Geometric mean is the n^th root of the product of n items of a series. Thus if the geometric mean of 3, 6 and 8 is to be calculated it would be equal to the cube root of the product of these figures. Similarly the geometric mean of 8, 9, 12 and 16 would be the 4th root of the product of these four figures.                    

             Symbolically GM = √(n&x₁..x₂..x₃………x_n ) 

where GM stands for the geometric mean, N for the number of items and X for the values of the variable.           

 

Example : find geometric mean of the following data:

6, 8,9,12

GM = 4^th root of (6 x 8 x 9 x 12)

                =4^th root(5184) =6√2

 

The calculation of the geometric mean by this process is possible only if the number of items is very few. If the number of items is large and their size is big, it is not possible to apply this  method .In such cases calculations have to be done with the help of logs. In terms of logs.

Log GM =log x₁ +log x₂+ log x₃ + ...+log x_n

                               N

Here GM=geometric mean

N: number of items in dataset.

The value of the geometric mean is always less than the value of the arithmetic average unless all the items have equal value in which case the geometric mean and arithmetic average have identical values.

Sub Category