The geometric mean is often used in business and economics for finding average r

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 12.2%, 4.4%, and 2.5% can be found by computing the geometric mean of 1.122, 1.044, and 1.025. Find that average growth factor, or geometric mean. What single percentage growth rate would be the same as having three successive growth rates of 12.2%, 4.4%, and 2.5%? Is that result the same as the mean of 12.2%, 4.4%, and 2.5%? The average growth factor is .

Explanation / Answer

Geometric Mean = ((X1)(X2)(X3)........(XN))1/NWhere, X = Individual score N = Sample size (Number of scores)

=(1.122*1.044*1.025)^1/3

=1.06285

Part b.

Single % growth rate can be calculated by taking 100 as the nase.

Increase in 100 by 12.2% is 112.2.

Again increase in 112.2 by 4.4% is 117.1368

Again  increase in 117.1368 by 2.5% is 120.0652

Hence a single growth rate of (120.0652-100) = 20.0625 is the answer.

Mean of 12.2%,4.4% and 2.5 % is 6.36% hence, it is not the same

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