# How to represent weighted score average calculation in sigma notation?

I have 20 questions and they are further divided in to a set of 4 questions in 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 respectively.

I can calculate this something like this.

`14/20 * 20/20 = Weighted Percent of A 14/20 * 20/20 = Weighted Percent of B 29/20 * 16/20 = Weighted Percent of C`

Does anyone know how to represent this calculation in Sigma notation?

Thanks,
Arvind.