When an observation in the data is zero, then its geometric mean is :

The correct answer is - Zero

Key Points

• Geometric mean
  • The geometric mean is calculated by taking the nth root of the product of all data points, where n is the total number of observations.
• Impact of zero in the dataset
  • If any observation in the dataset is zero, the product of all data points becomes zero.
  • The nth root of zero is also zero, making the geometric mean zero.
• Reason why the answer is zero
  • Since the geometric mean involves multiplication, the presence of zero ensures the value of the product is zero, leading to a geometric mean of zero.

Additional Information

• Applications of geometric mean
  • Used in finance to calculate average growth rates (e.g., returns on investment).
  • Applied in statistics to measure central tendency for data that follows a multiplicative relationship.
• Difference between arithmetic and geometric mean
  • The arithmetic mean calculates the average by summing data points and dividing by their count, unaffected by zero values.
  • The geometric mean, involving multiplication, is directly affected by zero values in the dataset.
• Special cases
  • If all observations are positive, the geometric mean is also positive.
  • If the dataset contains negative values, the geometric mean may not be defined for certain scenarios (e.g., even roots of negative numbers).