Statistics
 Introduction Central Tendency Measures Mean Geometric Mean Media Armónica Mediana Moda Measures of Location Centiles Deciles Cuartiles Ejercicio Measures of Position Introducción Desviación media Varianza Desviación típica Coeficiente de variación Ejercicio Medidas de Forma Asimetría Apuntamiento Test
Geometric Mean.

The geometric mean of a set of n values of a variable is the n th root of their product. If a variable x assumes n values , then its geometric mean, denoted by is

For a frequency distribution, , where

Properties:

• If the given values of a variable are all equal, then the geometric mean will be equal to their common value.
• The logarithm of the geometric mean of a set of values of a variable is the aritmetic mean of their logarithms.
• If y is a function of a variable x in the form y=ax, then the geometric mean of y is related to that of x in the similar form.
• The geometric mean of the ratio of two variables is the ratio of their geometric means.
• If there are two sets of values of a variable x, consisting of n1 and n2 values, and G1 and G2 are their respective geometric means, then the geometric mean, G, of the combined set is given by
• If a variable x chages over time t exponentially, then the value of the variable at the mid-point of an interval (t1,t2) i.e. at is the geometric mean of its values at t1 and t2.
• No es útil si algún valor es nulo.
• No es posible su cálculo cuando hay un número par de datos y el radicando es negativo.

• The geometric mean is ridigly defined.
• The geometric mean is directly based on all the observations.
• Generally, the presence of a few extremely small or large values has no considerable effect on geometric mean.