American Journal of Mathematical and Computational Sciences  
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Derivation of Some Formulations of Average from One Technique of Construction of Mean
American Journal of Mathematical and Computational Sciences
Vol.3 , No. 3, Publication Date: Jun. 1, 2018, Page: 62-68
524 Views Since June 1, 2018, 159 Downloads Since Jun. 1, 2018

Dhritikesh Chakrabarty, Department of Statistics, Handique Girls’ College, Gauhati University, Guwahati, India.


Average is a vital measure which is used not only in research but almost in every day to day work. A number of definitions/formulations are available to be used in different situations. On the other hand, it is possible to construct more and more definitions/formulations of average by a single technique and one such technique has been identified for construction of definition/formulation of average. A number of definitions/formulations of average have been constructed by the technique identified. This paper describes the definitions/formulations of average constructed in the study.


Average, Definitions, Formulations, Construction, One Technique


Bakker Arthur (2003): “The early history of average values and implications for education”, Journal of Statistics Education, 11 (1), 17─26.


Cantrell David W. (...........): “Pythagorean Means”, Math World.


Cook John (2017): “Unicode / LaTeX conversion”, John Cook Consulting.


Cornelli G., McKirahan R., Macris C. (2013): “On Pythagoreanism”, Berlin, Walter de Gruyter.


de Carvalho Miguel (2016): “Mean, what do you Mean?”, The American Statistician, 70, 764‒776.


John Bibby (1974): “Axiomatisations of the average and a further generalisation of monotonic sequences”, Glasgow Mathematical Journal, 15, 63–65.


Kendall D. G. (1991): “Andrei Nikolaevich Kolmogorov. 25 April 1903-20 October 1987”, Biographical Memoirs of Fellows of the Royal Society, 37, 300–326.


Kolmogorov Andrey (1930): “On the Notion of Mean”, in “Mathematics and Mechanics” (Kluwer 1991), 144 – 146.


Kolmogorov Andrey (1933): “Grundbegriffe der Wahrscheinlichkeitsrechnung (in German), Berlin: Julius Springer.


Krugman Paul (2014): “The Rich, the Right, and the Facts: Deconstructing the Income Distribution Debate”, The American Prospect.


Nastase Adrian S. (2015): “How to Derive the RMS Value of Pulse and Square Waveforms”,


O'Meara Dominic J. (1989): “Pythagoras Revived: Mathematics and Philosophy in Late Antiquity”, ISBN 0-19-823913-0, Clarendon Press, Oxford.


Parthasarathy K. R. (1988): “Obituary: Andrei Nikolaevich Kolmogorov”, Journal of Applied Probability, 25 (2), 445–450.


Plackett R. L. (1958): “Studies in the History of Probability and Statistics: VII. The Principle of the Arithmetic Mean”, Biometrika, 45 (1/2), 130-135.


Ray John (2015): “A Collection of English Words Not Generally Used”, London: H. Bruges.


Riedweg Christoph (2005): “Pythagoras: his life, teaching, and influence (translated by Steven Rendall in collaboration with Christoph Riedweg and Andreas Schatzmann, Ithaca)”, ISBN 0-8014-4240-0, Cornell University Press.


Rietz H. L. (1934): “Review: Grundbegriffe der Wahrscheinlichkeitsrechnung by A. Kolmogoroff”, Bull. Amer. Math. Soc., 40 (7), 522–523.


Svarovski Ladislav (2015): “Solid-Liquid Separation”, Google.


Youschkevitch A. P. (1983): “A. N. Kolmogorov: Historian and philosopher of mathematics on the occasion of his 80th birfhday”, Historia Mathematica, 10 (4), 383–395.


Weisberg H. F. (1992): “Central Tendency and Variability”, (ISBN: 0-8039-4007-6), Sage University book.

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