Maths question!
Discussion
Wasn't really sure where to put this, but since it's related to a job I'm doing, I stuck it in here.
Scenario:
I have a collection of percentage figures, in sets of 10 (months) . They represent KPI performance for a particular task. I need to know the average KPI performance figure across the 10 months.
Option 1: take the average of the 10 percentages. This is an average of the percentage results and NOT an average of averages.
Option 2: take the base numbers for each month (in KPI/out of KPI), add them together to get a total in/out for the 10 months, then calculate that into a percentage.
I say that the figures will be the same whichever method is used (a random sample of one set produced this result but possible that was a coincidence). Someone at work says they will be different and wants them recalculated.
Whaddya think?
Scenario:
I have a collection of percentage figures, in sets of 10 (months) . They represent KPI performance for a particular task. I need to know the average KPI performance figure across the 10 months.
Option 1: take the average of the 10 percentages. This is an average of the percentage results and NOT an average of averages.
Option 2: take the base numbers for each month (in KPI/out of KPI), add them together to get a total in/out for the 10 months, then calculate that into a percentage.
I say that the figures will be the same whichever method is used (a random sample of one set produced this result but possible that was a coincidence). Someone at work says they will be different and wants them recalculated.
Whaddya think?
It depends on the rounding present in the database.
You sometimes get this rounding discrepancy when you do something as simple as totalling subtotals and separately totalling all data.
It won't make that much difference to the outcome, but if the KPI's are rounded to the nearest percent, it could produce a significant discrepancy.
If in doubt, always use the original data set for any statistical analysis.
You sometimes get this rounding discrepancy when you do something as simple as totalling subtotals and separately totalling all data.
It won't make that much difference to the outcome, but if the KPI's are rounded to the nearest percent, it could produce a significant discrepancy.
If in doubt, always use the original data set for any statistical analysis.
From what you've said, I'm sorry to say that these are fundamentally different calculation, unless the same number of things are attempted each month.
In the first case, you are evaluating the following,
and in the second case, the following.
These are not, in general, equal.
Suppose (say) one month an enormous number of things were attempted, and as a result all failed. In other months, work was at a much more reasonable level, and the success rate was 80%. In the second of the calculations above, the bad month dominates the results, but in the first, it does not.
So which one is correct? I guess that's a business decision - which one most accurately reflects what you want to measure etc etc.
Hope that helps.
Edit: Sorry I think the factor of 1/10 shouldn't be there in the second one.
In the first case, you are evaluating the following,
and in the second case, the following.
These are not, in general, equal.
Suppose (say) one month an enormous number of things were attempted, and as a result all failed. In other months, work was at a much more reasonable level, and the success rate was 80%. In the second of the calculations above, the bad month dominates the results, but in the first, it does not.
So which one is correct? I guess that's a business decision - which one most accurately reflects what you want to measure etc etc.
Hope that helps.
Edit: Sorry I think the factor of 1/10 shouldn't be there in the second one.
Edited by EliseNick on Monday 31st March 15:46
Thanks for the edit, I thought I was going mad!
I'll just have to run these calcs and see what difference, if any, it makes.
As a quick check with sample numbers I get the following (can't set the layout correctly, the forum takes out any additional spaces, but the far-right 95.49% and the bottom row 95.59% are the results - so, close but different!)
1 2 3 4 5 6 7 8 9 10 TOT
91 89 105 97 102 91 88 88 89 91 931
100 93 106 97 103 92 89 105 94 96 975
91.00% 95.70% 99.06% 100.00% 99.03% 98.91% 98.88% 83.81% 94.68% 94.79% 95.49% Average of total numbers
Average of results 95.59%
I'll just have to run these calcs and see what difference, if any, it makes.
As a quick check with sample numbers I get the following (can't set the layout correctly, the forum takes out any additional spaces, but the far-right 95.49% and the bottom row 95.59% are the results - so, close but different!)
1 2 3 4 5 6 7 8 9 10 TOT
91 89 105 97 102 91 88 88 89 91 931
100 93 106 97 103 92 89 105 94 96 975
91.00% 95.70% 99.06% 100.00% 99.03% 98.91% 98.88% 83.81% 94.68% 94.79% 95.49% Average of total numbers
Average of results 95.59%
Only reason the results are close is because the scores are all around 90-100% and the denominators (100 93 106 97 103 92 89 105 94 96) are relatively similar numbers. Try some random numbers instead of your sample data and you'll see the difference.
If the denominators were the same (e.g. all the KPIs were scored out of 100) then the two methods will be the same. Otherwise they're almost always going to be different. In maths being close is as good as a million miles away
If the denominators were the same (e.g. all the KPIs were scored out of 100) then the two methods will be the same. Otherwise they're almost always going to be different. In maths being close is as good as a million miles away
A mathematician and a physicist agree to a psychological experiment.
The mathematician is put in a chair in a large empty room and a beautiful naked woman is placed on a bed at the other end of the room.
The psychologist explains, "You are to remain in your chair. Every five minutes, I will move your chair to a position halfway between its current location and the woman on the bed."
The mathematician looks at the psychologist in disgust. "What? I'm not going to go through this. You know I'll never reach the bed!"
And he gets up and storms out.
The psychologist makes a note on his clipboard and ushers the physicist in. He explains the situation, and the physicist's eyes light up and he starts drooling. The psychologist is a bit confused.
"Don't you realize that you'll never reach her?"
The physicist smiles and replied, "Of course! But I'll get close enough for all practical purposes!"
The mathematician is put in a chair in a large empty room and a beautiful naked woman is placed on a bed at the other end of the room.
The psychologist explains, "You are to remain in your chair. Every five minutes, I will move your chair to a position halfway between its current location and the woman on the bed."
The mathematician looks at the psychologist in disgust. "What? I'm not going to go through this. You know I'll never reach the bed!"
And he gets up and storms out.
The psychologist makes a note on his clipboard and ushers the physicist in. He explains the situation, and the physicist's eyes light up and he starts drooling. The psychologist is a bit confused.
"Don't you realize that you'll never reach her?"
The physicist smiles and replied, "Of course! But I'll get close enough for all practical purposes!"
Not 100% sure I get what you are being asked for but the first gives you an average month.
If you want a 10 month total percentage then surely it's (total in/(total in + total out))*100 to give you the percentage in over 10 months.
But it's late
so good luck.
Mike
If you want a 10 month total percentage then surely it's (total in/(total in + total out))*100 to give you the percentage in over 10 months.
But it's late
so good luck.Mike
Edited by MH on Thursday 3rd April 00:24
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