By the frequency of my questions, you know by now that I just hate doing word problems
In this question, I made a couple of mistakes starting off with:
Not scaling quiz grade with its respective total. I should have divided the average of (15, 17, 19) which is 17 by the total grades combined- 20 to scale it out so that it can be compared.
Another mistake was using 90% i.e. 90/100 for class score so I did (20/100)x(90/100) instead of (20/100)x(90)
Another mistake was using 90% as the final grade average i.e. putting the whole equation equal to 90/ 100 instead of 90
I understood 1st mistake, since total marks of each activity is different, to get that number as percentage we need to divide it by 20 which gives us 0.85 and in percentage form it is 85%
This gives me 0.9833 and then to get it in percentage form multiplying by 100. Now, this is a lot of work and additional steps. When I asked chatgpt, the easier way to solve this. It said - âyou are dividing the percentages by 100 again unnecessarily. The weights 20/100,50/100,30/100 already account for the scaling of the percentages into their contribution to the final grade. Multiplying the percentages 90/100 or 85/100 by these weights results in values that are too small because youâre effectively converting them twice.â Could you break down this reasoning for me properly because the respective total scores of each activity could be different right so how could we express percentages as absolute numbers?
Sorry, if this sounds too stupid but I get very confused in such conceptual things and I would appreciate a very layman explanation of the same. Thank you for your patience.
Also, if you could suggest where can I practice more of weighted average percentage problems in addition to GregMatâs materials?
Based on my interpretation of your reply. The changes you suggested should only be done for homework right? But if all the grades are out of 100 for homework only then the new equation would be-
20 + (50/100*85/100) + (30/100xY) = 90/100
Since final grade for homework is out of 100 it would be (20/100*100) we get 20
Okay, so if your final grade is out of 100 then 20 is the max score you can get from the homework alone. I guess this part is clear.
So if John has an average of 90% on the homework, then how much is his final grade? Again, letâs only account for the homeworkâs impact on the final grade for now. Weâll soon get to the rest of the question after we clarify this.
Okay sounds good, so heâd have 18/100 as the final grade from the homeworkâs alone. Now repeat the same procedure for the quiz and deduce what the final exam score should be.
Itâs the same up to a scale factor. If you can obtain a maximum of 20 marks out of 100 for your final grade then if your final grade was dropped to 50 your homework max drops to 10. In other words, if 100% of a number is 50 then 20% of that number is 10.
Iâm not sure if youâre using the same approach we reinforced earlier , but anyway this is how what we spoke about earlier would roughly look like:
Let our final grade be out of 100 and then we figure out the contribution of each assessment/homework towards the final grade.
Homeworks: 18 marks out of 20 possible marks.
Quizzes: Average score across the three quizzes happens to be 17/20 (which is 85%). Since you can obtain a maximum of 50 marks from the quizzes, thus rescaling with a max of 50 leads you to: 0.85 \cdot 50 = 42.5
Finally, we figure out how much we have to score on the final exam (out of 30) from the inequality:
Owing to this. it should be evident that we require at least \frac{29.5}{30} \approx 98.33\% on our final exam. Rescaling such that our final exam is scored out of 100 gives you that your \text{final exam score} \geq 98.\overline{3}.
, but anyway this is how what we spoke about earlier would roughly look like: