"Putting It Together: Online Homework Keeping students engaged in the learning process greatly increases their chance of success in a course. Traditional lecture-based math instruction has given way to a more student-engaged approach where students interact with the teacher in class and receive immediate feedback to their responses. The teacher presence allows students, when incorrect in a response, to be guided through a solution and then immediately be given a similar problem to attempt. A researcher conducted a study to investigate whether an online homework system using an attempt—feedback— reattempt approach improved student learning over traditional pencil-and-paper homework. The online homework system was designed to increase student engagement outside class, something commonly missing in traditional pencil-and-paper assignments, ultimately leading to increased learning.The study was conducted using two first-semester calculus classes taught by the researcher in a single semester. One class was assigned traditional homework and the other was assigned online homework that used the attempt—feedback—reattempt approach. The summaries are based on data from the study.

h. Could the data in the graph be presented in a pie chart? If so, what is the ""whole""? If not, why not?"

Verified step by step guidance

1. Step 1: Understand the type of data presented in the graph. The graph shows relative frequencies of letter grades earned on exams by students with no prior college experience, separated into two groups: Traditional and Online homework systems.
2. Step 2: Recall that a pie chart is used to represent parts of a whole, where the sum of all parts equals 100% or 1 in relative frequency terms. Each slice of the pie corresponds to a category's proportion of the total.
3. Step 3: Check if the relative frequencies for each group (Traditional and Online) sum to 1. This is necessary because a pie chart requires the data to represent a complete distribution of a single whole.
4. Step 4: Since the graph shows relative frequencies for letter grades within each group separately, each group’s relative frequencies sum to 1, meaning each group can be considered a 'whole' on its own.
5. Step 5: Conclude that the data for each group (Traditional or Online) could be presented in a pie chart individually, where the 'whole' is the total number of students in that group, and each slice represents the proportion of students earning each letter grade.

Key Concepts

Types of Graphs and Their Uses

Different types of graphs serve different purposes. Bar graphs compare quantities across categories, while pie charts show parts of a whole as percentages. Understanding when to use each graph type is essential for accurately representing data.

Definition of the 'Whole' in Pie Charts

A pie chart represents data as parts of a whole, where the whole is the total sum of all categories combined. Identifying the correct 'whole' is crucial; without a meaningful total, a pie chart is inappropriate.

Categorical vs. Quantitative Data

Categorical data represent distinct groups or categories, while quantitative data represent numerical values. Pie charts are suitable for categorical data that sum to a whole, but not for comparing unrelated numerical values or averages.