Geometric Mean
The geometric mean is a type of average that is used to compare different sets of data. It is defined as the n-th root of the product of n values. The geometric mean often is used to indicate an overall rate of growth or decrease, when dealing with sets of numbers that increase and decrease in value, or that have different rates of growth.
For example, if you wanted to compare the growth rates of stocks A, B and C over the past year, you would take the product of each closing price of the three stocks at the end of each period, and then find the 3rd root of that product. This would give you the geometric mean of the 3 stocks.
The geometric mean is also commonly used in computing the performance of mutual funds or in calculating the annualized rate of return on investment. To calculate the geometric mean, you take the product of all of the monthly returns of a fund, and then take the nth root, where n equals the number of months in a year.
When using the geometric mean to compare different sets of data, it is important to note that the geometric mean values typically appear lower than the arithmetic mean. This occurs because the geometric mean gives equal weight to each data point, while the arithmetic mean calculated an average based on the total sum of all numbers.
The geometric mean is a helpful tool for quantifying measured data that is subject to variation. It is especially useful in situations where there is a large range of values and where the results that are being measured are subject to increasing or decreasing rates of growth. By calculating the geometric mean, it is possible to find an overall average that accurately reflects the impact of each data point on the whole.