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# ​​Finding the Mean Geometric Value (Non-Group and Group Data)

Calculations on the geometric mean are based on all observations, which means that the geometric mean is influenced by all variable values. In this case if there are extreme values, the effect can be reduced if the calculation uses geometric means, the resulting value will be better if compared to the arithmetic mean.

### Non-group Data

The mean set of observations is to have the same value as the results of the multiplication of these values ​​to the rank of one divided by the number of observations.
The formula is

The simplest method of finding the mean value is to use logarithms. If we use the logarithm obtained:

Where: G = mean
xi = observation value
n = number of observations

#### Example

find the mean of the wholesale price index of 8 major commodity groups namely 107, 132, 120, 116, 130, 126, 116, and 122.
So:
G = antilog 2.0899 = 123

### Group Data

To find the mean value of grouped data (distribution formulas), the formula used is:

Or if we use the logarithm obtained:
Where: G = mean
xi = observation value
fi  = frequency
n = number of observations

#### Example

The data below shows the reproductive age classification of 100 samples of married women studied.
So,
G = Antilog 1.430808269 = 26.96548704