JoVE Logo

Sign In

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 MeanCentral TendencyMultiplicative DataStatistical AnalysisData SetProduct Of ElementsNth RootAverage Growth FactorCompound InterestNatural Logarithmic FunctionArithmetic MeanSample Data Set

From Chapter 3:

article

Now Playing

3.3 : Geometric Mean

Measure of Central Tendency

3.4K Views

article

3.1 : ما هو الاتجاه المركزي؟

Measure of Central Tendency

14.1K Views

article

3.2 : المتوسط الحسابي

Measure of Central Tendency

13.4K Views

article

3.4 : الوسط التوافقي

Measure of Central Tendency

3.1K Views

article

3.5 : متوسط مشذب

Measure of Central Tendency

2.8K Views

article

3.6 : المتوسط المرجح

Measure of Central Tendency

4.9K Views

article

3.7 : جذر متوسط مربع

Measure of Central Tendency

3.2K Views

article

3.8 : المتوسط من توزيع التردد

Measure of Central Tendency

16.1K Views

article

3.9 : ما هو الوضع؟

Measure of Central Tendency

18.1K Views

article

3.10 : متوسط

Measure of Central Tendency

17.9K Views

article

3.11 : المدى المتوسط

Measure of Central Tendency

3.6K Views

article

3.12 : الانحراف

Measure of Central Tendency

10.9K Views

article

3.13 : أنواع الانحراف

Measure of Central Tendency

11.4K Views

JoVE Logo

Privacy

Terms of Use

Policies

Research

Education

ABOUT JoVE

Copyright © 2025 MyJoVE Corporation. All rights reserved