Result:
Understanding the Geometric Mean
The geometric mean is a type of average often used to find the central tendency of a set of numbers in multiplicative relationships. It is especially useful in growth rates and ratios.
Formula: \( \text{Geometric Mean} = \sqrt[n]{x_1 \times x_2 \times \dots \times x_n} \)
Real-Life Example
Suppose you want to calculate the average growth factor of an investment over 5 years with annual growth rates of 1.05, 1.08, 1.02, 1.04, and 1.06. The geometric mean provides the consistent annual growth rate that would give the same total growth over 5 years.
Calculation: \( \sqrt[5]{1.05 \times 1.08 \times 1.02 \times 1.04 \times 1.06} \approx 1.05 \)
Thus, the equivalent annual growth rate is approximately 1.05 (or 5%).