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Ch. 2 - Descriptive Statistics
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 2 - Descriptive StatisticsProblem 2.3.46
Chapter 2, Problem 2.3.46

Finding a Weighted Mean In Exercises 41– 46, find the weighted mean of the data.


Grades A student receives the grades shown below, with an A worth 4 points, a B worth 3 points, a C worth 2 points, and a D worth 1 point. What is the student’s grade point average?


Table showing a student's grades and class credits: A in 1 four-credit class, B in 2 three-credit classes, C in 1 three-credit class, D in 1 two-credit class.

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Step 1: Understand the problem. The goal is to calculate the weighted mean, which is the grade point average (GPA) based on the grades and their corresponding credit hours. Each grade has a point value: A = 4, B = 3, C = 2, D = 1.
Step 2: Multiply each grade's point value by the number of credit hours for the corresponding class to find the weighted contribution of each grade. For example, for the A grade in a 4-credit class, the contribution is 4 × 4.
Step 3: Add up all the weighted contributions from Step 2. This gives the total weighted points.
Step 4: Add up all the credit hours from the classes. For example, the total credit hours are 4 (A) + 6 (B) + 3 (C) + 2 (D).
Step 5: Divide the total weighted points (from Step 3) by the total credit hours (from Step 4) to calculate the weighted mean, which is the GPA.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Weighted Mean

The weighted mean is a type of average that takes into account the relative importance or weight of each value in a dataset. In this context, each grade is assigned a point value, and the number of credits for each class serves as the weight. The formula for the weighted mean is the sum of the products of each value and its weight, divided by the total weight.
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Grade Point Average (GPA)

The Grade Point Average (GPA) is a numerical representation of a student's academic performance, calculated by averaging the weighted grades received in courses. Each letter grade corresponds to a specific point value (A=4, B=3, C=2, D=1), and the GPA is computed by multiplying these point values by the credit hours of each course, summing the results, and dividing by the total credit hours.
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Credits

Credits represent the value assigned to a course, reflecting the amount of time and effort required to complete it. In this scenario, different classes have varying credit values, which influence the calculation of the GPA. The more credits a class has, the greater its impact on the overall GPA, as it contributes more weight to the average.
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