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,) | |
| Results | |
| 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.
