Elementary Statstics

6.5.1 Geometric Mean

Geometric mean of a set of n observations is the nth root of their product. Thus the geometric mean, G, of n observations x_i, i=1,2 …. n is

G = (x₁ x₂ …… x_n) 1/n

The computation is facilitated by the use of logarithms. Taking logarithm on both sides, we get

G=antilog $${1\over n}\sum^n_{i=1}\log x_{i}$$

In case of frequency distribution x_i/f_i, (I = 1, 2 ……n) geometric mean, G is given by

Taking logarithm of both sides, we get

l

Thus we see that logarithm of G is the arithmetic mean of the logarithms of the given values. We get

G=antilog

In the case of grouped or continuous frequency distribution, x is taken to be the value corresponding to the mid-points of the classes.