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91Ó°ÊÓ

In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth \(25 \%\) of your total grade, each major test is worth \(22.5 \%\), and the final exam is worth \(30 \%\). Compute the weighted average for the following scores: 92 on the lab, 81 on the first major test, 93 on the second major test, and 85 on the final exam.

Short Answer

Expert verified
The weighted average, and thus the final grade, is 87.65.

Step by step solution

01

Understand the Components

The final grade is calculated using the lab score, two major test scores, and a final exam score. Each component has a different weight in the overall grade calculation.
02

Identify the Scores and Weights

The lab score is 92 and contributes 25% to the final grade. The first major test score is 81 and contributes 22.5%, the second major test score is 93 and contributes another 22.5%, and the final exam score is 85, which contributes 30%.
03

Calculate Weighted Contribution for Each Score

Each score is multiplied by its respective weight to find its contribution to the final grade:- **Lab Contribution:** \(92 \times 0.25 = 23\)- **First Major Test Contribution:** \(81 \times 0.225 = 18.225\)- **Second Major Test Contribution:** \(93 \times 0.225 = 20.925\)- **Final Exam Contribution:** \(85 \times 0.30 = 25.5\)
04

Sum All Contributions

Add together all the contributions from each score: \[23 + 18.225 + 20.925 + 25.5 = 87.65\]
05

Interpret the Result

The sum from Step 4, which is 87.65, represents the weighted average and thus the final grade for the course.

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Key Concepts

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

Grade Calculation
In many academic settings, grade calculation is crucial for determining a student's performance. Essentially, it involves aggregating diverse scores from various assessments to arrive at a final grade.

This calculation is not a simple averaging of scores. Instead, it considers the weight of each assessment. The idea is to reflect the significance or emphasis placed on each component by educators.
  • Different classes or subjects may have different calculations.
  • Understanding how each component affects your final grade is key.
In the example of the biology class, the class's final grade includes a lab score, two major tests, and a final exam. Each of these has been assigned a specific percentage, which is crucial for determining their influence on the overall grade. By calculating how much each contributes, students can better understand their performance and what areas require more focus.
Weighting System
A weighting system is a method used to assign a relative importance to different components of a grade, reflecting their role in the overall evaluation.

Not every component of a class carries the same weight. For the biology course example:
  • Lab scores are worth 25%.
  • Each of the major tests contributes 22.5%.
  • The final exam carries the most weight at 30%.
These percentages show that the final exam can have the biggest influence on the final grade.

Understanding the weighting system helps students prioritize their studies effectively. If a component like the final exam is weighted more heavily, then a strong performance there can significantly impact the final grade. Conversely, poorer performance on heavily weighted tasks can more negatively affect one's grade.
Academic Grades
Academic grades play a pivotal role in a student's educational journey. They indicate a student's level of understanding and achievement in a subject.

Grades are typically derived from multiple sources, including tests, assignments, and projects. They are essential as they contribute to a student's overall academic profile, influencing future opportunities in education and career choices.
  • They can motivate students to excel.
  • They provide feedback on areas that need improvement.
Academic grades, while defining a student's current standing, also reflect the effort and dedication invested in a subject. This clear picture helps both students and educators identify strengths and areas for development.
Exam Scores
Exam scores are numerical reflections of a student's performance on a specific test or exam. In educational contexts, these scores often make up a significant part of a student's final grade.

For example, in the given biology class, the final exam alone accounts for 30% of the total grade. Therefore, it's crucial for students to prepare thoroughly for exams to enhance their scores:
  • Exam scores can significantly affect the overall grade, based on their weight.
  • They assess a student's grasp over the studied material.
Exam scores not only indicate how well you understand the coursework but also help in evaluating broader competencies such as time management, problem-solving skills, and the ability to perform under pressure. These are vital in guiding further learning paths and academic success.

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Most popular questions from this chapter

One standard for admission to Redfield College is that the student must rank in the upper quartile of his or her graduating high school class. What is the minimal percentile rank of a successful applicant?

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You do not need a lot of money to invest in a mutual fund. However, if you decide to put some money into an investment, you are usually advised to leave it in for (at least) several years. Why? Because good years tend to cancel out bad years, giving you a better overall return with less risk. To see what we mean, let's use a 3 -year moving average on the Calvert Social Balanced Fund (a socially responsible fund). (a) Use a calculator with mean and standard deviation keys to verify that the mean annual return for all 11 years is approximately \(9.45 \%\), with standard deviation \(9.57 \%\) (b) To compute a 3 -year moving average for 1992, we take the data values for 1992 and the prior two years and average them. To compute a 3 -year moying average for 1993, we take the data values for 1993 and the prior two years and average them. Verify that the following 3 -year moving averages are correct. (c) Use a calculator with mean and standard deviation keys to verify that for the 3 -year moving average, the mean is \(10.68 \%\) with sample standard deviation \(4.53 \%\). (d) Compare the results of parts (a) and (c). Suppose we take the point of view that risk is measured by standard deviation. Is the risk (standard deviation) of the 3 -year moving average considerably smaller? This is an example of a general phenomenon that will be studied in more detail in Chapter 6 .

What symbol is used for the standard deviation when it is a sample statistic? What symbol is used for the standard deviation when it is a population parameter?

Clayton and Timothy took different sections of Introduction to Economics. Each section had a different final exam. Timothy scored 83 out of 100 and had a percentile rank in his class of \(72 .\) Clayton scored 85 out of 100 but his percentile rank in his class was 70 . Who performed better with respect to the rest of the students in the class, Clayton or Timothy? Explain your answer.

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