Below are the costs for a year of college in public and private colleges in 1992 and 2007. What is the geometric mean annual increase for the period for the two types of colleges? Compare the rates of increase.
Type of college 1992 2007
Public $4,975 $11,354
Private 12,284 27,516
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To calculate the geometric mean annual increase, we need to find the ratio of the final value to the initial value, raise it to the power of 1 divided by the number of years, and subtract 1.
For public colleges:
Initial value = $4,975
Final value = $11,354
Number of years = 2007 - 1992 = 15
Geometric mean annual increase for public colleges = (11,354/4,975)^(1/15) - 1 ≈ 0.0585 or 5.85%
For private colleges:
Initial value = $12,284
Final value = $27,516
Number of years = 2007 - 1992 = 15
Geometric mean annual increase for private colleges = (27,516/12,284)^(1/15) - 1 ≈ 0.0577 or 5.77%
Comparing the rates of increase, the geometric mean annual increase for public colleges was 5.85% while for private colleges it was 5.77%. The rate of increase was slightly higher for public colleges.
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