By Kardi Teknomo, PhD.
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There are so many averages and means. Mean is function to map input of positive real numbers into somehow a midvalue, or expected value. The midvalue or expected value is also a positive real number. This tutorial consists of two parts. The first part shows some famous of means or averages. In the second part, I derived fundamental relationship between averages of measurement sequence. I also proposed average composition diagram and fundamental theorem on average that can be used to obtain the relationship between timeaverage, delayedaverage, movingaverage and delayedmovingaverage.
Many performance indicators in information fusion, financial analysis,
data mining, statistical pattern recognition and machine learning are actually one of these means or averages. At least, this tutorial may serve as a revelation that you can create many means or average beyond the traditional Pytagorean means of arithmetic, geometric and harmonic means.
Part 1: Mean
What is mean?
Arithmetic mean
Geometric mean
Harmonic mean
Quadratic mean
Some relationship between means
Minkowski Mean
Lehmer mean
Kolmogorov Generalized Mean
Archimedean Double Mean Process
Archimedean HarmonicGeometric Mean (AHGM)
Gaussian Double Mean Process
ArithmeticGeometric Mean (AGM)
HarmonicGeometric Mean (HGM)
Part 2: Average
Averages of measurement sequence
Time Average
Addition or Subtraction of Two Averages
Multiplication of Averages
Distributive Law of Averages
DelayedAverage
MovingAverage
DelayedMovingAverage
Average Decomposition Diagram
Fundamental Relationship between Averages
Relationship of TimeAverage and Movingaverage
Relationship of DelayedAverage and DelayedMovingaverage
Relationship of DelayedAverage and Movingaverage and TimeAverage
Fundamental theorem of average
Shift Property of Average
Relationship of DelayedAverage and DelayedMovingAverage and TimeAverage
Resources on Mean and Average
Excel function reference related to this tutorial are listed here. Click here to download the Microsoft Excel file companion of this tutorial
See Also: Variance, Average Absolute Deviation, Distance, Similarity, Sum
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This tutorial is copyrighted.
Preferable reference for this tutorial is
Teknomo, Kardi. Mean and Average. http:\\people.revoledu.com\kardi\
tutorial\BasicMath\Average\
