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Assume that a class has four categories for calculating grades - tests, final exams, projects, and homework. Assume that tests are $40\%$ of the class grade, final exams are $30\%$ of the class grade, projects are $10\%$ of the class grade, and homework is $20\%$ of the class grade.

Should we multiply each score for each category by its category weights, add these results, then divide by the sum of the weights? For example: Let's say a students scores are

Tests: $84, 78, 84, 72$

Final exam: $78$ (just one score)

Projects: $86$ (just one score)

Homework: $87$ (just one score)

Should the class grade be $0.4\cdot 84 + 0.4\cdot 78 + 0.4\cdot 84 + 0.4\cdot 72 + 0.3\cdot 78 + 0.1\cdot 86 + 0.2\cdot 87 = 176.6$ (sum of products)

$0.4 + 0.4 + 0.4 + 0.4 + 0.3 + 0.1 + 0.2 = 2.2$ (sum of the weights for assignments)

Total grade: $176.6 / 2.2 = 80.27$

Or is there a different approach that should be used to calculate the grade for the course?

Thank you in advance.

Stephen Donovan
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    I agree with your general method, but note that if all of the tests together have a weight of $40%,$ each one only has a weight of $10%.$ – Stephen Donovan Apr 21 '21 at 13:17
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    You should average the tests to get a single test score, and then use a $0.4$ weight on that average score. – DreiCleaner Apr 21 '21 at 13:29
  • It should be $0.4\cdot (\frac{84+78+84+72}{4})+0.3\cdot (\frac{78}{1})+0.1\cdot(\frac{86}{1})+0.2\cdot(\frac{87}{1}) = 81.2$ – JMoravitz Apr 21 '21 at 13:47

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