Statistics Calculator: Harmonic Mean

Calculate the harmonic mean from a set of numbers.

Data is from: Population Sample

Harmonic Mean Calculator

How to use this calculator

This calculator will calculate the harmonic mean of a set of numbers.

Enter the numerical values in the box above. All numbers must be positive and must be separated by commas or spaces. Alternatively they may be entered on separate lines. The 'population or sample' option selector is only used for calculating the variance or standard deviation. For this calculation it will be ignored. Click on "Submit Data" to perform the calculation and display the result. Under the result you fill find links to other relevant calculations applicable to the same set of data. Press "Reset" to clear the data and start again.

Harmonic mean

The harmonic mean, like the arithmetic mean and the geometric mean is a type of average, a measure of central tendency.

All values must be positive. See the Wikipedia article for more information.

Harmonic mean formula

This calculator uses the following formula to calculate the harmonic mean:

$ H = \frac{n}{\sum_{i=1}^n \frac{1}{x_i}} $

where n is the total number of values and xi (x2, x1, ... ,xn) are the individual numbers in the data set. The formula is equivalent to:

$ \frac{n}{ \frac{1}{x_1}+\frac{1}{x_2}+\frac{1}{x_3}+\cdot\cdot\cdot+\frac{1}{x_n} } $

In words: The reciprocal of the arithmetic mean of the reciprocals.