Final answer:
The annual rate increase of the Dow Jones from 1980 to 1998 is best described by the geometric mean, due to its suitability for compounded rates of change. This reflects the trend of substantial growth in the stock market during the 1980s and the volatility experienced from 2000 to 2013, where prices ended at similar levels as where they started.
Step-by-step explanation:
The annual rate increase of the Dow Jones Industrial Average from 961 in 1980 to 8900 in the first quarter of 1998 is best described by the geometric mean. This is because the geometric mean is the most appropriate measure when dealing with rates of change that are compounded over time, such as stock price indices. The geometric mean considers exponential growth or decay, which is typical in finance when analyzing investment returns over various periods. The arithmetic mean (simple average) would not be appropriate here because it does not account for the compounding effect.
When observing the Dow Jones Industrial Average over a period of time as it fluctuates, one can notice significant periods of growth, decline, and stagnation. For instance, stock prices escalated dramatically from the 1980s up to about 2000, then from 2000 to 2013 the prices experienced volatility, bouncing up and down and ending approximately at the same level. Recognizing these trends is essential for investors and reflects the variable nature of the stock market, with intervals of robust gains often followed by times of increased uncertainty or plateauing prices.