Contraharmonic Mean
Formula and examples for the contraharmonic mean of a number series
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:
\(\displaystyle C(x_1, x_2,, x_3, x_4, x_5)\)\(\displaystyle =\frac{x^2_1+x^2_2+x^2_3+x^2_4+x^2_5}{x_1+x_2+x_3+x_4+x_5}\)
\(\displaystyle C(5,3,4,2,6) \)\(\displaystyle = \frac{25+9+16+4+36}{5+3+4+2+6}= \frac{90}{20}= 4.5\)
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