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Home Univariate Data Measures of Location Mean Generalized Mean
See also: Literature References - Survey, Matrix Algebra - Fundamentals, Mean 

Generalized Mean

The various means, such as the arithmetic, harmonic, or geometric mean, may be generalized into a single concept. Given an integer number p these means can be calculated according to the following formula:

Depending on the parameter p the following metrics of the observed values xi result from the formula:

p calculated metric
- minimum
-1 harmonic mean
0 geometric mean
1 arithmetic mean
2 root mean square (RMS)
+ maximum

For p = 0 one can show that the limit for p0 approaches the geometric mean. If the arithmetic mean is equal to zero the RMS value corresponds to the standard deviation of the observed values xi.

Home Univariate Data Measures of Location Mean Generalized Mean