# Percentage Got Me Puzzled!

It may seem pretty naive and stupid but this problem got me thinking for a very long time.

Assume I have three subject marks: 70 (first), 80 (second), and (76, 67, 90) for the third subject. Percentage is calculated in the following ways. Max marks of each subject is 100

1. thirdR = (76 + 67 + 90) / 300; result = (70 + 80 + thirdR)/300; result = 75.88%
2. result = (70 + 80 + 76 + 67 + 90)/ 500; result = 76.6

I know that (2.) is a wrong way of calculating percentage but why is there a difference? It kind of seems legit. Is there any correction factor? Thank you in advance

• Consider that the 76, 67, 90, 80, and 70 do not weigh equally in the final calculation – sjb Aug 17 '15 at 15:29
• No question is stupid, its just our way of looking at it. The more you do math, the more you will get this stuff – Taylor Ted Aug 17 '15 at 15:32

If you expand your first calculation, you get $\frac {70+80+\frac{76+67+90}{300}}{300}$ which shows that the first two papers each account for $\frac 13$ of the grade. Your second has the first two papers accounting for $\frac 15$ of the grade. If all five papers are supposed to be equally weighted, this is correct.