Kardi Teknomo
Kardi Teknomo Kardi Teknomo Kardi Teknomo
   
 
  Research
  Publications
  Tutorials
  Resume
  Personal
  Contact

 

Mean and Average

By Kardi Teknomo, PhD.

 

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. He 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 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.

Mean

What is mean?

Arithmetic mean

Geometric mean

Harmonic mean

Quadratic mean

Some relationship between means

Minkowski Mean

Lehmer mean

Phillips Generalized Mean

Archimedean Double Mean Process

Archimedean Harmonic-Geometric Mean (AHGM)

Gaussian Double Mean Process

Arithmetic-Geometric Mean (AGM)

Harmonic-Geometric Mean (HGM)

Excel function reference related to this tutorial are listed here. Click here to download the Microsoft Excel file companion of this tutorial.

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

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

Rate this tutorial or give your comments about this tutorial

 

Share and save this tutorial
Add to: Del.icio.us  Add to: Digg  Add to: StumbleUpon   Add to: Reddit   Add to: Slashdot   Add to: Technorati   Add to: Netscape   Add to: Newsvine   Add to: Mr. Wong Add to: Webnews Add to: Icio Add to: Oneview Add to: Folkd Add to: Yigg Add to: Linkarena Add to: Simpy Add to: Furl Add to: Yahoo Add to: Spurl Add to: Google Add to: Blinklist Add to: Blogmarks Add to: Diigo Add to: Blinkbits Add to: Ma.Gnolia Add to: Smarking Add to: Netvouz Information

This tutorial is copyrighted.

Preferable reference for this tutorial is

Teknomo, Kardi. Mean and Average. http:\\people.revoledu.com\kardi\ tutorial\BasicMath\Average\

 

 

 

 
© 2007 Kardi Teknomo. All Rights Reserved.
Designed by CNV Media