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Relationship between Means
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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