The geometric mean is often used in business and economics for nding average rat

Question

The geometric mean is often used in business and economics for nding average rates o change, average rates of gro rth or average ratios. she values a which are positive), the geometric mean is the nth root of their product. The average growth factor for money compounded at annual interest rates of 11.6%,5.4%, and 1.5% can be found by computing the geometric mean of 1 116, 1.054, and 1.015. Find hat average growth factor or geometric mean what single percentage owth ate would be the same as having three successive growth rates of 11 6%, 54% and 15% s that result the same as the meanof 16% 5.4%, and 1.5%? The average growth factor is (Round to four decimal places as needed.)

Explanation / Answer

=(1.116*1.054*1.015)^(1/3)

=1.0609

The average growth factor is 1.0609

The single percentage growth rate that would be the same as having three successive growth rates of 11.6%, 5.4%, and 1.5% is 6.09%.

=(1.0609-1)*100 = 6.09

The mean of 11.6%, 5.4%, and 1.5% is

=(11.6+5.4+1.5)/3

= 6.17

The single percentage growth rate is not the same as the mean of 11.6%, 5.4%, and 1.5%

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