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 $$$H = \frac{4}{\frac{61}{30}} = \frac{120}{61}$$$.
Answer
The harmonic mean is $$$\frac{120}{61}\approx 1.967213114754098$$$A.