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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 Pytagorean means of arithmetic, geometric and harmonic means.

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Part 1: Mean
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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 ProcessArchimedean Harmonic-Geometric Mean (AHGM)Gaussian Double Mean ProcessArithmetic-Geometric Mean (AGM)

Harmonic-Geometric Mean (HGM)

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Part 2: Average
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Averages of measurement sequence

Time AverageAddition or Subtraction of Two AveragesDelayed-Average

Multiplication of Averages

Distributive Law of Averages

Moving-Average

Delayed-Moving-Average

Average Decomposition Diagram

Fundamental Relationship between AveragesRelationship of Time-Average and Moving-averageResources on Mean and Average

Relationship of Delayed-Average and Delayed-Moving-average

Relationship of Delayed-Average and Moving-average and Time-AverageFundamental theorem of averageRelationship of Delayed-Average and Delayed-Moving-Average and Time-Average

Shift Property of Average

Excel function reference related to this tutorial are listed here.

Click here to download the Microsoft Excel file companion of this tutorial

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See Also
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:
Variance
,
Average Absolute Deviation
,
Distance
,
Similarity
,
Sum

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