Chapter 8: Problem 53
Draw a circle graph showing each percent. A poll shows that \(36 \%\) of participants agree with a proposed bill, \(48 \%\) disagree, and the rest have no opinion. (GRAPH CANT COPY)
Short Answer
Expert verified
Answer: In the circle graph, Agree has 129.6 degrees, Disagree has 172.8 degrees, and No Opinion has 57.6 degrees.
Step by step solution
01
Set up the Circle Graph and Percentages
To begin, let's list the given percentages for each category:
1. Agree: \(36 \%\)
2. Disagree: \(48 \%\)
3. No Opinion: The remaining percentage
Now, we'll find the percentage of people who have no opinion. Since the total percentage should sum up to \(100\%\), we subtract the sum of agree and disagree from \(100\%\).
No Opinion percentage:
\(= 100 \% - (36 \% + 48 \%)\)
\(= 100 \% - 84 \%\)
\(= 16 \%\)
Now we have:
1. Agree: \(36 \%\)
2. Disagree: \(48 \%\)
3. No Opinion: \(16 \%\)
02
Convert Percentages to Degrees
Next, we need to convert the percentages into degrees as a circle has \(360^\circ\). To find the degrees for each category, multiply each percentage by \(360^\circ\) and divide by \(100\).
Agree degrees: \((36 \% \times 360^\circ) / 100 = 129.6^\circ\)
Disagree degrees: \((48 \% \times 360^\circ) / 100 = 172.8^\circ\)
No Opinion degrees: \((16 \% \times 360^\circ) / 100 = 57.6^\circ\)
Now we have the degrees for each category:
1. Agree: \(129.6^\circ\)
2. Disagree: \(172.8^\circ\)
3. No Opinion: \(57.6^\circ\)
03
Draw the Circle Graph
Now it's time to draw the circle graph. First, draw a circle and divide it into sectors according to the degrees calculated in Step 2. When drawing each sector, start by placing a dot in the middle of the circle, then draw an arc equal to its respective angle around the circle. Label each sector with its respective degree and percentage along with the category name.
1. Agree sector: \(129.6^\circ\), representing \(36 \%\) of the circle
2. Disagree sector: \(172.8^\circ\), representing \(48 \%\) of the circle
3. No Opinion sector: \(57.6^\circ\), representing \(16 \%\) of the circle
After completing these steps, you will have a circle graph that accurately represents the percentage of participants who agree, disagree, and have no opinion about a proposed bill.
Unlock Step-by-Step Solutions & Ace Your Exams!
-
Full Textbook Solutions
Get detailed explanations and key concepts
-
Unlimited Al creation
Al flashcards, explanations, exams and more...
-
Ads-free access
To over 500 millions flashcards
-
Money-back guarantee
We refund you if you fail your exam.
Over 30 million students worldwide already upgrade their learning with Vaia!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Understanding Percentages
When working with circle graphs, percentages are an essential part, as they help to represent a portion of a whole.
Think of percentages as a way to express a number out of 100. This makes them very handy for portraying data, especially in surveys and polls, like in our example of participants agreeing or disagreeing with a bill.
In this example, the total of all participants equals 100%. Out of these, 36% agree with the bill, 48% disagree, and the remaining percentage—16%—have no opinion. By working with percentages, we are able to quickly understand how a larger group is divided into smaller parts. This makes it easier to see the larger picture and identify trends or common views.
In this example, the total of all participants equals 100%. Out of these, 36% agree with the bill, 48% disagree, and the remaining percentage—16%—have no opinion. By working with percentages, we are able to quickly understand how a larger group is divided into smaller parts. This makes it easier to see the larger picture and identify trends or common views.
Degrees Conversion in Circle Graphs
To turn percentages into a form suitable for a circle graph, it's important to convert them into degrees. A circle graph divides a circle into sectors, where each sector is a portion of 360 degrees.
To convert percentages into degrees:
To convert percentages into degrees:
- Use the formula: \( \text{Degrees} = \left( \frac{\text{Percentage} \times 360}{100} \right) \).
Sector Division for Visual Clarity
Sector division is critical when organizing data into a circle graph.
Once percentages are converted into degrees, each part of the circle graph is allocated based on these converted values.
In practice, you start by drawing a full circle, then divide it into sectors using the angle degrees you calculated:
In practice, you start by drawing a full circle, then divide it into sectors using the angle degrees you calculated:
- An angle of 129.6° is drawn for the "agree" section.
- Another angle of 172.8° for "disagree."
- The remaining 57.6° completes the "no opinion" section.
Effective Data Representation Using Circle Graphs
Circle graphs, also known as pie charts, are effective visual tools for representing data.
They provide a quick, intuitive snapshot of how a total is distributed among its parts.
In the given survey data, the circle graph is divided into three parts:
In the given survey data, the circle graph is divided into three parts:
- The sector reflecting "agree" shows how a smaller portion of participants support the bill.
- The "disagree" section, being larger, illustrates stronger opposition overall.
- The "no opinion" sector reflects a neutral group with no decided stance.