3 Ways to Calculate the Geometric Mean

In other words, it is the average return of an investment over time, a metric used to evaluate the performance of a single investment or an investment portfolio. The geometric mean differs from the arithmetic mean, or arithmetic average, in how it is calculated. The former takes into account the compounding that occurs from period to period, whereas the latter does not. Because of this, investors usually consider the geometric mean to be the more accurate measure of returns. The geometric mean differs from the arithmetic average, or arithmetic mean, in how it is calculated because it takes into account the compounding that occurs from period to period. Because of this, investors usually consider the geometric mean a more accurate measure of returns than the arithmetic mean.

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. 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. Simply add up the various estimates and divide by the number of estimates.

The mean of a data set, for example, provides an overview of the data. To create a graph in Prism displaying the geometric mean of a dataset along with its 95% confidence interval, start by selecting the Column table type on the Welcome dialog. For the graph in this example, choose the data table option “Enter or import data into a new table”, and “Enter replicate values, stacked into columns”.

It is best used in calculations involving items that, while the same type, have no relationship with each other. The geometric mean of growth over periods yields the equivalent constant growth rate that would yield the same final amount. 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.

From your data table, click the Analyze button and select Descriptive Statistics. The median would be the value found where half the items in the measured sample appear above it and half appear below it. In an ellipse, the semi-minor axis is the geometric mean of the maximum and minimum distances of the ellipse from a focus; it is also the geometric mean of the semi-major axis and the semi-latus rectum. The semi-major axis of an ellipse is the geometric mean of the distance from the center to either focus and the distance from the center to either directrix. Replacing the arithmetic and harmonic mean by a pair of generalized means of opposite, finite exponents yields the same result. Thus, the geometric mean provides a summary of the samples whose exponent best matches the exponents of the samples (in the least squares sense).

When Is It Best to Use the Arithmetic Mean?

1. The arithmetic mean is the ratio of the total number of values to the sum of the provided values.
2. The different types of mean are Arithmetic Mean (AM), Geometric Mean (GM), and Harmonic Mean (HM).
3. Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader.
4. The mean, median, mode, and range are the most essential metrics of central tendency.
5. Or, the arithmetic mean could be used to determine a moving average for a stock price.
6. Find the geometric mean of each page of X by specifying the first and second dimensions using the vecdim input argument.

The Geometric Mean (GM) is the average value or mean which signifies the central tendency of the set of numbers by finding the product of their values. In mathematics and statistics, measures of central tendencies describe the summary of whole data set values. 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. The different types of mean are Arithmetic Mean (AM), Geometric Mean (GM), and Harmonic Mean (HM).

geomean

The arithmetic mean is the ratio of the total number of values to the sum of the provided values. We how to calculate geometric mean multiply the “n” number of values and then take the nth root of the product in the geometric mean. The geometric mean is the average value or mean that depicts the central tendency of a group of numbers or data by applying the root of the product of the values. The mean, median, mode, and range are the most essential metrics of central tendency.

1. The mean of a data set, for example, provides an overview of the data.
2. However, in the 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.
3. However, when there are many numbers, it is more difficult to calculate unless a calculator or computer program is used.
4. In the arithmetic mean, data values are added and then divided by the total number of values.
5. In this case, this dimension is the first dimension of X.

When the return or growth amount is compounded, the investor needs to use the geometric mean to calculate the final value of the investment. This sort of relationship is useful when comparing portfolio returns, bond yields, and total returns on equities. They affect the return for each succeeding period measured. 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. Its closing prices and the resulting figure for the moving average are shown below.

Adam received his master’s in economics from The New School for Social Research and his Ph.D. from the University of Wisconsin-Madison in sociology. He is a CFA charterholder as well as holding FINRA Series 7, 55 & 63 licenses. He currently researches and teaches economic sociology and the social studies of finance at the Hebrew University in Jerusalem.

Geometric Mean Formula

The geometric mean is best used to calculate the average of a series of data where each item has some relationship to the others. That’s because the formula takes into account serial correlation. Or, the arithmetic mean could be used to determine a moving average for a stock price. A moving average is helpful for traders and investors because, when calculated and plotted over time, it smooths out a long series of price movements to present a big picture of a price trend. Market participants can also chart long-term points of support and resistance with a moving average.

Formulation

Here is a vectorized, zero- and NA-tolerant function for calculating geometric mean in R. The verbose mean calculation involving length(x) is necessary for the cases where x contains non-positive values. By default, geomean operates along the first dimension of X whose size does not equal 1. In this case, this dimension is the first dimension of X. By comparing the result with the actual data shown on the table, the investor will find a 1% return is misleading. In computer implementations, naïvely multiplying many numbers together can cause arithmetic overflow or underflow.

The geometric mean is useful whenever the quantities to be averaged combine multiplicatively, such as population growth rates or interest rates of a financial investment. Suppose for example a person invests $1000 and achieves annual returns of +10%, −12%, +90%, −30% and +25%, giving a final value of $1609. The average percentage growth is the geometric mean of the annual growth ratios (1.10, 0.88, 1.90, 0.70, 1.25), namely 1.0998, an annual average growth of 9.98%. The arithmetic mean of these annual returns – 16.6% per annum – is not a meaningful average because growth rates do not combine additively. 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.

The Geometric Mean Calculator is an online tool for calculating the geometric mean of numbers.