Question

The National Confectioners Association asked 1006 adults the following question: "Do you set aside a personal stash of Halloween candy?" Fifty-five percent of those surveyed responded no, \(41 \%\) responded yes, and \(4 \%\) either did not answer the question or said they did not know (USA Today. October 22, 2009). Use the given information to construct a pie chart.

Short answer

The pie chart would represent 'No' responses with an angle of 198°, 'Yes' responses with an angle of 147.6°, and 'Didn't answer or Don't Know' responses with 14.4°. The chart needs to be accordingly labelled with their respective percentages 55%, 41% and 4% respectively.

Step-by-step solution

Calculating Degrees for Each Category

The first step is to calculate the number of degrees each category should occupy in the pie chart. For this, convert the percentage for each category into degrees. As a full circle occupies 360 degrees, the number of degrees corresponding to each category is calculated as: (Percentage/100) * 360. So for 'no' it is (55/100 * 360) = 198°, for 'yes' it is (41/100 * 360) = 147.6° and for 'did not answer or did not know' it is (4/100 * 360) = 14.4°.

Drawing the Pie Chart

With the degrees for each category calculated, the pie chart can now be drawn. Most often, pie charts start from the top and go clockwise. Start with a circle and draw a line straight up from the center of the circle. From this line, draw an arc to the right that measures 198° for the 'no' category, then from the end of that arc, draw an arc that measures 147.6° for the 'yes' category, and from the end of that arc draw an arc that measures 14.4° for the 'did not answer or did not know' category. Now, you should have divided your circle into sections representing their respective responses.

Labelling the Pie Chart

Finally, label each arc of the pie chart with its corresponding category and percentage. The 'no' category should be labeled as '55%', 'yes' category as '41%', and 'didn't answer or do not know' as '4%'.

Key concepts

Pie Chart

A pie chart is a circular graph that divides into slices to illustrate numerical proportions. Each slice represents a category's percentage share of the total. This visualization method is excellent for showing how parts contribute to a whole, often making the data easier to understand at a glance.
To create a pie chart, follow these steps:

• Calculate the degrees each slice will occupy based on its percentage. Since a pie chart is a full circle, it represents 360 degrees. Convert the percentage of each category into degrees using the formula: \(\text{Degrees} = (\text{Percentage}/100) \times 360\)
• Draw a circle and use a protractor to measure the angle for each slice. Start from the top center and move clockwise for consistency.
• Label each slice with the category it represents and the percentage to enhance readability.

Although pie charts are informative, they are most effective with a smaller number of categories. Too many slices can make them hard to read.

Data Visualization

Data visualization is a technique to present data in visual formats like charts, graphs, and images. It helps people understand intricate data sets by showing patterns, trends, and outliers that might not be apparent in raw data.
Visual aids are invaluable when conveying survey results as they transform complex information into accessible visuals. Various tools are available for data visualization, including:

• Bar graphs for comparing quantities.
• Pie charts to show parts of a whole.
• Line graphs for tracking changes over time.
• Scatter plots for identifying correlations between variables.

Regardless of the type of chart you use, ensure it is clear, concise, and meaningful to your audience.

Survey Analysis

Survey analysis involves collecting and interpreting data from responses to a set of questions. This process usually begins with designing a survey to gather precise information about the topic in question.
Key steps in survey analysis include:

• Defining the goal: Understand the purpose of the survey, like gathering thoughts on a product or feedback on services.
• Collecting the data: Conduct your survey and gather responses.
• Organizing data: Tabulate the responses and use tools such as Excel or Google Sheets to keep things ordered.
• Analyzing and interpreting: Use descriptive statistical tools to summarize the data, extract insights, and make informed decisions.

Effective survey analysis can uncover new trends and behaviors in the target population, providing valuable insights for decision-making.

Percentage Calculation

Percentage calculation is a fundamental mathematical concept used to figure out the ratio of a number relative to 100. It is crucial for determining proportions in data analysis, helping to measure variations, changes, and make comparisons efficiently.
To calculate percentages:

• Identify the part and the whole. For example, if 55 people say no out of 100, "no" is the part and 100 is the whole.
• Use the formula: \(\text{Percentage} = (\text{Part}/\text{Whole}) \times 100\).
• For example, calculate "no" as: \(\text{Percentage} = (55/100) \times 100 = 55\%\).

Remember, percentages express how one quantity relates to another, and make results more digestible, especially in data presentations like pie charts.