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- Statistics - Discussion
Statistics - Geometric Mean
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 }$
Thus geometric mean of given numbers is $ 9 $.
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