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Lehmer Mean

By Kardi Teknomo, PhD.

 

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Lehmer mean is another type of Generalized mean, somewhat similar to Minkowski mean, a generalization of arithmetic, geometric and harmonic mean but with different parameter value

For two numbers and the Lehmer mean is defined as

Example:

Setting , we have arithmetic mean

 

Example:

When (take a limit to approach zero), we have harmonic mean

 

Example:

When , and only for two input numbers, we have geometric mean

 

Note:

  • However, we do not have a specific p in Lehmer mean to represent Quadratic mean



Experiment with the interactive program below to compute Lehmer mean of a list of numbers separated by comma. Try different input values and parameter p and compare the result with other Means.

Input list of numbers separated by comma, then press the button "Get Lehmer Mean". The program will compute directly when you change the input data or parameter.


Parameter p = or

Table below provides the summary of parameter to relate Lehmer generalized mean and other means.

Name

Parameter p

Arithmetic Mean

Lehmer Mean

Geometric mean

Lehmer Mean (only two inputs)

Harmonic mean

Lehmer Mean (limit)

 

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See also: Minkowski mean, generalized mean, arithmetic mean, harmonic mean, geometric 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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