Savitri’s marks in Kashmiri are as follows: 35 out of 50 in internal tests, 44 out of 60 in the project, and 80 out of 100 in the final exam. The annual percentage score is calculated by combining the internals, project, and final exam in the ratio 3:4:5. Which of the following expression(s) gives her annual score (as a percentage) in Kashmiri?
- (i)(35 × 3 + 44 × 4 + 80 × 5) / (3 + 4 + 5)
- (ii)[(35/100) × 3 + (44/100) × 4 + (80/100) × 5] / (3 + 4 + 5)
- (iii)([(35/50) × 3 + (44/60) × 4 + (80/100) × 5] / (3 + 4 + 5)) × 100
- (iv)[((35/50) × 100) × 3 + ((44/60) × 100) × 4 + ((80/100) × 100) × 5] / (3 + 4 + 5)
The percentage score for each assessment is:
Using the weighted mean formula:
Expression (i) is incorrect because it uses raw marks without considering the different maximum marks.
Expression (ii) is incorrect because it divides all marks by 100, instead of their respective maximum marks.
Expression (iii) is correct because it combines the fractional scores using the given weights and multiplies the result by 100.
Expression (iv) is correct because it converts each score into a percentage before combining the percentages using the given weights.