Contraharmonic Mean Calculator
Calculate the contraharmonic mean, which is always greater than or equal to the arithmetic mean and complements the harmonic mean.
Enter Positive Values
Example Data Sets:
Contraharmonic Mean
8.142857
Arithmetic Mean
7.000000
Harmonic Mean
5.693395
Geometric Mean
6.358650
Quadratic Mean
7.549834
Calculation Details:
Sum of Squares:
285.0000
Sum:
35.0000
Count:
5
Identity Verification:
CM = AM + Var/AM
CM = 7.000000 + 8.000000/7.000000
Calculated: 8.142857
What is Contraharmonic Mean?
The contraharmonic mean is the ratio of the sum of squares to the sum of values. It is called "contraharmonic" because it is the complement of the harmonic mean with respect to the arithmetic mean. The contraharmonic mean is always greater than or equal to the arithmetic mean, with equality only when all values are identical.
Formula
CM = (x1^2 + x2^2 + ... + xn^2) / (x1 + x2 + ... + xn)
Also known as the Lehmer mean with p = 2.
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Editorial Note
MyCalcBuddy Editorial Team
This page is maintained as an educational calculator reference.
Formula Source: Standard Mathematical References
by Various