When to Use Geometric Mean
- Growth Rates and Compounding
- Reason: The geometric mean is ideal for calculating average growth rates over time, as it takes into account the compounding effect.
- Example: When determining the average annual growth rate of an investment portfolio over several years. If an investment grows by 10% in the first year, 20% in the second year, and 15% in the third year, the geometric mean provides a more accurate average growth rate. Case Example 1:
- Normalised or Indexed Data
- Reason: When working with data that has been normalised or transformed into indices, the geometric mean is more appropriate.
- Example: In financial markets, indices like the Consumer Price Index (CPI) or stock market indices often use geometric mean to ensure that the average change reflects relative, not absolute, changes. Difference between Relative and Absolute Changes Case Example 2
When to Use Arithmetic Mean
- Additive Processes:
- When the data involves additive processes or sums.
- Example: Calculating the average score of students in a test or average temperature over a week. Case Example 6
- Independent and Identically Distributed Variables:
- When the variables are independent and have the same units.
- Example: Average height or weight of a group of people. Case Example
- Log-Normally Distributed Data
- Reason: For datasets that are log-normally distributed (the logarithms of the values are normally distributed), the geometric mean is a better measure of central tendency than the arithmetic mean.
- Example: Income distribution or asset prices often follow a log-normal distribution. Case Example 3
- Proportional Changes
- Reason: When the data represents proportional changes rather than absolute values.
- Example: Calculating the average percentage return on investment over multiple periods. If an investment changes by different percentages each year, the geometric mean gives the correct average annual return. Case Example 4
- Productivity and Efficiency Measurements
- Reason: In measuring productivity or efficiency, where different factors are multiplicative.
- Example: When analyzing the efficiency of production processes where multiple steps or factors contribute multiplicatively to the overall efficiency. Case Example 5
- Harmonic Relationships
- Reason: When dealing with rates or ratios that are inversely proportional.
- Example: In situations involving speed or other rate-based measurements, where the harmonic mean is often used, but the geometric mean can also be appropriate when dealing with multiplicative rates.