The mean of 13.8 percent, 5.3 percent, and 3.1 percent is? 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 ofwhich are positive), the geometric mean is the nth root of their product. The average growth factor for money compounded at annual interest rates of 13.8%, 5.3%, and3.1% can be found by computing the geometric mean of 1.138, 1.053, and 1.031. Find that average growth factor, or geometric mean. Whatsingle percentage growth rate would be the same as having three successive growth rates of 13.8%, 5.3%, and 3.1%? Is that result the same as the mean of 13.8%,5.3%, and 3.1%?

Answered: n of 13.8 percent, 5.3 percent, and 3.1…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The mean of 13.8 percent, 5.3 percent, and 3.1 percent is?

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 13.8%, 5.3%, and
3.1% can be found by computing the geometric mean of 1.138, 1.053, and 1.031. Find that average growth factor, or geometric mean. What
single percentage growth rate would be the same as having three successive growth rates of 13.8%, 5.3%, and 3.1%? Is that result the same as the mean of 13.8%,
5.3%, and 3.1%?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1

First, we need to obtain the average growth factor or the geometric mean. It is calculated as follows:

$A v e a r g e g r o w t h f a c t o r {= (1.138 * 1.053 * 1.031)}^{\frac{1}{3}} = 1.073025$

Hence, average growth factor=1.073025

The single percentage growth rate is obtained as follows;

$S i n g l e p e r c e n t a g e g r o w t h r a t e = (A v e a r g e g r o w t h f a c t o r - 1) * 100 = (1.073025 - 1) * 100 = 0.073025 * 100 = 7.3025 %$