## Task 1 - 050811

A student had attached the following overview of participation in the 1st stage of the 4th Olympiad of Young Mathematicians of the GDR to the wall newspaper:

Class 8a: Out of 33 students, 20 participated, which is approximately 60.6 percent.

Class 8b: Out of 32 students, 21 participated, which is approximately 65.6 percent.

Class 8c: Out of 27 students, 19 participated, which is approximately 70.4 percent.

The students of these classes are tasked with determining the overall percentage of participation of the 8th grade students. Some students calculate the arithmetic mean of the percentages, while others calculate the quotient of the total number of participants and the total number of students in these classes, multiplied by 100.

a) How large is the difference that results from the two calculations?

b) Which students have calculated the percentage in the correct way?
The students of the second group correctly calculated the percentage and obtained $\frac{60}{92} \cdot 100 \% \approx 65.22 \%$, while the other students, using an incorrect method, obtained $65.53 \%$. The difference between the two results is $0.31 \%$.