Geometric Mean is a type of mean or average that indicates the central tendency or typical value of a set of given numbers. Geometric Mean is defined as the nth root of the product of the n units in a data set. Geometric mean is a kind of average of a set of numbers that is different from the arithmetic average. Geometric mean is calculated for sets of positive real numbers. This is calculated by multiplying all the numbers (call the number of numbers n), and taking the nth root of the total.
Geometric Mean is used in the case when finding an average for set of numbers presented as percentages. The geometric mean is an average that is useful for sets of positive numbers that are interpreted according to their product and not their sum (as is the case with the arithmetic mean) e.g. rates of growth. The online Geometric Mean Calculator is useful in calculating the geometric mean for the given set of numbers.
Example:
Calculate the geometric mean for the given set of numbers.
25,56,85,71,4,12,3,2,5
Solution:
Apply Formula:
Geometric Mean = ((X_{1})(X_{2})(X_{3})........(X_{N}))^{1/N}
N = 9
1/N = 1/9
1/N = 0.111
Geometric mean = [(25)(56)(85)(71)(4)(12)(3)(2)(5)] 0.111
Total Numbers: 9
Geometric Mean = 13.20001