About Geometric Mean Formula
The Geometric Mean (GM) is an average value or mean that represents the central tendency of a group of numbers by calculating the product of their values. Measures of central tendencies are used in mathematics and statistics to characterise the summary of complete data set values. The mean, median, mode, and range are the most essential indicators of central tendency. Among these, the data set's mean provides an overall picture of the data. The mean is the average of the data set's numbers.
What do you mean by Geometric Mean?
By taking the root of the product of their values, the Geometric Mean (GM) represents the central tendency of a set of numbers. Basically, we add all of the 'n' values together and subtract the nth root, where n is the total number of values. For example, the geometric mean of a pair of numbers such as 8 and 1 is √(8×1) = √8 = 2.
As a result, the geometric mean is also the nth root of the product of n integers. This is not to be confused with the arithmetic mean. The arithmetic mean is calculated by adding data values and then dividing them by the total number of values. However, in geometric mean, the given data values are multiplied, and the final product of data values is calculated by taking the root with the radical index.
Geometric Mean Formula
The nth root of the product of the values is the Geometric Mean (G.M) of a data set with n observations. Consider the case where x?, x?, ..., x? are the observations for which the geometric mean is to be calculated. The following is the formula for calculating the geometric mean:
GM = √(x? · x? · ... · x?) or GM = (x? · x? · ... · x?)1/n
It is also represented as:
G.M. = antilog (∑ log x?) / n
Therefore, geometric mean, G.M. = antilog (∑ log x?) / n
Note: For any grouped data, G.M can be calculated using:
GM = Antilog (∑ f log x?) / n, where n = f? + f? + ... + f?.
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