Poll of Usage of the Word, "Average"
aruzinsky
central tendency," e.g., see http://en.wikipedia.org/wiki/Average .
Under this definition, the median is a type of average.
Have you ever used "average" in that sense"
Honestly, I have never met anyone in mathematics, engineering or
science who used "average" in that sense. When I (electrical
engineer) mean measure of central tendency, I say "measure of central
tendency." When I say "average" (without other modifiers) I usually
mean a sum divided the number of terms. When the terms are random
variables, I sometimes say "sample mean." I Iooked for "average" in
the indexes of several statistics books. I could only find one
incidence which was in the context of "average distance." Apparently,
statisticians rarely say "average."
David Winsemius
4433-bdb7-f...@e4g2000hsg.googlegroups.com:
> A lot of references define "average" as synonymous with "measure of
> central tendency," e.g., see http://en.wikipedia.org/wiki/Average .
> Under this definition, the median is a type of average.
>
> Have you ever used "average" in that sense"
I don't, but I have seen justifications for such use. See:
<http://economicsbulletin.vanderbilt.edu/2004/volume3/EB-04C10011A.pdf>
The median minimizes one Minkowski norm, sum(abs(x_i-m)), while the
arithmetic mean minimizes another, sum((x_i-am)^2). Take your pick.
> Honestly, I have never met anyone in mathematics, engineering or
> science who used "average" in that sense. When I (electrical
> engineer) mean measure of central tendency, I say "measure of central
> tendency." When I say "average" (without other modifiers) I usually
> mean a sum divided the number of terms. When the terms are random
> variables, I sometimes say "sample mean." I Iooked for "average" in
> the indexes of several statistics books. I could only find one
> incidence which was in the context of "average distance." Apparently,
> statisticians rarely say "average."
This is really a replay of a question (or assertion) that generated an
acrimonious thread a year or two ago in the sci.stat.* groups.
See threads:
Message-ID: <pN0Ag.2619$No6....@news.tufts.edu>
Message-ID: <1154546044....@m73g2000cwd.googlegroups.com>
When I want to specify the sum(x_i)/n, I say arithmetic mean or
arithmetic average. You would, of course, be free to rewrite the
Wikipedia article.
--
David Winsemius
kcstats
wrote:
> On Sat, 22 Dec 2007 10:22:00 -0800 (PST), aruzinsky
>
> <aruzin...@general-cathexis.com> wrote:
> >A lot of references define "average" as synonymous with "measure of
> >central tendency," e.g., seehttp://en.wikipedia.org/wiki/Average.
> >Under this definition, the median is a type of average.
>
> >Have you ever used "average" in that sense"
>
>
> Defining median as a type of average is confusing. Median can be equal
> to average but it is never a type of average.
>
> Steve
>
> --
> Neural Planner Software Ltd
>
> http://www.easynn.comhttp://www.tropheus.demon.co.uk
Well actually, the median is an extreme example of a "trimmed mean"; a
type of arithmetic mean where you first throw out a percentage of the
largest and smallest values in your data set and then average those
left. Tukey liked these.
When the press reports on the "average American family", or "average
price of a house", and many other items, do you think they are always
refering to the arithemetic mean? Seems doubtful. Sometimes they are
even accurate and report the median price of houses.
Here is the first definition of average found in Bookshelf "A
number that typifies a set of numbers of which it is a function."
Excerpted from The American Heritage® Dictionary of the English
Language, Third Edition © 1996 by Houghton Mifflin Company.
Electronic version licensed from INSO Corporation; further
reproduction and distribution in accordance with the Copyright Law of
the United States. All rights reserved.
So you can be the judge, but in general use I suspect when somewhen
says "average" they are thinking more often of a median than a mean.
David L. Wilson
"aruzinsky" <aruz...@general-cathexis.com> wrote in message
news:eb821d14-2bb4-4433...@e4g2000hsg.googlegroups.com...
>A lot of references define "average" as synonymous with "measure of
> central tendency," e.g., see http://en.wikipedia.org/wiki/Average .
> Under this definition, the median is a type of average.
>
> Have you ever used "average" in that sense"
>
> Honestly, I have never met anyone in mathematics, engineering or
> science who used "average" in that sense.
I have seen it used that way but not frequently. Other people use it to use
the "mean". I have always consider it best when teaching statistics to
avoid the term "average" and explain why.
...
I Iooked for "average" in
> the indexes of several statistics books. I could only find one
> incidence which was in the context of "average distance." Apparently,
> statisticians rarely say "average."
True--statisticians almost always say "mean", "arithmetic mean" (often when
there is a chance of confusion with "geometric mean" or "expected value"
(often when calculating the mean of an expression).
Anon.
gives an example of the use of "average" to include the median.
We rarely use average because it is a vague term, covering a host of
different measures of central tendency. I use it when that sort of
vagueness is required, i.e. when I don't want to be specific about the
type of average.
In the technical literature, one should be careful about its use, but
out in the real world, it's probably better in general to "average",
rather than (say) "arithmetic mean". Well, unless you want to scare
people. :-)
Bob
--
Bob O'Hara
Department of Mathematics and Statistics
P.O. Box 68 (Gustaf Hällströmin katu 2b)
FIN-00014 University of Helsinki
Finland
Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
Fax: +358-9-191 51400
WWW: http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results - EEB: www.jnr-eeb.org
aruzinsky
>
> When the press reports on the "average American family", or "average
> price of a house", and many other items, do you think they are always
> refering to the arithemetic mean? Seems doubtful. Sometimes they are
> even accurate and report the median price of houses.
>
Yes, because that is the American layman's concept of average. I
think that is what I was taught in elementary school. Add to that the
laymen phrase, "averages out." Who says, "medians out" or "central
tendencies out?"
Personally, I prefer "average" to "arithmetic mean" because it is
shorter. If I want to be vague, I say "sort of average." Sometimes I
use "simple average" within the context of weighted averages to
indicate equal weights.