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Lehmer mean
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.
Table below provides the summary of parameter to relate Lehmer generalized mean and other means.
Name |
Parameter p |
Arithmetic Mean |
|
Geometric mean |
(only two inputs) |
Harmonic 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 (2015) Mean and Average. https:\\people.revoledu.com\kardi\tutorial\BasicMath\Average\