”;
Geometric mean of n numbers is defined as the nth root of the product of n numbers.
Formula
${GM = sqrt[n]{x_1 times x_2 times x_3 … x_n}}$
Where −
-
${n}$ = Total numbers.
-
${x_i}$ = numbers.
Example
Problem Statement:
Determine the geometric mean of following set of numbers.
| 1 | 3 | 9 | 27 | 81 |
Solution:
Step 1: Here n = 5
$ {GM = sqrt[n]{x_1 times x_2 times x_3 … x_n} \[7pt]
, = sqrt[5]{1 times 3 times 9 times 27 times 81} \[7pt]
, = sqrt[5]{3^3 times 3^3 times 3^4} \[7pt]
, = sqrt[5]{3^{10}} \[7pt]
, = sqrt[5]{{3^2}^5} \[7pt]
, = sqrt[5]{9^5} \[7pt]
, = 9 }$
, = sqrt[5]{1 times 3 times 9 times 27 times 81} \[7pt]
, = sqrt[5]{3^3 times 3^3 times 3^4} \[7pt]
, = sqrt[5]{3^{10}} \[7pt]
, = sqrt[5]{{3^2}^5} \[7pt]
, = sqrt[5]{9^5} \[7pt]
, = 9 }$
Thus geometric mean of given numbers is $ 9 $.
Advertisements
”;