https://arxiv.org/abs/2003.01973

close this message

Donate to arXiv

Please join the Simons Foundation and our generous member
organizations in supporting arXiv during our giving campaign
September 23-27. 100% of your contribution will fund improvements and
new initiatives to benefit arXiv's global scientific community.

DONATE

[secure site, no need to create account]

Skip to main content
Cornell University
We gratefully acknowledge support from
the Simons Foundation and member institutions.
 
arXiv.org > stat > arXiv:2003.01973
[                    ]

Help | Advanced Search

[All fields        ]
Search
arXiv
Cornell University Logo
[                    ] GO
quick links

  * Login
  * Help Pages
  * About

Statistics > Other Statistics

arXiv:2003.01973 (stat)
[Submitted on 4 Mar 2020]

Title:What Does the "Mean" Really Mean?

Authors:Nozer D. Singpurwalla, Boya Lai
Download PDF

    Abstract: The arithmetic average of a collection of observed
    values of a homogeneous collection of quantities is often taken
    to be the most representative observation. There are several
    arguments supporting this choice the moment of inertia being the
    most familiar. But what does this mean?
    In this note, we bring forth the Kolmogorov-Nagumo point of view
    that the arithmetic average is a special case of a sequence of
    functions of a special kind, the quadratic and the geometric
    means being some of the other cases. The median fails to belong
    to this class of functions. The Kolmogorov-Nagumo interpretation
    is the most defensible and the most definitive one for the
    arithmetic average, but its essence boils down to the fact that
    this average is merely an abstraction which has meaning only
    within its mathematical set-up.

Subjects: Other Statistics (stat.OT)
Cite as:  arXiv:2003.01973 [stat.OT]
          (or arXiv:2003.01973v1 [stat.OT] for this version)

Submission history

From: Boya Lai [view email]
[v1] Wed, 4 Mar 2020 09:51:36 UTC (7 KB)
Full-text links:

Download:

  * PDF
  * PostScript
  * Other formats

(license)
Current browse context:
stat.OT
< prev   |   next >
new | recent | 2003
Change to browse by:
stat

References & Citations

  * NASA ADS
  * Google Scholar
  * Semantic Scholar

a export bibtex citation Loading...

Bibtex formatted citation

x
[loading...          ]
Data provided by:

Bookmark

BibSonomy logo Mendeley logo Reddit logo ScienceWISE logo
(*) Bibliographic Tools

Bibliographic and Citation Tools

[ ] Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
[ ] Litmaps Toggle
Litmaps (What is Litmaps?)
( ) Code & Data

Code and Data Associated with this Article

[ ] arXiv Links to Code Toggle
arXiv Links to Code & Data (What is Links to Code & Data?)
( ) Related Papers

Recommenders and Search Tools

[ ] Connected Papers Toggle
Connected Papers (What is Connected Papers?)
[ ] Core recommender toggle
CORE Recommender (What is CORE?)
( ) About arXivLabs

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and
share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have
embraced and accepted our values of openness, community, excellence,
and user data privacy. arXiv is committed to these values and only
works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community?
Learn more about arXivLabs and how to get involved.

Which authors of this paper are endorsers? | Disable MathJax (What is
MathJax?)

  * About
  * Help

  * Click here to contact arXiv Contact
  * Click here to subscribe Subscribe

  * Copyright
  * Privacy Policy

  * Web Accessibility Assistance
  * arXiv Operational Status
    Get status notifications via email or slack