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Statistics - Geometric Mean of Individual Series
When data is given on individual basis. Following is an example of individual series:
| Items | 5 | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
|---|
In case of individual items, Geometric Mean is computed using following formula.
Formula
$G.M. = Antilog\ of\ \frac{\sum logx}{n} \\[7pt]
\, = Antilog\ of\ \frac{logx_1+logx_2+...+logx_n}{n}$
Where −
${G.M.}$ = Geometric Mean
${x_1,x_2,x_3,...,x_n}$ = Different values of variable x.
${n}$ = Number of variables
Example
Problem Statement:
Calculate Geometric Mean for the following individual data:
| Items | 14 | 36 | 45 | 70 | 105 |
|---|
Solution:
Based on the given data, we have:
| ${x}$ | ${logx}$ |
|---|---|
| 14 | 1.1461 |
| 36 | 1.5563 |
| 45 | 1.6532 |
| 70 | 1.8450 |
| 105 | 2.0211 |
| Total | 8.2217 |
Based on the above mentioned formula, Geometric Mean $G.M.$ will be:
$G.M. = Antilog\ of\ \frac{\sum logx}{n} \\[7pt]
\, = Antilog\ of\ \frac{8.2217}{5} \\[7pt]
\, = Antilog\ of\ 1.6443 \\[7pt]
\, = 44.09$
The Geometric Mean of the given numbers is 44.09.
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