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Consider this addition of the fractions: \begin{align} \dfrac{1}{2}+\dfrac{10}{30}=\dfrac{5}{6}. \end{align}

Then consider a case where a person has got $\dfrac12$ in a subject and $\dfrac{10}{30}$ in another subject: \begin{align} \text{Percentage obtained =} \dfrac{\text{Marks obtained}×100}{\text{Total marks}}=\dfrac{(1+10)×100}{30+2}=34.375. \end{align}

So, the person scored $34.375\%.$ This is how all teachers calculate.

But isn't this wrong? Doesn't this method violate laws of fractions?

As in, $1$ mark obtained in the first subject has more “value” compared to the $1$ mark obtained in the second subject?

ryang
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Aleph
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  • As currently stated, it does not hold more value for either exam because you are summing up the total mark? – UnsinkableSam Mar 08 '22 at 17:44
  • Adding up the fractions can give you a ratio in excess of $1$, which would imply that the student has gotten more than the total possible number of marks... – abiessu Mar 08 '22 at 17:57
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    "This is the way all teachers calculate"??!! What teachers have told you this? If the 2-point assignment counts only 1/15 as much as the 30-point assignment, then this makes sense; you're just adding total points. – Ted Shifrin Mar 08 '22 at 18:06
  • So which method is correct? – Aleph Mar 08 '22 at 18:14
  • Second is the correct way. If you have two problems, each worth 10 points, and if you get half of each then your grade should be half of the maximum possible. – Andrei Mar 08 '22 at 18:21
  • @ryang +1 for explaining in detail why the methods are different – Andrei Mar 08 '22 at 18:56

1 Answers1

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Your top example needs to be corrected from $$\require{cancel} \cancel{\dfrac{1}{2}+\dfrac{10}{30}=83.333\%}$$ to $$\frac12\left(\dfrac{1}{2}+\dfrac{10}{30}\right)=41.667\%;$$ this computes the simple average of the scaled scores of the various subjects.

In contrast, in your bottom example $$\frac{1+10}{2+30}\color{green}{=\frac2{32}\left(\dfrac{1}{2}\right)+\frac{30}{32}\left(\dfrac{10}{30}\right)}=34.375\%,$$ every mark in every subject is worth the same value; in other words, this is a different type of average score of the various subjects, this time each subject given a weightage corresponding to the total marks available in it.

A more illustrative example: say there are two Economics exam papers, Multiple-choice and Essay, in which you scored $55$ out of $60$ and $15$ out of $100,$ respectively. Then the simple average of the two scaled scores (every paper has the same score-worth) is $$\frac12\left(\frac{55}{60}+\frac{15}{100}\right)=53.3\%,$$ whereas the weighted average of the two scores (every mark has the same score-worth) is $$\frac{55+15}{60+100}\color{green}{=\frac{60}{160}\left(\dfrac{55}{60}\right)+\frac{100}{160}\left(\dfrac{15}{100}\right)}=43.75\%.$$

Neither average is more correct than the other; the choice of formula just depends on the assessment scheme.

ryang
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