Help on Percent

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zen554

New member
Joined
Jan 16, 2010
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Pls help explain why the calculated average percent is "out of range", here's my problem -

Product A:
Before: 100/33=3.03
After: 120/37=3.24
Change: (3.24/3.03)-1 = 7%

Product B:
Before: 5/4.7=1.06
After: 7/6=1.17
Change: (1.17/1.06)-1 = 9.7%
Total of Product A and B:
Before: 105/37.7 = 2.79
After: 127/43 = 2.95
Change: (2.95/2.79)-1 = 6%

I cant understand why the calculated total average change (which is 6%) is lower than change for product A and B. Shouldn't the total ave change within the range of 7% to 9.7%? Pls. explain to me, I dont quite understand. Thanks!
 
Hello, zen554!



Product A
Before: 100/33 = 3.03
After: 120/37 = 3.24
Change: (3.24/3.03) - 1 = 7%

Product B
Before: 5/4.7 = 1.06
After: 7/6 = 1.17
Change: (1.17/1.06)-1 = 9.7%

Total of Product A and B
Before: 105/37.7 = 2.79
After: 127/43 = 2.95
Change: (2.95/2.79)-1 = 6%

I cant understand why the calculated total average change (which is 6%)
is lower than change for product A and B.
Shouldn't the total ave change within the range of 7% to 9.7%?
Pls. explain to me, I dont quite understand. Thanks!
Click to expand...

It would help if you explained what those quantities are.
Some quantities can not be freely averaged.


An executive gets $18,000 per month: $600 per day (for 30 days).
Her salary is raised to $24,000 per month: $800 per day.
Her increase is: 800/600 - 1 = 25%

An employee gets $2800 per week: $400 per day (for 7 days).
His salary is raised to $3500 per week: $500 per day.
His increase is: 500/400 - 1 = 20%


"Combined" (?): Two methods

Their original "average pay" is: $20,800/37 = $562.16
Their new "average pay" is: $27,500/37 = $743.24
Their increase is: 743.24/562.16 - 1 = 32%

Their original daily pay is: $600 + 400 = $10,000
The new daily pay is: $800 + 500 = $13,000
Their increase is: 13,000/10,000 - 1 = 30%

Either way, the average increase is "out of range".


I believe this is quite possible, depending on the quantities involved.
(However, there are some logical errors in my work above.)

 
thanks soroban for taking the time to solve my problem. to address your question on what these quantities are, the numerator pertains to the sales of the product while the denominator is the expense incurred. the change being measured is the improvement in 'productivity' (sale generated per dollar spent in advertising) after the product was relaunched. showing the total (of the 2 products) attempts to show the improvement in productivity due to the relaunch of the products. is there a principle in math which could explain why the calculated total average is 'out of range'?
 
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