a. Discuss when a pictograph might be more appropriate than a circle graph. b. Discuss when a circle graph might be more appropriate than a bar graph. c. Give an example of a set of data for which a stem-and-leaf plot would be more informative than a histogram. A. A stem-and-leaf plot is more informative when maintaining the original data in the display is important. A small data set such as test grades for a class would benefit from maintaining the data in the display. B. A stem-and-leaf plot is more informative when maintaining the original data in the display is not important. A large data set such as personal income for a country would not benefit from maintaining the data in the display. C. A stem-and-leaf plot is more informative when maintaining the original data in the display is important. A large data set such as personal income for a country would benefit from maintaining the data in the display D. A stem-and-leaf plot is more informative when maintaining the original data in the display is not important. A small data set such as test grades for a

Let's address each part of your question systematically: --- ### **a. When Might a Pictograph Be More Appropriate Than a Circle Graph?** **Pictographs** use icons or images to represent data, making them highly visual and often more engaging for certain audiences. They are particularly useful when you want to: - **Represent Data in Context:** For example, using icons like apples to represent sales of apples. - **Simplify Complex Data:** When presenting to a general audience, pictographs can make data more relatable and easier to understand. - **Emphasize Specific Data Points:** Pictographs can highlight particular categories or comparisons effectively. **Example Scenario:** A school wants to show the number of students participating in various extracurricular activities. Using different icons for each activity can make the information more engaging for students and parents. --- ### **b. When Might a Circle Graph Be More Appropriate Than a Bar Graph?** **Circle graphs**, also known as **pie charts**, are best used when you want to show **part-to-whole relationships**. They are effective when: - **Displaying Proportions:** When you need to illustrate how different segments contribute to the total. - **Showing Relative Sizes:** To emphasize the size of each category in relation to the entire dataset. - **Highlighting a Few Categories:** Pie charts work best when there are limited categories (typically less than five) to avoid clutter. **Example Scenario:** A company wants to display the market share distribution among four major competitors. A pie chart can clearly show each company's proportion of the total market. --- ### **c. When Is a Stem-and-Leaf Plot More Informative Than a Histogram?** **Stem-and-leaf plots** are particularly useful when you want to **retain the original data values** while also displaying the distribution. They are more informative than histograms in scenarios where: - **Small to Moderate-Sized Datasets:** They work best with smaller datasets where individual data points can be easily displayed. - **Preserving Data Details:** Unlike histograms, stem-and-leaf plots show the actual values, making it easier to identify specific data points. **Correct Option:** **A.** *A stem-and-leaf plot is more informative when maintaining the original data in the display is important. A small data set such as test grades for a class would benefit from maintaining the data in the display.* **Explanation:** Option A correctly identifies that stem-and-leaf plots are advantageous when you need to preserve the original data values and when dealing with smaller datasets, such as test grades for a class. This allows for both a visual representation of the distribution and access to individual data points. **Why the Other Options Are Less Appropriate:** - **B.** Incorrect because stem-and-leaf plots are not ideal when maintaining original data is *not* important, especially for large datasets. - **C.** Incorrect as stem-and-leaf plots become cumbersome and less informative with large datasets, such as personal income for a country. - **D.** Incomplete, but it starts similarly to option A and seems to suggest an inappropriate scenario for stem-and-leaf plots. --- ### **Summary** - **Pictographs** are best for visual, engaging representations with contextual icons, suitable for simpler or more relatable data presentations. - **Circle graphs (pie charts)** effectively display part-to-whole relationships, especially when highlighting proportions among a few categories. - **Stem-and-leaf plots** are ideal for small datasets where retaining individual data points is valuable, as correctly identified in **Option A** for part **c**. If you have any further questions or need additional clarification on these topics, feel free to ask!