# Harmonic Mean Calculator

For the given group of values, the calculator will find their harmonic mean, with steps shown.

Related calculators: Average (Mean) Calculator, Geometric Mean Calculator

## Your Input

**Find the harmonic mean of $$$5$$$, $$$1$$$, $$$2$$$, $$$3$$$.**

## Solution

The harmonic mean of data is given by the formula $$$H = \frac{n}{\sum_{i=1}^{n} \frac{1}{x_{i}}}$$$, where $$$n$$$ is the number of values and $$$x_i, i=\overline{1..n}$$$ are the values themselves.

Since we have $$$4$$$ points, $$$n = 4$$$.

The sum of the reciprocals of the values is $$$\frac{1}{5} + \frac{1}{1} + \frac{1}{2} + \frac{1}{3} = \frac{61}{30}$$$.

Therefore, the harmonic mean is $$$H = \frac{4}{\frac{61}{30}} = \frac{120}{61}$$$.