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Teaching the Median with Terms of Absolute Value, Differentiability, and Optimization

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  • Mehmet Hakan Satman

Abstract

The verbal definition of the sample median sounds a bit strange in the early Statistics courses in the context of being non-mathematical or non-functional. It is also interesting that estimators based on an analytical calculation such as the sample mean are equally strange, but not seen as strange by the students as the median estimator. In this study, we have expanded the studies on teaching the sample median with its optimization definitions. We have also shown that such definitions provide a natural way of understanding the sample median in multivariate case and regression analysis. Seeing that statistical estimators, from the simplest to the most complex, are obtained as a solution to an optimization problem can pave the way for other types of insights.

Suggested Citation

  • Mehmet Hakan Satman, 2022. "Teaching the Median with Terms of Absolute Value, Differentiability, and Optimization," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 10(1), pages 41-50, June.
    • Handle: RePEc:anm:alpnmr:v:10:y:2022:i:1:p:41-50
    DOI: https://doi.org/10.17093/alphanumeric.1041138
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    References listed on IDEAS

    as
    1. Kani Chen & Zhiliang Ying & Hong Zhang & Lincheng Zhao, 2008. "Analysis of least absolute deviation," Biometrika, Biometrika Trust, vol. 95(1), pages 107-122.
    2. A. Charnes & W. W. Cooper & R. O. Ferguson, 1955. "Optimal Estimation of Executive Compensation by Linear Programming," Management Science, INFORMS, vol. 1(2), pages 138-151, January.
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    More about this item

    Keywords

    Absolute Value; Median; Optimization; Statistics; Teaching;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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