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definition of the Average- wikipedia

  • 1.  definition of the Average- wikipedia

    Posted 06-21-2022 18:40

    I was helping a friend interpret some results on a physics website.  The website included a statement about the average.
    I thought it might be helpful to cite the definition from a possibly more authoritative source, wikipedia

    here is the entry for Average on wikipedia
    https://en.wikipedia.org/wiki/Average
    I was puzzled by the  interpretation of things like the median as an average . I have over the years criticized some written documents where the median was reported but labelled as the average.

    cut/paste from the wikipedia
    For example, the average personal income is often given as the median-the number below which are 50% of personal incomes and above which are 50% of personal incomes-because the mean would be misleadingly high by including personal incomes from a few billionaires
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    I think that the average is, the average. not a median or other summary statistic. .

    that aside the  wiki does have some very interesting history of the etymology of the word average, referring to origins from  arabic and 12th century Genoa Latin etc. :)

    • Is the wikipedia wrong about referring to a median, mode etc.  as an average?


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    Chris Barker, Ph.D.
    2022 Statistical Consulting Section
    Chair-elect
    Consultant and
    Adjunct Associate Professor of Biostatistics
    www.barkerstats.com


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    "In composition you have all the time you want to decide what to say in 15 seconds, in improvisation you have 15 seconds."
    -Steve Lacy
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  • 2.  RE: definition of the Average- wikipedia

    Posted 06-21-2022 22:41
    Interesting topic.

    I "grew up" in statistics seeing multiple times and in multiple sources that the "average" had three possible designations: mean (understood to be the arithmetic mean), median or mode. I rarely use the word "average," unless the writing was speaking to an audience that would overwhelmingly expect it to be the arithmetic mean. Almost always I do not use "average," but, instead, I use mean or median. I have never found occasion to use "mode."

    Of course, I am just an average statistician, so what weight does this carry? 

    Nayak

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    Nayak Polissar
    Principal Statistician
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  • 3.  RE: definition of the Average- wikipedia

    Posted 06-21-2022 23:39
    I'm not surprised about this. Statisticians have 5 names for everything :)

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    Elaine Eisenbeisz
    Owner and Principal Statistician
    Omega Statistics
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  • 4.  RE: definition of the Average- wikipedia

    Posted 06-26-2022 01:46
    One of my triggers is the use of average suggesting "typical" when mean is intended, such as presenting the mean salary of statisticians as the salary of the average statistician (whatever that is).
    David

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    David Bristol
    Statistical Consulting Services, Inc.
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  • 5.  RE: definition of the Average- wikipedia

    Posted 06-23-2022 18:04
    I have seen "average" as a synonym for "typical" - e.g. "the average man" - hence the need to define terms better (i.e. the algebraic mean).
    My comment is more in reference to Nayak's comment "I have never found occasion to use "mode.""  When I first started teaching, I was upset by how some computer packages determined the mode - and how students might determine if a distribution is "multimodal" rather than some nuance of the number of bins, and took time to think about when a mode might be appropriate.  In some cases, it might be to note that one may be including multiple "populations" in a sample (e.g. birthweights of all infants will be bimodal in that multips will weigh less than singletons, so it may be helpful to determine a population you are interested in). The other case is in marketing, where there is a characteristic that may be bimodal, where the median and mean would not help in defining a population to market to - the example I used is hair dye - that "younger" people may dye hair for fun (I was once a red-head), or that "older" people may want to color gray hair.  Regardless, a marketing campaign to a "middle-age" would likely be less successful than two marketing campaigns to different age groups.

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    Mary Kwasny
    Professor
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  • 6.  RE: definition of the Average- wikipedia

    Posted 06-22-2022 00:25

    The entire second chapter of Darrel Huff's How to Lie with Statistics is about "choosing" average from mean, median and mode which is more about explaining the differences among them. From time to time, particularly in older texts, I see reference to different definitions of "average". Now, I am curious if it began or was popularized by Huff (who was a reporter, not a statistician).

    If there is anybody still using "average" for the median (or mode!?), I would consider this sloppy, imprecise language, bordering on linguistically incorrect.



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    Daniel Coven
    Graduate Statistics Consultant
    Daniel.Coven@asu.edu
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  • 7.  RE: definition of the Average- wikipedia

    Posted 06-22-2022 11:14
    And there is always the geometric mean.  Average is such a vague term. If we use the word average we should be very precise about what we mean, arithmetic mean presumably.

    Elizabeth Newton
    Newton Statistical Consulting





  • 8.  RE: definition of the Average- wikipedia

    Posted 06-22-2022 11:20
    Yes! So many terms, long run odds, expected value...

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    Elaine Eisenbeisz
    Owner and Principal Statistician
    Omega Statistics
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  • 9.  RE: definition of the Average- wikipedia

    Posted 06-22-2022 11:23
    Agree very much with Elizabeth!

    Arun

    (Dr Arun Chind)
    Physician and Statistician 
    Proshen Health and Risk Consulting Ltd 
    Wakefield, England 







  • 10.  RE: definition of the Average- wikipedia

    Posted 06-23-2022 20:50
    Before Huff was published I was taught that the average meant a typical value that could be the mean, median, or mode. I was taught that many people erroneously considered average as synonymous with arithmetic mean. So it did not begin with Huff.

    Naomi B. Robbins

    naomi@nbr-graphs.com

    http://www.nbr-graphs.com

    http://www.forbes.com/sites/naomirobbins/

    twitter: @nbrgraphs

    Author of Creating More Effective Graphs

     





  • 11.  RE: definition of the Average- wikipedia

    Posted 06-23-2022 19:42
    There has been quite a bit of research in the statistics education field about confusion between various terms such as average-mean-median-mode, and other collections of ambiguous terms in Statistics. You can find papers by Kaplan and Rogness and their colleagues e.g. https://doi.org/10.1080/10691898.2009.11889535 and (** shameless self-promotion alert **) papers by Dunn and Richardson and their colleagues e.g. https://doi.org/10.52041/serj.v15i1.255.

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    Alice Richardson
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  • 12.  RE: definition of the Average- wikipedia

    Posted 06-23-2022 19:53
    The New Oxford American Dictionary gives one definitions of "average" as something to the effect that it is the central or typical value, as in median, mode, or (most typically) mean. If one thinks about average as central or typical tendency, any of those statistics will suffice

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    Vicki Hertzberg
    Professor and Director
    Center for Data Science
    Nell Hodgson Woodruff School of Nursing
    Emory University
    Atlanta, GA USA
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