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.