# Harmonic Mean Calculator

## Calculate harmonic mean step by step

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

Related calculators: Average 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 $$$H = \frac{4}{\frac{61}{30}} = \frac{120}{61}$$$.