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 $GM$.


The geometric mean for a grouped data is given by

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


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

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.

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