Comparing Methods: Averaging Gaps with Arithmetic/Geometric Mean

[nabilaUSTHB]

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!

 

[Wilmer]

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%

 

[Wilmer]

I disagree with your 4.91% results; should be 3.36%.
A comparison after TOTALLING is required:

    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.

 

[nabilaUSTHB]

I disagree with your 4.91% results; should be 3.36%.
A comparison after TOTALLING is required:

    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

 

[Wilmer]

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

 

[mikey92]

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.

 

[Wilmer]

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%:

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!