To determine which scenarios should use the geometric mean, it's essential to understand that the geometric mean is typically used when working with percentages, rates, and ratios, particularly when these figures are changing over time. It is more appropriate for situations involving compound growth rates, where the interest or growth compounds over multiple periods.
Let's evaluate each option:
1. Average number of items sold on six consecutive days at a store:
- This situation involves a simple average of quantities (items), not percentages or rates. The arithmetic mean is more appropriate here.
2. Average rainfall for a series of ten years:
- Rainfall data over years usually involves simple averaging of quantities (millimeters or inches of rain). Again, the arithmetic mean would generally be used here.
3. Average percentage annual yield for a portfolio of stocks:
- This involves percentages that typically change and compound over time. The geometric mean is more appropriate for averaging these kinds of rates to account for compounding effects over multiple periods.
4. Average growth rate for four years of sales figures:
- This involves growth rates (likely percentages) that change over several periods. As these are rates that compound over time, the geometric mean is suitable for this calculation.
Given this reasoning, the scenarios that should be calculated using the geometric mean are:
- Average percentage annual yield for a portfolio of stocks.
- Average growth rate for four years of sales figures.
