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.

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

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See also: Minkowski mean, generalized mean, arithmetic mean, harmonic mean, geometric mean
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Preferable reference for this tutorial is

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