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i.e.,$G={\left({x}_{1}{x}_{2}\dots {x}_{n}\right)}^{\frac{1}{n}}$where G denotes the Geometric mean. It is also denoted by GM.When n is large, we make use of logarithms and reduce the formula to the form:

$\begin{array}{cc}\mathrm{Geometric}\mathrm{mean}& =\mathrm{antilog}\left[\frac{\mathrm{log}{x}_{1}+\mathrm{log}{x}_{2}+\cdots +\mathrm{log}{x}_{n}}{n}\right]\\ =\mathrm{antilog}\left[\frac{{\sum }_{1}^{n}f\mathrm{log}{x}_{i}}{n}\right]\end{array}$

2. GM of discrete series: If x1, x2, …, xn denote n observations with frequencies f1, f2, …, fn respectively then, the GM of the series is defined by

$G=\mathrm{antilog}\left[\frac{{f}_{1}\mathrm{log}{x}_{1}+{f}_{2}\mathrm{log}{x}_{2}+\cdots +{f}_{n}\mathrm{log}{x}_{n}}{n}\right]=\mathrm{antilog}\left[\frac{{\sum }_{1}^{n}{f}_{i}\mathrm{log}{x}_{i}}{n}\right]$

where $n=\sum {f}_{i}$

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