Waiting
Login-Verarbeitung ...

Trial ends in Request Full Access Tell Your Colleague About Jove

3.3: Geometric Mean

TABLE OF
CONTENTS
JoVE Core
Statistics

Ein Abonnement für JoVE ist erforderlich, um diesen Inhalt ansehen zu können. Melden Sie sich an oder starten Sie Ihre kostenlose Testversion.

Education
Geometric Mean
 
TRANSCRIPT

3.3: Geometric Mean

The mean is a measure of the central tendency of a data set. In some data sets, the data is inherently multiplicative, and the arithmetic mean is not useful. For example, the human population multiplies with time, and so does the credit amount of financial investment, as the interest compounds over successive time intervals.

In cases of multiplicative data, the geometric mean is used for statistical analysis. First, the product of all the elements is taken. Then, if there are n elements in the dataset, the nth root of the products is defined as the geometric mean of the data set. It can also be expressed via the use of the natural logarithmic function.

For example, suppose money compounds at annual interest rates of 10%, 5%, and 2%. In that case, the average growth factor can be calculated by computing the geometric mean of 1.10, 1.05, and 1.02. Its value comes out to be 1.056, which means that the average growth rate is 5.6% per annum.

It can be shown that the geometric mean of a sample data set is always quantitatively less than or at most equal to the arithmetic mean of the sample.

Tags

Geometric Mean Central Tendency Statistical Analysis Multiplicative Data Arithmetic Mean Financial Investment Compound Interest Growth Factor Average Growth Rate Sample Data Set

Get cutting-edge science videos from JoVE sent straight to your inbox every month.

Waiting X
Simple Hit Counter