• Best Practices has the following caveats:
• • Use a bar chart to show the frequencies of a categorical variable.
• • Use a pie chart to show the proportions of a categorical variable.
• • Preserve the ordering of an ordinal variable.
• • Respect the area principle. The relative size of a bar or slice should match the count of the associated category in the data relative to the
total number of cases.
• • Choose the best plots to answer the motivating question that you are studying.
• • Label your chart to show the categories and indicate whether some have been combined or omitted.
For the scenario below, suggest a plot of your own design to summarize the data. Support your conclusions.
Wireless phone company customers across the United States were surveyed and asked to rate the quality of service delivered by their wireless carrier. A publication of the consumer group summarizes the rating provided by each respondent as Excellent, Good, Fair, or Poor. What does it mean for a provider to get a modal rating of Excellent or a median rating of Excellent?
Choose a topic of your choice on which to collect data. Indicate the topic you have chosen, and describe how you would go about setting up and carrying through with your choice. What could you learn from this type of analysis? How meaningful is the range of a data set?
To summarize the data on the quality of service provided by wireless carriers, one plot that can be used is a bar chart. The frequencies of the categorical variable (ratings) can be represented using bars of different heights. Each rating category (Excellent, Good, Fair, Poor) can be plotted on the x-axis, and the count of respondents who gave each rating can be plotted on the y-axis. This will provide a visual representation of the distribution of ratings.
Using a bar chart allows for a clear comparison of the frequencies of each rating category. The bars can be easily labeled to show the categories and indicate whether any categories have been combined or omitted. By respecting the area principle, the relative size of the bars can be directly proportional to the count of each rating category in the data relative to the total number of respondents.
The modal rating refers to the most frequently occurring rating, while the median rating refers to the middle rating when all the ratings are arranged in order. If a provider gets a modal rating of Excellent, it means that the majority of respondents rated the quality of service as Excellent. This indicates a high level of satisfaction among customers. Similarly, if a provider gets a median rating of Excellent, it means that half of the respondents rated the quality of service as Excellent. This suggests that the provider is performing well overall.
For the chosen topic, let's consider "Student Performance in Mathematics." To collect data, one approach could be to randomly select a sample of students from different schools and administer a standardized math test to them. The test scores can be recorded along with additional information such as the students' age, gender, and socioeconomic background.
To carry out this study, the following steps could be followed:
1. Define the target population: Determine the specific group of students for whom you want to analyze math performance (e.g., high school students, 8th graders, etc.).
2. Sample selection: Use a random sampling method to select a representative sample from the target population.
3. Test administration: Administer a standardized math test to the selected sample of students in a controlled environment.
4. Data collection: Record the test scores of each student along with any additional variables of interest (age, gender, socioeconomic background, etc.).
5. Data analysis: Analyze the collected data using appropriate statistical methods. This may include calculating descriptive statistics (mean, median, mode), performing inferential statistics (hypothesis testing, confidence intervals), and exploring potential relationships between variables (gender differences, socioeconomic impact, etc.).
From this analysis, you can learn about the overall performance of students in mathematics, identify any patterns or trends, and explore potential factors that may be associated with student performance. The analysis can help identify areas in which students may need additional support or intervention, and inform educational policy and practices.
The range of a data set refers to the difference between the maximum and minimum values. It provides a measure of the spread or variability in the data. However, on its own, the range may not provide a complete picture of the data distribution as it only considers the extreme values. Therefore, it is often useful to complement the range with other measures of variability, such as the variance or standard deviation, to gain a more comprehensive understanding of the data.