Comparing Methods: Averaging Gaps with Arithmetic/Geometric Mean

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In summary, the two methods had different results, with the first method being better than the second. The gap was computed to be 4.91% and the average gaps was -24.77%.
  • #1
nabilaUSTHB
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View attachment 8930
However I have an optimization problem (minimization problem), and the table (attached fill) represents a comparative study between the results of two methods, the first one performed better than the second one and to quantify the effectiveness of the first method we computed the gap which equal to:
GAP=((Method2-method1)/method1)*100

To compute the average gaps I used the arithmetic mean which equal to:
Mean-gaps=-(10+2.47+6.5+0.40+5.18)/5=-4.91%
And in conclusion I sad that method1 improved method 2 by 4.91 on average.
I used the average mean since the gaps results with no significant outliers, and the gaps are independents and not normalized ( normal)!
My question in is In this case which one I should use whether the arithmetic or the geometric mean to compute the average gaps!
 

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  • #2
Check your calculator or program:

Benchmark2 GAP should be -24.77%; you show -2.47%

Benchmark3 GAP should be -8.58%; you show -6.50%
 
  • #3
I disagree with your 4.91% results; should be 3.36%.
A comparison after TOTALLING is required:
Code:
    1200        1320  -10.00%
   22000       27450  -24.77%
   48000       52124  - 8.59%
  745000      748000  - 0.40%
  904522      951422  - 5.18%
-----------------------------
 1720722     1780316  - 3.36%

You are using an average of the percentages
which distorts the picture.
As example, you could have a small amount
like 10 increasing to 20 for a 100% increase,
and you would be using the 100% in calculating
the final effect with as much "weight" as the others.
 
  • #4
Wilmer said:
I disagree with your 4.91% results; should be 3.36%.
A comparison after TOTALLING is required:
Code:
    1200        1320  -10.00%
   22000       27450  -24.77%
   48000       52124  - 8.59%
  745000      748000  - 0.40%
  904522      951422  - 5.18%
-----------------------------
 1720722     1780316  - 3.36%

You are using an average of the percentages
which distorts the picture.
As example, you could have a small amount
like 10 increasing to 20 for a 100% increase,
and you would be using the 100% in calculating
the final effect with as much "weight" as the others.
............
But you have not replied yet...which one I should use in this case arithmetic or geometric mean
 
  • #5
nabilaUSTHB said:
But you have not replied yet...which one I should use in this case arithmetic or geometric mean
That's YOUR decision...ask your teacher.
I showed you the method that represents the actual percentage change.

In case this helps you:
https://www.investopedia.com/ask/answers/06/geometricmean.asp
 
  • #6
nabilaUSTHB, you definitely should use the second one (arithmetic). Why? Cause the final effect is really with as much "weight" as the others. https://bestcalculators.net - will help you make the right choice of calculator you need, to understand all the steps, that lead to the right solution.
 
  • #7
mikey92 said:
nabilaUSTHB, you definitely should use the second one (arithmetic). Why? Cause the final effect is really with as much "weight" as the others. https://bestcalculators.net - will help you make the right choice of calculator you need, to understand all the steps, that lead to the right solution.
Mikey, that makes no sense. Are you a salesman "in disguise"?:)

Let's take a simple example:
you invest 1000 for 1 year at 5% and 100 for 1 year at 50%:
Code:
Jan.1  Rate   Dec.31
1000    5%    1050
 100   50%     150
------------------
1100    9%    1200
Clear enuff? Same as investing 1100 at 9% for 1 year.

Now, if using your method, then we'd get:
(5 + 50) / 2 = 27.5% : quite ridiculous when the actual is 9%.

You both (you and the OP) need help from your teachers.
I'm outta here!
 

FAQ: Comparing Methods: Averaging Gaps with Arithmetic/Geometric Mean

What is the purpose of comparing methods using arithmetic and geometric mean when calculating gaps?

The purpose of comparing methods using arithmetic and geometric mean is to determine the most accurate and reliable method for calculating gaps between data points. This is important in scientific research and data analysis, as it allows for more accurate and meaningful comparisons between different sets of data.

What is the difference between arithmetic and geometric mean?

Arithmetic mean is the sum of all values in a set divided by the total number of values, while geometric mean is the nth root of the product of all values in a set, where n is the number of values. In other words, arithmetic mean takes into account the individual values of the data set, while geometric mean considers the magnitude of the values as well.

Which method is more appropriate for comparing small gaps between data points?

Arithmetic mean is more appropriate for comparing small gaps between data points, as it gives equal weight to each data point and is not affected by extreme values. Geometric mean may give more weight to larger gaps and can be skewed by outliers.

When is it more appropriate to use geometric mean for comparing gaps?

Geometric mean is more appropriate for comparing large gaps between data points, as it takes into account the magnitude of the values and can reduce the effect of extreme values. It is also useful when working with exponentially increasing or decreasing data.

Can both arithmetic and geometric mean be used together in comparing gaps?

Yes, both arithmetic and geometric mean can be used together in comparing gaps. In some cases, it may be useful to compare the results from both methods in order to get a more comprehensive understanding of the gaps in the data set. However, it is important to use caution and consider the nature of the data and the purpose of the comparison before using multiple methods.

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