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?
Some relationship between means
Kolmogorov Generalized Mean
Archimedean Double Mean Process Gaussian Double Mean Process
Part 2: Average
Averages of measurement sequence
Time Average Delayed-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-Average Relationship of Delayed-Average and Delayed-Moving-Average and Time-Average
Excel function reference related to this tutorial are listed here.
Click here to download the Microsoft Excel file companion of this tutorial