Statistical Techniques for Transportation Engineering

i.e.,$G={(x_1{x}_2\dots x_n)}^{\frac{1}{n}}$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:

$\begin{array}{cc}\mathrm{Geometric}\mathrm{mean}& =\mathrm{antilog}\left[\frac{\log x_1+\log x_2+\cdots +\log x_n}{n}\right]\\ =\mathrm{antilog}\left[\frac{{\sum }_1^{n}f\log x_i}{n}\right]\end{array}$

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

$G=\mathrm{antilog}\left[\frac{f_1\log x_1+f_2\log x_2+\cdots +f_n\log x_n}{n}\right]=\mathrm{antilog}\left[\frac{{\sum }_1^n{f}_i\log x_i}{n}\right]$

where $n=\sum f_i$