Question 1187335
.
Harris had an investment that yielded the following results over the last 4 years:
10.0%; 7.0%; 13.5%; -12.0%.
What is the arithmetic mean? The geometric mean?
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<pre>
When the yield coefficients (the growing coefficients) of the account are given as the percentages,

from year to year, as in this given problem, which means


    {{{r[1]}}} = 1.10 in the 1st year;  {{{r[2]}}} = 1.07 in the 2nd year;  {{{r[3]}}} = 1.135 in the 3rd year;  {{{r[4]}}} = 0.88 in the 4th year,


then the geometric mean DENOTES the geometric mean of these groving coefficients  1.1, 1.07, 1.135 and 0.88.



It MAKES SENSE, since allows to measure / (to evaluate) the average effective annual growing coefficient over the four years.



This geometric mean of the growing coefficients obeys to the usual definition


    G(1.1, 1.07, 1.135, 0.88) = {{{root(4, 1.1*1.07*1.135*0.88)}}} = {{{root(4, 1.17588)}}} =  1.041271 = 1.04 (rounded).    <U>ANSWER</U>


The geometric mean growing coefficient, effective over the four years, is 1.04, and the average percentage yield is about 4%.
</pre>

Solved, answered and carefully/thoroughly explained.


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See my lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Average/Geometric-Mean.lesson>WHAT IS Geometric mean</A>

in this site.