American Journal of Computation, Communication and Control
Manuscript Information
 
 
Generalized fG -Mean: Derivation of Various Formulations of Average
American Journal of Computation, Communication and Control
Vol.5 , No. 3, Publication Date: Nov. 22, 2018, Page: 101-108
219 Views Since November 22, 2018, 88 Downloads Since Nov. 22, 2018
 
 
Authors
 
[1]    

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

 
Abstract
 

Average is a basic concept and averaging is a basic technique/tool behind the most of the measures associated to characteristics of data. A number of definitions/formulations of average have been developed so far. These definitions/formulations have been found suitable to be used in different situations. There are still many situations where there are scarcities of definitions/formulations of average to deal with the respective situations. It has been found possible to compose general definition of average so that the definitions/formulations of average, already developed, can be obtained/derived from it as well as more new definitions/formulations of average can be obtained/derived from it. One general definition of average, termed in this paper as Generalized fG -Mean, has been introduced with a view to obtain different definitions/formulations of average. Applying the technique, some definitions/formulations have been derived for various types of averages. This paper describes this general definition and the derivation of a number of definitions/formulations of average.


Keywords
 

Average, Generalized fG -Mean, Existing Means, Derivations


Reference
 
[01]    

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

[02]    

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

[03]    

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

[04]    

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.

[05]    

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

[06]    

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

[07]    

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

[08]    

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.

[09]    

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

[10]    

Dhritikesh Chakrabarty (2018): “Derivation of Some Formulations of Average from One Technique of Construction of Mean”, American Journal of Mathematical and Computational Sciences, 3 (3), 62 – 68. Available in http://www.aascit.org/journal/ajmcs.

[11]    

Dhritikesh Chakrabarty (2018): “One Generalized Definition of Average: Derivation of Formulations of Various Means”, Journal of Environmental Science, Computer Science and Engineering & Technology, Section C, (E-ISSN: 2278 – 179 X), 7 (3), 212 – 225, Also available in www.jecet.org.

[12]    

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

[13]    

Kolmogorov Andrey (1930): “On the Notion of Mean”, in “Mathematics and Mechanics” (Kluwer 1991), 144 – 146. [7]

[14]    

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

[15]    

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

[16]    

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

[17]    

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.

[18]    

Dhritikesh Chakrabarty (2018): “fH -Mean: One Generalized Definition of Average”, Journal of Environmental Science, Computer Science and Engineering & Technology, Section C, (E-ISSN: 2278 – 179 X), 7 (4), 301 – 314, Also available in www.jecet.org.





 
  Join Us
 
  Join as Reviewer
 
  Join Editorial Board
 
 
  ISSN Online: 2375-3943
 
 
Regeister
 
 
Submission
 
 
Membership