Harmonic Mean Calculator

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

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 $H = \frac{4}{\frac{61}{30}} = \frac{120}{61}$.

The harmonic mean is $\frac{120}{61}\approx 1.967213114754098$A.