Mean and Average

There are so many averages and means. Mean is function to map input of positive real numbers into somehow a mid-value, or expected value. The mid-value 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 time-average, delayed-average, moving-average and delayed-moving-average.

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 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 Harmonic-Geometric Mean (AHGM)
Gaussian Double Mean Process
Arithmetic-Geometric Mean (AGM)
Harmonic-Geometric Mean (HGM)

Part 2: Average

Averages of measurement sequence
Time Average
Addition or Subtraction of Two Averages
Multiplication of Averages
Distributive Law of Averages
Delayed-Average
Moving-Average
Delayed-Moving-Average
Average Decomposition Diagram
Fundamental Relationship between Averages
Relationship of Time-Average and Moving-average
Relationship of Delayed-Average and Delayed-Moving-average
Relationship of Delayed-Average and Moving-average and Time-Average
Fundamental theorem of average
Shift Property of Average
Relationship of Delayed-Average and Delayed-Moving-Average and Time-Average
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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