... It assumes that the low
>score is always toward the low end of its value and that the upper value
>is always toward the high end of its value... Sort of a maximum range... I
>prefer not including the additional one unit...
Another problem with the add one notion based on real limits is that it
does not necessarily apply to many real limits situations.
The way I introduce real limits to a class is to pass around a piece of
paper asking each student to write down their weight. The paper comes to
the front of the room while I go through the announcements, review
questions, etc. I then write all the numbers on the board and point out
that nearly all the students wrote down their weight to the nearest 5th
pound. A few went to the nearest single pound. We then discuss in the
context of real limits how a weight of 125 pounds represents weights from
122.5 to 127.5, etc. Then we can discuss how all measurements are
necessarily representing ranges of values which are beyond the precision
of the measuring system.
Note, if the idea of real limits necessitating the adding one to the
calculation of the range were valid, then in the case of figuring the
range of weights for a class, I would do well to add 5. In all cases the
amount added to the range calculation depends on the precision of
measurement, which becomes a problematic notion, IMO.
Paul
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