When data consist of percentages, ratios, compounded growth rates, or other rates of change, the geometric mean is a useful measure of central tendency. For n data values, the geometric mean, assuming all data values are positive, is as follows. To find the average growth factor over 5 years of an investment in a mutual fund with growth rates of 8.7% the first year, 11.5% the second year, 15.2% the third year, 3% the fourth year, and 7.1% the fifth year, take the geometric mean of 1.087, 1.115, 1.152, 1.03, and 1.071.Find the average growth factor of this investment. (Round your answer to four decimal places.) When data consist of percentages, ratios, compounded growth rates, or other rates of change, the geometric mean is a useful measure of central tendency. For n data values, the geometric mean,assuming all data values are positive, is as follows. To find the average growth factor over 5 years of an investment in a mutual fund with growth rates of 8.7% the first year, 11.5% the second year,15.2% the third year, 3% the fourth year, and 7.1% the fifth year, take the geometric mean of 1.087, 1.115, 1.152, 1.03, and 1.071. Find the average growth factor of this investment. (Round youranswer to four decimal places.)Geometric mean = V product of the n data values

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Description: When data consist of percentages, ratios, compounded growth rates, or other rates of change, the geometric mean is a useful measure of central tendency. For n data values, the geometric mean, assuming all data values are positive, is as follows. To f

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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When data consist of percentages, ratios, compounded growth rates, or other rates of change, the geometric mean is a useful measure of central tendency. For n data values, the geometric mean, assuming all data values are positive, is as follows. To find the average growth factor over 5 years of an investment in a mutual fund with growth rates of 8.7% the first year, 11.5% the second year, 15.2% the third year, 3% the fourth year, and 7.1% the fifth year, take the geometric mean of 1.087, 1.115, 1.152, 1.03, and 1.071.

Find the average growth factor of this investment. (Round your answer to four decimal places.)

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 + ...

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Introduction:

The geometric mean is a mean or average that uses the product of its values, indicating the central tendency or the typical value of a set of numbers. For several purposes, the geometric mean is an important instrument for measuring portfolio results, but one of the most important is that it takes the effects of compounding into account.

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The given growth rates of 5 years are:

$\begin{array}{rcl} 1^{s t} year & = & 8.7 % \\ 2^{n d} year & = & 11.5 % \\ 3^{r d} year & = & 15.2 % \\ 4^{t h} year & = & 3 % \\ 5^{t h} year & = & 7.1 % \end{array}$

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