Means Relationship

By Kardi Teknomo, PhD .

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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

Mean relationship , or Mean relationship

  • For any real data, quadratic mean is always greater or equal to absolute value of arithmetic mean

Mean relationship , or Mean relationship

  • Special for only two positive numbers Mean relationship and Mean relationship , we have

    Arithmetic mean Mean relationship

    Geometric mean Mean relationship

    Quadratic mean Mean relationship

    Harmonic mean Mean relationship

    If Mean relationship , then all the means are equal: Mean relationship

    If Mean relationship , then the order is Mean relationship

    Example

    Mean relationship , Mean relationship

    Mean relationship ,

    Mean relationship ,

    Mean relationship

    Mean relationship

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See also: Arithmetic Mean , Geometric Mean , Harmonic mean , Quadratic mean
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