The information below shows the cost for a year of college...

The information below shows the cost for a year of college in public and private colleges in 1992 and $2003 .$ What is the geometric mean annual increase for the period for the two types of colleges? Compare the rates of increase.

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Key Concepts

Geometric Mean

The geometric mean is a statistical measure used to determine the central tendency of a set of numbers by using the product of their values. In growth rate calculations, it is particularly useful because it accounts for compounding over time. It is calculated by taking the nth root of the product of n numbers, which allows for determining an average rate of change over multiple periods of time.

Compound Growth Rate

The compound growth rate represents the rate at which something grows over a period of time when the effects are compounded. It is calculated using the formula (Ending Value/Beginning Value)^(1/number of periods) - 1, which gives the average annual growth rate that, when compounded, leads from the initial amount to the final amount.

Comparison of Growth Rates

Comparing growth rates involves analyzing the percentage increase over time to determine how quickly different quantities are growing. By computing the geometric mean annual increase for each case, one can directly compare the underlying annual compounded growth, highlighting which scenario has experienced faster or slower change over the period in question.

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