Geometric Mean for grouped data

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

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

Geometric Mean for grouped data

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

$$ \begin{equation*} G.M. = \biggr(x_1^{f_1}\cdot x_2^{f_2} \cdots x_n^{f_n}\biggl)^{1/N}= \biggr(\prod_{i=1}^{n} x_i^{f_i}\biggl)^{1/N}\mbox{ where }N = \sum_{i=1}^{n} f_i \end{equation*} $$

OR $$ \begin{equation*} \log (G.M.) = \frac{1}{N}\sum_{i=1}^{n} f_i\log x_i \end{equation*} $$

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

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