Question

The geometric mean is often used in business and economics for finding average rates of​ change, average rates of​ growth, or average ratios. given n values​ (all of 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 14.814.8​%, 6.46.4​%, and 1.71.7​% can be found by computing the geometric mean of 1.1481.148​, 1.0641.064​, and 1.0171.017. find that average growth​ factor, or geometric mean. what single percentage growth rate loading... would be the same as having three successive growth rates of 14.814.8​%, 6.46.4​%, and 1.71.7​%? is that result the same as the mean of 14.814.8​%, 6.46.4​%, and 1.71.7​%?

Answer 1

Over the three years, we've grown by a factor of

$1.148\times 1.064\times 1.017= 1.242237024$

The average growth is given by the geometric mean,

$\sqrt[3]{1.148 \times 1.064\times 1.017} = 1.0749827360...$

Answer: 7.5%

The geometric mean is always smaller than the arithmetic mean:

$\frac 1 3(14.8\% + 6.4\% + 1.7\%)=7.633\%$