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Chapter 3: Problem 16

In Marissa's calculus course, attendance counts for \(5 \%\) of the grade, quizzes count for \(10 \%\) of the grade, exams count for \(60 \%\) of the grade, and the final exam counts for \(25 \%\) of the grade. Marissa had a \(100 \%\) average for attendance, \(93 \%\) for quizzes, \(86 \%\) for exams, and \(85 \%\) on the final. Determine Marissa's course average.

Short Answer

Expert verified
87.15

Step by step solution

01

Identify the weight of each component

Attendance counts for 5% of the grade, quizzes for 10%, exams for 60%, and the final exam for 25%.
02

Determine the grades for each component

Marissa's grades are: Attendance = 100%, Quizzes = 93%, Exams = 86%, Final Exam = 85%.
03

Convert percentages to decimal form

Convert each component weight into decimal form: 5% = 0.05, 10% = 0.10, 60% = 0.60, and 25% = 0.25.
04

Calculate the weighted score for each component

Multiply each grade by its respective weight: Attendance: 100% * 0.05 = 5, Quizzes: 93% * 0.10 = 9.3, Exams: 86% * 0.60 = 51.6, Final Exam: 85% * 0.25 = 21.25.
05

Sum the weighted scores

Add up all the weighted scores to find Marissa's course average: 5 + 9.3 + 51.6 + 21.25 = 87.15.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

percentage weights
When calculating a weighted average, it's important to understand the concept of percentage weights. These weights represent the relative importance of each component in the final result. For example, in Marissa's calculus course, attendance counts for 5% of her grade, meaning it's less critical compared to exams, which count for 60%. By assigning different weights, you can prioritize certain components over others, ensuring a more representative final grade.
To clearly establish the weights, let's say that:
  • Attendance = 5%
  • Quizzes = 10%
  • Exams = 60%
  • Final Exam = 25%
These weights should add up to 100% to cover the entire course's assessment criteria.
converting percentages to decimals
To properly use percentage weights in calculations, you need to convert those percentages into decimals. This step is easy but crucial for correctly computing weighted scores.
Converting a percentage to a decimal is straightforward: simply divide the percentage by 100. Here are the calculations for Marissa鈥檚 course components:
  • 5% = 5 / 100 = 0.05
  • 10% = 10 / 100 = 0.10
  • 60% = 60 / 100 = 0.60
  • 25% = 25 / 100 = 0.25
Now you have the decimal forms of the weights, ensuring you can multiply them accurately with the corresponding grades.
weighted scores
Once you have the grades and their respective weights in decimal form, it's time to calculate the weighted scores. This involves multiplying each grade by its corresponding weight. Here鈥檚 how it's done for Marissa's grades:
  • Attendance: 100% * 0.05 = 5
  • Quizzes: 93% * 0.10 = 9.3
  • Exams: 86% * 0.60 = 51.6
  • Final Exam: 85% * 0.25 = 21.25
These calculations give you the weighted contribution of each component to the final grade. By scaling the grades according to their importance, you get a more accurate reflection of overall performance.
final grade calculation
The final step in calculating the course average is to sum up all the weighted scores. This gives you the final grade, taking into account the various weights and scores:
  • Attendance = 5
  • Quizzes = 9.3
  • Exams = 51.6
  • Final Exam = 21.25
Adding these together:
5 + 9.3 + 51.6 + 21.25 = 87.15
So, Marissa鈥檚 course average is 87.15%. This integrated approach of converting percentages, computing weighted scores, and then summing them up helps in accurately determining the final grade.

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