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.

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