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Means Relationship

By Kardi Teknomo, PhD.

 

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Here are some relationship between the means or averages (Bronshtein et al, 2003)

  • If the data is all positive, the arithmetic mean is always greater than or equal to the geometric mean of the same data

, or

 

  • For any real data, quadratic mean is always greater or equal to absolute value of arithmetic mean

, or

 

  • Special for only two positive numbers and , we have

     

    Arithmetic mean

     

    Geometric mean

     

    Quadratic mean

     

    Harmonic mean

     

    If , then all the means are equal:

     

    If , then the order is

     

    Example

    ,

    ,

    ,

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See also: Arithmetic Mean, Geometric Mean, Harmonic mean, Quadratic mean
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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\

 

 

 

 
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