It is another measure of central tendency based on mathematical footing like arithmetic mean. Geometric mean can be defined in the following terms:
“Geometric mean is the nth positive root of the product of “n” positive given values”
            Hence, geometric mean for a value containing  values such as  is denoted by  of   and given as under:
                   (For Ungrouped Data)
            If we have a series of  positive values with repeated values such as  are repeated  times respectively then geometric mean will becomes:
                   (For Grouped Data)
            Where

Example:
            Find the Geometric Mean of the values 10, 5, 15, 8, 12
Solution:
            Here,  and
           
                                   

Example:
            Find the Geometric Mean of the following Data

Solution:
            We may write it as given below:
            Here,
                   , , , ,
                 
            Using the formula of geometric mean for grouped data, geometric mean in this case will become:
           
                                   
                                   
                                   

            The method explained above for the calculation of geometric mean is useful when the numbers of values in given data are small in number and the facility of electronic calculator is available. When a set of data contains large number of values then we need an alternative way for computing geometric mean. The modified or alternative way of computing geometric mean is given as under:

Example:
            Find the Geometric Mean of the values 10, 5, 15, 8, 12

Example:
            Find the Geometric Mean for the following distribution of students’ marks:

Solution: