## Harmonic Mean for grouped data

Use this calculator to find the Harmonic Mean for grouped (frequency distribution) data.

Harmonic Mean Calculator (Grouped Data)
Type of Freq. Dist. DiscreteContinuous
Enter the Classes for X (Separated by comma,)
Enter the frequencies (f) (Separated by comma,)
Results
Number of Obs. (N):
Harmonic Mean :
freq dist :

## Harmonic Mean for grouped data

Let $x_1, x_2, \cdots , x_n$ have frequencies $f_1, f_2, \cdots ,f_n$ respectively, then the Harmonic Mean is given by

$$\begin{equation*} \frac{1}{HM} = \frac{1}{N}\sum_{i=1}^{n}\frac{f_i}{x_i}\quad \mbox{ where }N = \sum_{i=1}^{n} f_i \end{equation*}$$

In case of continuous frequency distribution, $x_i$’s are the mid-values of the respective classes.

Harmonic mean is undefined if any one value of the variable is zero.