## Geometric Mean for grouped data

Let $(x_i,f_i), i=1,2, \cdots , n$ be given frequency distribution. Then the Geometric Mean of a frequency distribution is denoted by $GM$.

## Formula

The geometric mean for a grouped data is given by

OR

### $\log (GM) =\frac{1}{N}\sum_{i=1}^n f_i\log(x_i)$.

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.