Geometric mean

Definition

The geometric mean is a measure of central tendency that is calculated by multiplying all the values in a data set and then taking the nth root, where n is the number of values. It is especially useful for sets of numbers whose values are meant to be multiplied together or are exponential in nature.

5 Must Know Facts For Your Next Test

1. The geometric mean is always less than or equal to the arithmetic mean for any given data set.
2. It is particularly useful in finance for calculating average rates of return over multiple periods.
3. The geometric mean can only be used with positive numbers; it does not work with negative or zero values.
4. In financial contexts, it provides a more accurate measure of central tendency when dealing with volatile returns compared to the arithmetic mean.
5. To calculate the geometric mean, you need to take the product of all data points and raise it to the power of 1/n, where n is the number of data points.

Review Questions

• Why is the geometric mean preferred over the arithmetic mean in calculating average rates of return?
• Can you use the geometric mean if your data set includes zero or negative numbers? Why or why not?
• How do you calculate the geometric mean for a data set with five values?

Related terms

arithmeticMean: A measure of central tendency calculated by adding all values and dividing by their count.

median: The middle value in a data set when it has been arranged in ascending order.

harmonicMean: A measure of central tendency calculated as the reciprocal of the arithmetic mean of reciprocals.