Ch. 2 - Descriptive Statistics

Larson - Elementary Statistics: Picturing the World 8th Edition

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Larson 8th Edition

Ch. 2 - Descriptive Statistics

Problem 2.3.48

Chapter 2, Problem 2.3.48

Grades In Exercise 46, one of the student’s B grades gets changed to an A. What is the student’s new grade point average?

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Identify the grading scale used to calculate the grade point average (GPA). For example, A = 4.0, B = 3.0, C = 2.0, etc. Confirm the weights assigned to each grade.

Determine the total number of grades the student has, including the original B grade that is being changed to an A.

Calculate the total grade points before the change. Multiply the number of each grade by its corresponding grade point value and sum them up.

Adjust the total grade points by replacing one B grade (3.0) with an A grade (4.0). Subtract the grade points for the B and add the grade points for the A.

Divide the updated total grade points by the total number of grades to compute the new GPA. Use the formula: GPA = (Total Grade Points) / (Total Number of Grades).

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Key Concepts

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

Grade Point Average (GPA)

Grade Point Average (GPA) is a numerical representation of a student's academic performance, calculated by assigning a point value to each grade and averaging these values. Typically, an A is worth 4.0 points, a B is worth 3.0 points, and other grades have corresponding values. The GPA is calculated by dividing the total grade points earned by the total number of credit hours attempted.

Impact of Grade Change

Changing a grade from B to A affects the overall GPA by increasing the total grade points earned. This change alters the numerator in the GPA calculation, potentially raising the average if the course has a significant weight in the total credit hours. Understanding how each grade contributes to the GPA is crucial for accurately determining the new average after a grade change.

Weighted vs. Unweighted GPA

GPA can be calculated as either weighted or unweighted. An unweighted GPA treats all courses equally, while a weighted GPA gives additional points for advanced courses (like honors or AP classes). Knowing whether the GPA in question is weighted or unweighted is essential for accurately calculating the new average after a grade change, as it influences the overall point distribution.

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Textbook Question

Putting Graphs in Context In Exercises 5–8, match the plot with the description of the sample.

a. Times (in minutes) it takes a sample of employees to drive to work

b. Grade point averages of a sample of students with finance majors

c. Top speeds (in miles per hour) of a sample of high-performance sports cars

d. Ages (in years) of a sample of residents of a retirement home

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Textbook Question

Constructing Data Sets In Exercises 25–28, construct a data set that has the given statistics.

N = 6

μ = 5

σ ≈ 2

Textbook Question

Comparing Variation in Different Data Sets In Exercises 45–50, find the coefficient of variation for each of the two data sets. Then compare the results.

Heights and Weights The heights (in inches) and weights (in pounds) of every France national soccer team player that started the 2018 FIFA Men’s World Cup final are listed. (Source: ESPN)

Textbook Question

Graphical Analysis In Exercises 59 and 60, the letters A, B, and C are marked on the horizontal axis. Describe the shape of the data. Then determine which is the mean, which is the median, and which is the mode. Justify your answers.

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Textbook Question

Constructing a Frequency Distribution and a Frequency Polygon In Exercises 35 and 36, construct a frequency distribution and a frequency polygon for the data set using the indicated number of classes. Describe any patterns.

Ages of the Presidents Number of classes: 7 Data set: Ages of the U.S. presidents at Inauguration (Source: The White House) 57 61 57 57 58 57 61 54 68 51 49 64 50 48 65 52 56 46 54 49 51 47 55 55 54 42 51 56 55 51 54 51 60 62 43 55 56 61 52 69 64 46 54 47 70 78

Textbook Question

Graphical Analysis In Exercises 13 and 14, use the box-and-whisker plot to identify the five-number summary.

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