Contraharmonic Mean Calculator

On this page the contraharmonic mean of a series of numbers is calculated.

To perform the calculation, enter a series of numbers. Then click the 'Calculate' button. The list can be entered unsorted.

Input format

The data can be entered as a series of numbers, separated by semicolons or spaces. You can enter the data as a list (one value per line). Or from a column from Excel spreadsheet by copy & paste

In mathematics, a contraharmonic mean is a function that is complementary to the harmonic mean.

The contraharmonic mean is a term from statistics. The contraharmonic mean of a set of positive numbers is defined as the arithmetic mean of the squares of the numbers divided by the arithmetic mean of the numbers.

Formulas for the contraharmonic center

\(\displaystyle C(x_1, x_2,...x_n)=\frac{x^2_1+x^2_2+ ... +x^2_n}{x_1+x_2+ ... +x_n}\)

Example

In the following example we calculate the mean of the 5 numbers

\(\displaystyle 5,3,4,2,6 \)

The formula is:

\(\displaystyle C(x_1, x_2,, x_3, x_4, x_5)\)\(\displaystyle =\frac{x^2_1+x^2_2+x^2_3+x^2_4+x^2_5}{x_1+x_2+x_3+x_4+x_5}\)

\(\displaystyle C(5,3,4,2,6) \)\(\displaystyle = \frac{25+9+16+4+36}{5+3+4+2+6}= \frac{90}{20}= 4.5\)

More statistics functions

Arithmetic Mean • Contraharmonic Mean • Covariance • Empirical distribution CDF • Deviation • Five-Number Summary • Geometric Mean • Harmonic Mean • Inverse Empirical distribution CDF • Kurtosis • Log Geometric Mean • Lower Quartile • Median • Pooled Standard Deviation • Pooled Variance • Skewness (Statistische Schiefe) • Upper Quartile • Variance