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When to Use Geometric Mean

When to Use Geometric Mean

  1. 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:
  2. 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

  1. 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
  2. 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
  1. 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
  1. 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
  1. 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
  1. 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.