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Mean, What do You Mean?

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  • Miguel de Carvalho

Abstract

When teaching statistics we often resort to several notions of mean, such as arithmetic mean, geometric mean, and harmonic mean, and hence the student is often left with the question: The word mean appears in all such concepts, so what is actually a mean? I revisit Kolmogorov's axiomatic view of the mean, which unifies all these concepts of mean, among others. A population counterpart of the notion of regular mean, along with notions of regular variance and standard deviation will also be discussed here as unifying concepts. Some examples are used to illustrate main ideas.

Suggested Citation

  • Miguel de Carvalho, 2016. "Mean, What do You Mean?," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 270-274, July.
    • Handle: RePEc:taf:amstat:v:70:y:2016:i:3:p:270-274
    DOI: 10.1080/00031305.2016.1148632
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    References listed on IDEAS

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    1. Gelman, Andrew & Nolan, Deborah, 2002. "Teaching Statistics: A Bag of Tricks," OUP Catalogue, Oxford University Press, number 9780198572244.
    2. Gelman, Andrew & Nolan, Deborah, 2002. "Teaching Statistics: A Bag of Tricks," OUP Catalogue, Oxford University Press, number 9780198572251.
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    Cited by:

    1. Feehan, Dennis & Wrigley-Field, Elizabeth, 2020. "How do populations aggregate?," SocArXiv 2fkw3, Center for Open Science.
    2. Mátyás Barczy & Zsolt Páles, 2023. "Limit Theorems for Deviation Means of Independent and Identically Distributed Random Variables," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1626-1666, September.
    3. Clive Hunt & Ross Taplin, 2019. "Aggregation of Incidence and Intensity Risk Variables to Achieve Reconciliation," Risks, MDPI, vol. 7(4), pages 1-14, October.
    4. Guerrero, Victor M. & Solis-Lemus, Claudia, 2020. "A generalized measure of dispersion," Statistics & Probability Letters, Elsevier, vol. 164(C).
    5. Curto, José Dias & Serrasqueiro, Pedro, 2022. "Averaging financial ratios," Finance Research Letters, Elsevier, vol. 48(C).
    6. Adam Gorajek, 2022. "Quasilinear‐mean regression," Journal of Economic Surveys, Wiley Blackwell, vol. 36(5), pages 1288-1310, December.
    7. Dennis Feehan & Elizabeth Wrigley-Field, 2021. "How do populations aggregate?," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 44(15), pages 363-378.

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