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Chapter 3: Problem 33

A student of the author earned grades of \(\mathrm{A}, \mathrm{C}, \mathrm{B}, \mathrm{A}\), and \(\mathrm{D}\). Those courses had these corresponding numbers of credit hours: \(3,3,3,4\), and \(1 .\) The grading system assigns quality points to letter grades as follows: \(\mathrm{A}=4 ; \mathrm{B}=3 ; \mathrm{C}=2 ; \mathrm{D}=1 ; \mathrm{F}=0\). Compute the grade-point average (GPA) and round the result with two decimal places. If the dean's list requires a GPA of \(3.00\) or greater, did this student make the dean's list?

Short Answer

Expert verified
GPA = 3.14. The student made the dean's list.

Step by step solution

01

- Assign Quality Points to Each Grade

Assign the corresponding quality points to the letter grades based on the grading system:\[ \text{A} = 4, \text{C} = 2, \text{B} = 3, \text{A} = 4, \text{D} = 1 \]
02

- Multiply Quality Points by Credit Hours

Multiply the quality points by the corresponding credit hours for each course:\[ 4 \times 3 = 12 \]\[ 2 \times 3 = 6 \]\[ 3 \times 3 = 9 \]\[ 4 \times 4 = 16 \]\[ 1 \times 1 = 1 \]
03

- Calculate Total Quality Points

Sum all the products from Step 2 to find the total quality points:\[ 12 + 6 + 9 + 16 + 1 = 44 \]
04

- Calculate Total Credit Hours

Sum the credit hours of all the courses:\[ 3 + 3 + 3 + 4 + 1 = 14 \]
05

- Compute GPA

Divide the total quality points by the total credit hours to find the GPA and round to two decimal places:\[ \text{GPA} = \frac{44}{14} \ = 3.14 \]
06

- Determine Dean's List Eligibility

Compare the calculated GPA to the required GPA for the dean's list (3.00). Since 3.14 is greater than 3.00, the student made the dean's list.

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Key Concepts

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

Quality Points
Quality points are numerical values assigned to letter grades.
They are used to calculate a student's GPA.
In this example, the grades and their corresponding quality points are:
  • A = 4
  • B = 3
  • C = 2
  • D = 1
  • F = 0
To convert letter grades into quality points, simply match each grade with its numerical value.
For instance, if you received an 'A' in a course, you would assign 4 quality points to that grade.
Understanding quality points is essential for the GPA calculation process.
Credit Hours
Credit hours represent the weight or importance of a course.
They typically indicate the number of hours spent in class each week.
In the example, the courses have the following credit hours:
  • 3, 3, 3, 4, 1
The higher the credit hours, the more significant the course is to your GPA.
When calculating your GPA, each grade's quality points are multiplied by the corresponding credit hours.
For example, a grade of 'A' in a 3-credit course contributes more to your GPA than an 'A' in a 1-credit course.
Grade Point Average
The Grade Point Average (GPA) is a numerical representation of a student's academic performance.
It is calculated by dividing the total quality points by the total credit hours.
Here鈥檚 the step-by-step process:
  • First, assign quality points to each grade.
  • Next, multiply each grade's quality points by the course's credit hours.
  • Add up all the products to get total quality points: \[ 12 + 6 + 9 + 16 + 1 = 44 \]
  • Sum the credit hours: \[ 3 + 3 + 3 + 4 + 1 = 14 \]
  • Finally, divide the total quality points by the total credit hours: \[ \text{GPA} = \frac{44}{14} \approx 3.14 \]
Calculating your GPA helps you understand your academic standing.
It鈥檚 often used by schools to determine eligibility for honors and academic programs.
Dean's List Eligibility
The Dean's List is an academic honor that recognizes high-achieving students.
To qualify, students must achieve a GPA above a certain threshold.
In most institutions, a GPA of 3.00 or higher is required.
In this case, the student's GPA is calculated as 3.14.
Since this is greater than 3.00, the student qualifies for the Dean's List.
Making the Dean's List can have benefits such as:
  • Scholarship opportunities
  • Special recognition on transcripts
  • Enhanced resume credentials
If you aim to be on the Dean's List, it's crucial to maintain strong academic performance each semester.

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Most popular questions from this chapter

Let a population consist of the values 9 cigarettes, 10 cigarettes, and 20 cigarettes smoked in a day (based on data from the California Health Interview Survey). Assume that samples of two values are randomly selected with replacement from this population. (That is, a selected value is replaced before the second selection is made.) a. Find the variance \(\sigma^{2}\) of the population \(\\{9\) cigarettes, 10 cigarettes, 20 cigarettes \(\\}\). b. After listing the nine different possible samples of two values selected with replacement, find the sample variance \(s^{2}\) (which includes division by \(n-1\) ) for each of them; then find the mean of the nine sample variances \(s^{2}\). c. For each of the nine different possible samples of two values selected with replacement, find the variance by treating each sample as if it is a population (using the formula for population variance, which includes division by \(n\) ); then find the mean of those nine population variances. d. Which approach results in values that are better estimates of \(\sigma^{2}\) : part (b) or part (c)? Why? When computing variances of samples, should you use division by \(n\) or \(n-1\) ? e. The preceding parts show that \(s^{2}\) is an unbiased estimator of \(\sigma^{2}\). Is \(s\) an unbiased estimator of \(\sigma\) ? Explain.

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