# 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

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