Question 1187335: 5. 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?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
 %, %, %, %
to calculate arithmetic mean, write percentage as decimal, add all and divide by 
arithmetic  or  %
geometric mean:
Geometric  , assuming data
values are 
in your case , , , , , geometric mean  be calculated
Geometric mean can only be calculated when all numbers have the same sign.
Geometric mean cannot be calculated for negative values.
Answer by ikleyn(52784)  (Show Source):
You can put this solution on YOUR website! .
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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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
 = 1.10 in the 1st year;  = 1.07 in the 2nd year;  = 1.135 in the 3rd year;  = 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) =  =  = 1.041271 = 1.04 (rounded). ANSWER
The geometric mean growing coefficient, effective over the four years, is 1.04, and the average percentage yield is about 4%.
Solved, answered and carefully/thoroughly explained.
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See my lesson
- WHAT IS Geometric mean
in this site.
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