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Chapter 12: Problem 64

In one common system for finding a grade-point average, or GPA, $$ \mathrm{A}=4, \mathrm{~B}=3, \mathrm{C}=2, \mathrm{D}=1, \mathrm{~F}=0 . $$ The GPA is calculated by multiplying the number of credit hours for a course and the number assigned to each grade, and then adding these products. Then divide this sum by the total number of credit hours. Because each course grade is weighted according to the number of credits of the course, GPA is called a weighted mean. Calculate the GPA for this transcript: Sociology: 3 cr. A; Biology: \(3.5\) cr. C; Music: 1 cr. B; Math: 4 cr. B; English: 3 cr. C.

Short Answer

Expert verified
The calculated GPA is 2.76.

Step by step solution

01

Convert Letter Grades to Numerical Grades

First, we need to convert letter grades to their numerical counterparts. According to the provided conversion table: A=4, B=3, C=2, D=1, F=0. So, the grades for the courses become: Sociology: 4, Biology: 2, Music: 3, Math: 3, English: 2.
02

Multiply Course Credits by Numerical Grades

Each course credit will be multiplied by the numerical grade of the same course: Sociology: \(3 * 4 = 12\), Biology: \(3.5 * 2 = 7\), Music: \(1 * 3 = 3\), Math: \(4 * 3 = 12\), English: \(3 * 2 = 6\). Add these products together to get the total weighted credit points: \(12 + 7 + 3 + 12 + 6 = 40\).
03

Calculate Total Credit Hours

We add together the number of credits for each course to get the total number of credit hours: \(3 + 3.5 + 1 + 4 + 3 = 14.5\) hours.
04

Calculate GPA

Finally, divide the total weighted credit points (40) by total credit hours (14.5). The result is the GPA: \( \frac{40}{14.5} = 2.76\). This is a weighted mean, as each grade has been proportionally accounted for by the course credits.

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Key Concepts

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

Weighted Mean
The concept of a weighted mean is crucial when calculating a GPA because it ensures that courses with more credit hours have a greater impact on the final average. Unlike a simple average, where each value is equally important, a weighted mean assigns different levels of importance to each value based on a given weight.
In the context of GPA calculation, the weight is the number of credit hours associated with each course. This means that more extensive courses, which typically require more work, will have a greater influence on the overall GPA than shorter ones.
  • Multiply the numerical grade by the credit hours to determine the weighted score for each course.
  • Add all the weighted scores together to get a sum.
  • Divide by the total credit hours to find the weighted mean, which in this case is the GPA.
Credit Hours
Credit hours play a fundamental role in the GPA calculation process by determining the weight of each course grade. Essentially, credit hours are a measure of the time commitment a course requires.
They give each course a relative value indicating how much work or effort is expected.
  • More credit hours mean a course carries more weight in the GPA calculation.
  • Courses with fewer credit hours will have a lesser impact on the overall GPA.
  • Accurate tracking of credit hours is important as they are the foundation for calculating the weighted mean GPA.
Numerical Grades
Numerical grades are used as a standardized way to measure a student's performance across different courses. In many educational systems, letter grades like A, B, C, D, and F are converted into numbers so that they can be consistently applied in mathematical calculations.
In our example, the conversion is:
  • A = 4
  • B = 3
  • C = 2
  • D = 1
  • F = 0
These numerical equivalents allow for a precise calculation of GPA by multiplying them with credit hours to give the weighted score for each course.
Grade-Point Average Calculation
GPA calculation is a process that combines numerical grades and credit hours to give a single value reflecting overall academic performance. This value, commonly known as the Grade-Point Average, serves as an indicator of a student's academic achievement.
Here's how to calculate it:
  • First, convert all letter grades to their numerical counterparts.
  • Next, multiply the numerical grade by the course's credit hours to find the weighted score.
  • Add all the weighted scores together.
  • Finally, divide the total by the sum of all credit hours to calculate the GPA.
The GPA embodies the weighted mean concept, emphasizing courses with higher credit hours. In our example, the calculated GPA was 2.76, which represents the average academic performance of a student across different courses with varying credit loads.

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Most popular questions from this chapter

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