## Harmonic Mean for grouped data

Let `$(x_i,f_i), i=1,2, \cdots , n$`

be given frequency distribution. Then the Harmonic Mean is denoted by $HM$.

## Formula

The harmonic mean for grouped data is given by

`$\dfrac{1}{HM} = \dfrac{1}{N}\sum_{i=1}^{n}\dfrac{f_i}{x_i}$`

where `$N = \sum_{i=1}^{n} f_i$`

.

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.