Geometric mean of n numbers is defined as the nth root of the product of n numbers.

Formula

GM=x1×x2×x3…xn−−−−−−−−−−−−−−√nGM=x1×x2×x3…xnn

Where −

·        nn = Total numbers.

·        xixi = numbers.

Example

Problem Statement:

Determine the geometric mean of following set of numbers.

Solution:

Step 1: Here n = 5

GM=x1×x2×x3…xn−−−−−−−−−−−−−−−√n=1×3×9×27×81−−−−−−−−−−−−−−−√5=33×33×34−−−−−−−−−−√5=310−−−√5=325−−−√5=95−−√5=9GM=x1×x2×x3…xnn=1×3×9×27×815=33×33×345=3105=3255=955=9

Thus geometric mean of given numbers is 9.