Question

Use the following for questions 24-25. Sylvia has credit hours and grades as shown on the chart. Her school gives 4 points for an \(A, 3\) points for a \(B, 2\) points for a \(C, 1\) point for a \(D\), and nothing for an \(F\). $$ \begin{array}{|c|c|c|c|c|c|} \hline \text { Grades } & \text { A } & \text { B } & \text { C } & \text { D } & \text { F } \\ \hline \text { Credit hours } & 16 & 27 & 18 & 8 & 1 \\ \hline \begin{array}{c} \text { Grade points } \\ \text { per credit } \\ \text { hour } \end{array} & 4 & 3 & 2 & 1 & 0 \\ \hline \end{array} $$ What is her grade point average, the weighted mean of her grades? A. 2.50 B. 2.70 C. 3.37 D. 3.50

Short answer

B. 2.70

Step-by-step solution

- Understand the problem

We need to find Sylvia's grade point average (GPA), which is the weighted mean of her grades. To do this, we will use the credit hours and grade points to calculate the total grade points earned and then divide by the total credit hours.

- Calculate total grade points earned

For each grade, multiply the number of credit hours by the grade points per credit hour: - For grade A, total grade points = 16 credit hours * 4 grade points per credit hour = 64 grade points - For grade B, total grade points = 27 credit hours * 3 grade points per credit hour = 81 grade points - For grade C, total grade points = 18 credit hours * 2 grade points per credit hour = 36 grade points - For grade D, total grade points = 8 credit hours * 1 grade point per credit hour = 8 grade points - For grade F, total grade points = 1 credit hour * 0 grade points per credit hour = 0 grade points Now, sum all the grade points.

- Sum the total grade points and credit hours

Sum the total grade points: 64 (A) + 81 (B) + 36 (C) + 8 (D) + 0 (F) = 189 total grade pointsSum the total credit hours: 16 (A) + 27 (B) + 18 (C) + 8 (D) + 1 (F) = 70 total credit hours

- Calculate GPA

Divide the total grade points by the total credit hours: GPA = \( \frac{189 \text{ total grade points}}{70 \text{ total credit hours}} \) = 2.70

- Choose the correct answer

The closest choice to our calculated GPA of 2.70 is option B. Therefore, the answer is B. 2.70.

Key concepts

weighted mean

To understand Sylvia's Grade Point Average (GPA), we need to dive into the concept of weighted mean. Unlike a simple average, a weighted mean takes into account the importance, or weight, of each value. In this case: the credit hours. GPA is a perfect example of a weighted mean where the grade points earned in different courses are weighted by the number of credit hours for those courses.

When calculating a weighted mean:

• First, multiply each data point by its corresponding weight. For Sylvia, this means multiplying her grades (or grade points) by the respective credit hours.
• Then, sum all these products together. This gives you the total grade points earned.
• Finally, divide this total by the sum of the weights (total credit hours) to get the weighted mean, or GPA in Sylvia's case.

By following these steps, we correctly account for the varying 'weights' of each data point, reflecting the true average performance.

credit hours

Credit hours are fundamental when calculating GPA. Essentially, they represent the amount of time committed to a course and, consequently, its weight in the GPA calculation.

For example, a high-credit course like a 4-credit class has a greater impact on your GPA than a course worth 1 credit hour. Sylvia's credit hours vary:

• 16 hours for her 'A' grades
• 27 hours for 'B' grades
• 18 hours for 'C' grades
• 8 hours for 'D' grades
• 1 hour for 'F' grades

This total of 70 credit hours weighs each of her grades appropriately in the final GPA calculation.

When you add up all the credit hours, you get the total weight, which is crucial for accurate GPA computation.

grade points

Grade points are numerical values assigned to letter grades to quantify academic performance. Different schools may have varying scales, but Sylvia's school uses the following scale:

• 4 points for an A
• 3 points for a B
• 2 points for a C
• 1 point for a D
• 0 points for an F

To find the GPA, the grade points are multiplied by the credit hours for each grade to determine the total grade points.

For Sylvia:

• 16 credit hours of A = 16 * 4 = 64 grade points
• 27 credit hours of B = 27 * 3 = 81 grade points
• 18 credit hours of C = 18 * 2 = 36 grade points
• 8 credit hours of D = 8 * 1 = 8 grade points
• 1 credit hour of F = 1 * 0 = 0 grade points

Adding these up, we get a sum of 189 grade points, which plays a pivotal role in calculating the GPA.