Discussion Questions

1. What are the steps involved in calculating the variance and the standard deviation as provided in chapter 4? Why is it necessary to square the deviation of each observation from the mean? For example, why can’t we just add these values up and use this quantity, ∑(-Ȳ ), as our measure of variability?

2. Instructors can provide the class with several scholarly articles that report the means and standard deviations in their tables. Discuss the following questions as a class: What do these values tell you about the shapes of these distributions? Should the author(s) have reported another measure of central tendency? If so, or if they did, which measure did they report and why?

3. When summarizing scale variable data using descriptive statistics, what do we lose in our understanding of a sample if we just report the mean and not any measures of dispersion like range or standard deviation? How does this question apply to a variable like age or test scores?

4. Explain why the standard deviation gets larger as people in a group score differently on an exam.