CODEWITHSUNDEEP
averagemeanweighted
Arvind K.
Arvind K.

Reputation: 1294

How to calculate individual weighted score for each set?

I have 20 questions and they are further divided in to a set of 4 questions each which means there are total 5 sets A, B, C, D and E. Each question has 5 marks so in a set the maximum number of marks that can be obtained is 20.

In two tests taken for each set i get the following results

20, 20 ,16, 14, 20 = 90%
16, 14, 20, 20, 20 = 90%

Now what i want is i want to weight C and D set, almost double than all other sets. To calculate the weighted percentage, this is done something like the following.

14*(20/20) + 14*(20/20) + 29*(16/20) + 29*(14/20) + 14*(20/20) = 66.2%
14*(16/20) + 14*(14/20) + 29*(20/20) + 29*(20/20) + 14*(20/20) = 89.64%

Now i want to calculate weighted percentage for each set individually. For example, what is the new weighted percent of set A and set C (of Test 1 ) considering it was 100% and 80% respectively previously, while no weight was in consideration. Similarly for all of individual percentages which make weighted average of 66.2% and 89.64% for Test 1 and Test 2 respectivly.

I tried to put some logic, something similar to the following but i am not getting it exactly. May be you could help me in this?

100% ? 0.14 = ?
100% ? 0.14 = ?
100%  ? 0.29 = ?
100%  ? 0.29 = ?
100% ? 0.14 = ?

Anyways, is this possible at all?

Upvotes: 2

Views: 4040

Answers (1)

John
John

Reputation: 16007

This is more of an algebra problem. You need to find the correct factors to multiply your raw scores.

You have five fractions. The sum of them must be 1.

Evenly weighted for each question type means each fraction is 0.2.

To get two of the types (C and D) weighted twice the others, let's say the weighting for A is x. Then the weighting for B and E will also be x, and for C and D it will be 2x. That means

x + x + 2x + 2x + x = 1, or x = 1/7 (0.142859) and therefore 2x = 2/7 (0.285914).

I'm afraid I don't understand the second part of your question.

Upvotes: 1

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