3 Ways to Calculate the Geometric Mean

Geometric Mean is defined as the nth root of the product of “n” number of given dataset. However, the arithmetic mean is not an appropriate method for calculating an average where the data exhibit serial correlation, or have some relationship to each other. We used an arithmetic mean for a moving average because the closing prices have no correlation. One closing price may be higher or lower than the next, but there’s no intrinsic relationship.

Formula and Calculation With Example

For GM formula, multiply all the “n” numbers together and take the “nth root of them. The formula for evaluating geometric mean is as follows if we have “n” number how to calculate geometric mean of observations. Navigate through a detailed, step-by-step guide on how to calculate the geometric mean. Each step is explained clearly, ensuring a seamless learning experience.

Answer Key:

Among these, the mean of the data set will provide the overall idea of the data. The different types of mean are Arithmetic Mean (AM), Geometric Mean (GM) and Harmonic Mean (HM). In this article, let us discuss the definition, formula, properties, applications, the relation between AM, GM, and HM with solved examples in detail.

Thus, the geometric mean is also defined as the nth root of the product of n numbers. 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 values, take the square root, or if you have three data values, then take the cube root, or else if you have four data values, then take the 4th root, and so on. To calculate a 14-day moving average for a stock, simply add up its closing price for the past 14 days and then divide that sum by 14.

The geometric mean will be displayed above together with links to calculate other measures using the same set of data. The geometric mean can be used to calculate average rates of return in finances or show how much something has grown over a specific period of time. In order to find the geometric mean, multiply all of the values together before taking the nth root, where n equals the total number of values in the set. You can also use the logarithmic functions on your calculator to solve the geometric mean if you want. In mathematics and statistics, the summary that describes the whole data set values can be easily described with the help of measures of central tendencies. The most important measures of central tendencies are mean, median, mode and the range.

The Formula for Arithmetic Mean

1. The numbers (either all positive or all negative) must be separated by commas or spaces, or they may be entered on separate lines.
2. Analysts, portfolio managers, and others commonly use the calculation of the geometric mean to determine the performance results of an investment or portfolio.
3. Uncover the reasons behind the prevalence of the geometric mean in statistical analysis and financial modeling.
4. The geometric mean of growth over periods yields the equivalent constant growth rate that would yield the same final amount.
5. In finance and investing, one might use the arithmetic mean to get an idea of the average earnings estimate for a series of estimates issued by a number of analysts covering a stock.

In computer implementations, naïvely multiplying many numbers together can cause arithmetic overflow or underflow. Calculating the geometric mean using logarithms is one way to avoid this problem. For various reasons, the geometric mean is an important tool for calculating portfolio performance.

Simply add up the various estimates and divide by the number of estimates. Hence, the logarithm of the geometric mean is the arithmetic mean of the logarithms. Keep visiting BYJU’S and get various other maths formulas which are explained in an easy way along with solved examples. Also, register now to get maths video lessons on different topics and several practice questions which will help to learn the maths concepts thoroughly.

Geometric mean formula

This method is great for comparing values that change over time, like investment returns or population growth. The geometric mean is a valuable tool for finding the average of numbers, especially when dealing with growth rates, ratios, or values that vary greatly. Unlike the arithmetic mean, it provides a more accurate reflection of data that involves multiplication or compounding.