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I came across the following while doing some questions from my textbook.
For eg. lets say we need to calculate the total percentage of marks for the following subjects:

  1. Maths 64/100
  2. English 78/100
  3. Science 30/50

Total percentage being calculated as (64+78+30)/250 = 68.8 %

The other method I followed was to calculate individual percentages and then take their average

  1. Maths 64/100 = 64%
  2. English 78/100 = 78%
  3. Science 30/50 = 60%

Their average being (64+78+60)/3 = 67.33 %
I know by forming equations I can prove the second method is different from the first, but is there any logical statements that proves the second method is wrong and the first correct.

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    @DayLateDon that's the main problem, that is why my first thought was there "may" exist some formal text which says which method to follow.2012-06-30

2 Answers 2

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In my opinion, the second method is a trick.

For the first method, we can simply get the answer is $\frac{64+78+60}{250}=68.8\%.$

For the second method, we get the average point of each subject like

  1. Maths $\frac{64}{100}=64\%$
  2. English $\frac{78}{100}=78\%$
  3. Science $\frac{60}{50}=30\%$

Now, we should calculate the average in the following way

$64\% \times\frac{100}{250}+78\% \times\frac{100}{250}+60\% \times\frac{50}{250}=68.6\%.$

It called weighted average, and $\frac{100}{250},\frac{100}{250},\frac{50}{250}$ is called weights.

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No, there exists no (meaningful) way to prove the second method wrong. Science could get weighted twice as much as English and Maths, as in Science could come as twice as important as English and twice as important as Maths, in which case both methods yield the same result.

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    If science is weighted twice as much as the other two, then 50 points in the science category equals 100 in the other categories. So, then, science percentage marks equal 60, and (((60+64)+78)/300)=.67333... the same result you got. It will also yield the same result in general.2012-06-30