To calculate Arden's total averages for the entire semester in each category (quiz, lab, and exam), we first need to determine the grades for each category.
Given grades for the second half of the semester:
- Quizzes:
- 80
- 60
- 90
- 50
- Labs:
- 100
- 80
- Exams:
- 100
Calculating the averages:
-
Quizzes:
- The grades for quizzes are: 80, 60, 90, 50
- To find the average: \[ \text{Average} = \frac{\text{Sum of Quiz Grades}}{\text{Number of Quizzes}} = \frac{80 + 60 + 90 + 50}{4} \]
- Calculate the sum: \[ 80 + 60 + 90 + 50 = 280 \]
- Now, calculate the average: \[ \frac{280}{4} = 70 \]
-
Labs:
- The grades for labs are: 100, 80
- To find the average: \[ \text{Average} = \frac{\text{Sum of Lab Grades}}{\text{Number of Labs}} = \frac{100 + 80}{2} \]
- Calculate the sum: \[ 100 + 80 = 180 \]
- Now, calculate the average: \[ \frac{180}{2} = 90 \]
-
Exams:
- The grades for exams are: 100
- To find the average: \[ \text{Average} = \text{Exam Grade} = 100 \]
Summary of the averages for the entire semester:
- Quizzes Average: \( 70 \)
- Labs Average: \( 90 \)
- Exams Average: \( 100 \)
Final Expressions and Results:
- Quiz Average: \( \frac{(80 + 60 + 90 + 50)}{4} = 70 \)
- Lab Average: \( \frac{(100 + 80)}{2} = 90 \)
- Exam Average: \( 100 \)
Thus, Arden's total averages for the semester are:
- Quiz Average: \( 70 \)
- Lab Average: \( 90 \)
- Exam Average: \( 100 \)