The arithmetic mean, often referred to as the average, is calculated by summing a set of values and then dividing by the number of values. It is a measure of central tendency that provides a simple way to represent a typical value in a dataset.
The geometric mean is calculated by multiplying a set of values together and then taking the nth root of the product, where n is the total number of values. It is particularly useful for sets of numbers that are exponentially related or for data that spans several orders of magnitude.
The arithmetic mean is appropriate when the data is normally distributed and there are no extreme outliers. It is best used for additive data, such as heights, weights, or test scores. In contrast, the geometric mean is more suitable for multiplicative data, such as growth rates or financial returns.
The geometric mean is less affected by extreme values and is more representative of typical values in skewed distributions. It is particularly useful for comparing different items with percentage changes or ratios, as it provides a more accurate measure of central tendency for such data.