The most important measures of central tendencies are mean, median, mode, and range. Among these, the mean of the data set provides the overall idea of the data. The mean defines the average of numbers in the data set. In this lesson, let us discuss the definition, formula, properties, applications, the relation between AM, GM, and HM with solved examples in the end.
The Geometric Mean GM is the average value or mean which signifies the central tendency of the set of numbers by taking the root of the product of their values. Basically, we multiply the 'n' values altogether and take out the n th root of the numbers, where n is the total number of values.
Thus, the geometric mean is also defined as the n th root of the product of n numbers. It is to be noted that the geometric mean is different from the arithmetic mean. In the arithmetic mean, data values are added and then divided by the total number of values.
But in geometric mean, the given data values are multiplied, and then you take the root with the radical index for the final product of data values.
For example, if you have two data, take the square root, or if you have three data, then take the cube root, or else if you have four data values, then take the 4 th root, and so on. The Geometric Mean G. M of a data set containing n observations is the n th root of the product of the values. The formula to calculate the geometric mean is given below:. Note that the length of each time period must be the same. As a general rule one should convert the percent values to its decimal equivalent multiplier.
It is important to recognize that when dealing with percents, the geometric mean of percent values does not equal the geometric mean of the decimal multiplier equivalents and it is the decimal multiplier equivalent geometric mean that is relevant. The Geometric Mean:. What is the average rate of return for the values that follow?
An investment grows from? What is the average rate of return? An initial investment of? What is its final value? A culture contains 1, bacteria. The bacteria grow to 2, in 10 hours. What is the rate at which the bacteria grow per hour to the nearest tenth of a percent? An investment of? What is the average rate of return to the nearest hundredth of a percent? What is the average return per year to the nearest hundredth of a percent?
Select personalised ads. Apply market research to generate audience insights. Measure content performance. Develop and improve products. List of Partners vendors. In statistics, the geometric mean is calculated by raising the product of a series of numbers to the inverse of the total length of the series.
The geometric mean is most useful when numbers in the series are not independent of each other or if numbers tend to make large fluctuations. Applications of the geometric mean are most common in business and finance, where it is frequently used when dealing with percentages to calculate growth rates and returns on a portfolio of securities. It is also used in certain financial and stock market indexes, such as the Financial Times' Value Line Geometric index.
The geometric mean is used in finance to calculate average growth rates and is referred to as the compounded annual growth rate. The geometric mean of the growth rate is calculated as follows:.
The geometric mean is commonly used to calculate the annual return on portfolio of securities. The geometric mean is also occasionally used in constructing stock indexes. Many of the Value Line indexes maintained by the Financial Times employ the geometric mean. The index is calculated by taking the geometric mean of the proportional change in price of each of the stocks within the index.
The geometric mean was first conceptualized by Greek philosopher Pythagoras of Samos and is closely associated with two other classical means made famous by him: the arithmetic mean and the harmonic mean.
The geometric mean is also used for sets of numbers, where the values that are multiplied together are exponential. Examples of this phenomena include the interest rates that may be attached to any financial investments, or the statistical rates if human population growth. Financial Times. Financial Analysis.
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