A teacher has asked all the students in the class what is their favorite color is and separates the responses into five categories. The results are shown in the table below. which of the following is the best way to display the frequency for each color?
Color Red Black Green White Other
Number of
students
12 25 8 5 10
A.
Histogram
B.
Pie chart
C.
Scatter plot
D.
Line graph
The Correct Answer and Explanation is:
The best way to display the frequency for each color from the given data is:
B. Pie chart
Explanation:
When presenting categorical data, such as favorite colors in this case, different types of charts can be employed, each serving specific purposes. Here’s why a pie chart is the most suitable option:
- Nature of Data: The data provided represents categorical responses with frequencies, meaning each color is a distinct category. The primary goal is to show how each category compares to the whole. A pie chart is specifically designed to illustrate proportions or percentages of a whole, making it an ideal choice for this type of data.
- Visualization of Proportions: A pie chart displays the data as slices of a pie, where each slice represents a category’s proportion relative to the total. This visual representation helps quickly convey which colors are most or least popular at a glance. For instance, the slice for “Black” would be the largest, visually indicating that it is the most favored color among students.
- Comparative Analysis: While other options like histograms, scatter plots, and line graphs have their merits, they serve different purposes. A histogram, for example, is used for numerical data divided into ranges, making it less effective for categorical data like favorite colors. Scatter plots are used to depict relationships between two quantitative variables and line graphs show trends over time, neither of which are suitable for comparing categorical data.
- Ease of Understanding: Pie charts are straightforward and easily interpreted by most audiences, providing a clear view of the distribution of responses. Each slice’s size directly corresponds to the frequency of the color, which simplifies the comparison of how popular each color is in the context of the whole group.
- Effective Communication: The primary objective in displaying categorical data such as favorite colors is to effectively communicate the relative sizes of each category’s frequency. A pie chart achieves this by providing a clear, visual representation that makes it easy for viewers to grasp the data’s significance and distribution.
In summary, a pie chart is the most effective tool for displaying the frequencies of each color as it visually represents the proportion of each category within the total dataset, making it the best choice for this scenario.