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